arXiv subjects

Marco Bochicchio

Publications and source records attributed to Marco Bochicchio.

At least 19 recordsLinked to original sources

arXiv2025

Twistor Wilson loops in large-$N$ Yang-Mills theory

It has been known for many years that, in Yang-Mills theories with $\mathcal{N}=4,2,2^*$ supersymmetry, certain nontrivial supersymmetric Wilson loops exist with v.e.v. either trivial or computable by localization that arises from a cohomological field theory, which also computes the nonperturbative prepotential in $\mathcal{N}=2,2^*$ theories. Moreover, some years ago it has been argued that, in analogy with the supersymmetric case, certain nontrivial twistor Wilson loops with trivial v.e.v. to the leading large-$N$ order exist in pure SU($N$) Yang-Mills theory and are computed, to the leading large-$N$ order, by a topological field/string theory that, to the next-to-leading $\frac{1}{N}$ order, conjecturally captures nonperturbative information on the glueball spectrum and glueball one-loop effective action as well. In fact, independently of the above, it has also been claimed that "every gauge theory with a mass gap should contain a possibly trivial topological field theory in the infrared", so that the aforementioned twistor Wilson loops realize a stronger version of this idea, as they have trivial v.e.v. at all energy scales and not only in the infrared. In the present paper, we provide a detailed proof of the triviality of the v.e.v. of twistor Wilson loops at the leading large-$N$ order in Yang-Mills theory that has previously been only sketched, opening the way to further developments.

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arXiv2025

On the structure of the large-$N$ expansion in SU($N$) Yang-Mills theory

Recently, we have computed the short-distance asymptotics of the generating functional of Euclidean correlators of single-trace twist-$2$ operators in the large-$N$ expansion of SU($N$) Yang-Mills (YM) theory to the leading-nonplanar order. Remarkably, it has the structure of the logarithm of a functional determinant, but with the sign opposite to the one that would follow from the spin-statistics theorem for the glueballs. In order to solve this sign puzzle, we have reconsidered the proof in the literature that in the 't Hooft topological expansion of large-$N$ YM theory the leading-nonplanar contribution to the generating functional consists of the sum over punctures of $n$-punctured tori. We have discovered that for twist-$2$ operators it contains -- in addition to the $n$-punctured tori -- the normalization of tori with $1 \leq p \leq n$ pinches and $n-p$ punctures. Once the existence of the new sector is taken into account, the violation of the spin-statistics theorem disappears. Moreover, the new sector contributes trivially to the nonperturbative $S$ matrix because -- for example -- the $n$-pinched torus represents nonperturbatively a loop of $n$ glueball propagators with no external leg. This opens the way for an exact solution limited to the new sector that may be solvable thanks to the vanishing $S$ matrix.

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arXiv2025

Generating functional of correlators of twist-$2$ operators in $\mathcal{N} = 1$ SUSY Yang-Mills theory, I

The present paper is the first installment where, extending our previous work in pure Yang-Mills (YM) theory, we compute the generating functional of correlators of collinear twist-$2$ operators that enter the components of balanced superfields -- i.e., superfields with an equal number of dotted and undotted indices in their spinor representation -- in $\mathcal{N} = 1$ SUSY SU($N$) YM theory in Minkowskian and Euclidean space-time, in the conformal limit and renormalization-group (RG) improved form, and to the leading and next-to-leading order in the large-$N$ expansion. Moreover, we compare our asymptotic RG-improved generating functional to the next-to-leading large-$N$ order with the corresponding nonperturbative object arising from the glueball/gluinoball one-loop effective action, which it should be asymptotic to at short distances because of the asymptotic freedom. Remarkably, we find that both have the structure of the logarithm of a functional superdeterminant. Hence, our large-$N$ computation sets strong ultraviolet asymptotic constraints on the nonperturbative solution of large-$N$ $\mathcal{N} = 1$ SUSY YM theory that may be a pivotal guide for the search of such a solution.

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arXiv2024

Low-energy theorem revisited and OPE in massless QCD

We revisit a low-energy theorem (LET) of NSVZ type in SU($N$) QCD with $N_f$ massless quarks derived in [1] by implementing it in dimensional regularization. The LET relates $n$-point correlators in the lhs to $n+1$-point correlators with the extra insertion of Tr$F^2$ at zero momentum in the rhs. First, we demonstrate that, for $2$-point correlators of an operator $O$ in the lhs, the LET implies that, in general, the integrated $3$-point correlator in the rhs needs in perturbation theory an infinite additive renormalization in addition to the multiplicative one. Second, we relate the above counterterm -- that is completely fixed by the LET -- to a corresponding divergent contact term in a certain coefficient of the OPE of Tr$F^2$ with $O$ in the momentum representation, thus extending by means of the LET to any operator $O$ an independent argument that first appeared for $O$=Tr$F^2$ in [2]. Third, we verify by direct computation that the latter divergent contact term first computed in [3] to order $g^4$ in perturbation theory and to all orders in [2] actually agrees with the one implied by the LET. Fourth, we evaluate the divergent contact terms for the above OPE coefficient both in the coordinate and momentum representation and discuss their relation. Fifth, we demonstrate that in the asymptotically free phase of QCD the aforementioned counterterm in the LET -- though divergent order by order in perturbation theory -- is actually finite nonperturbatively after resummation to all perturbative orders. Finally, we briefly recall the implications of the LET in the gauge-invariant framework of dimensional regularization for the perturbative and nonperturbative renormalization in large-$N$ QCD. The implications of the LET inside and above the conformal window of SU($N$) QCD with $N_f$ massless quarks will appear in a forthcoming paper.

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arXiv2023

UV asymptotics of $n$-point correlators of twist-$2$ operators in SU($N$) Yang-Mills theory

The generating functional $\mathcal{W}[J_{\mathcal O}]$ of Euclidean correlators of twist-$2$ operators in SU($N$) Yang-Mills theory admits the 't Hooft large-$N$ expansion: $\mathcal{W}[J_{\mathcal O}]=\mathcal{W}_{sphere}\,\,\,\,[J_{\mathcal O}]+\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}]+ \cdots$. Nonperturbatively, $\mathcal{W}_{sphere} \,\,\,\,[J_{\mathcal O}]$ is a sum of tree diagrams involving glueball propagators and vertices, while $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}]$ is a sum of glueball one-loop diagrams. Moreover, it has been predicted that $\mathcal{W}_{torus } \,\,\,[J_{\mathcal O}]$ should admit the structure of the logarithm of a functional determinant summing glueball one-loop diagrams. We work out in a closed form the ultraviolet (UV) asymptotics of $\mathcal{W}_{sphere} \,\,\,\,[J_{\mathcal O},λ] \sim \mathcal{W}_{asym \, sphere} \,\,\,\,\,\,\,[J_{\mathcal O},λ]$ and $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O},λ] \sim \mathcal{W}_{asym \, torus} \,\,\,\,\,\,[J_{\mathcal O},λ]$ in the coordinate representation as all the coordinates of the correlators are uniformly rescaled by a factor $λ\rightarrow 0$. Remarkably, we verify the above prediction that $\mathcal{W}_{asym \, torus} \,\,\,\,\,\,[J_{\mathcal O},λ]$ -- being asymptotic in the UV to $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}, λ]$ -- admits the structure of the logarithm of a functional determinant as well. Hence, the computation above sets strong UV asymptotic constraints on the nonperturbative solution of large-$N$ YM theory and it may be a pivotal guide for the search of such a solution.

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arXiv2022

Low-energy theorem and OPE in the conformal window of massless QCD

We develop a new technique, based on a low-energy theorem (LET) of NSVZ type derived in arXiv:1701.07833, for the nonperturbative investigation of SU(N) QCD with N${}_f$ massless quarks - or, more generally, of massless QCD-like theories - in phases where the beta function, $β(g)$, with $g=g(μ)$ the renormalized gauge coupling, admits an isolated zero, $g_*$, in the infrared (IR) or ultraviolet (UV). We point out that the LET sets constraints on 3-point correlators involving the insertion of $Tr\, F^2$, its anomalous dimension $γ_{F^2}$, and the anomalous dimensions of multiplicatively renormalizable operators at $g_*$. These constraints intertwine with the exact conformal scaling for $g(μ)\rightarrow g_*$ with $μ\neq 0,+\infty$ fixed and the IR/UV asymptotics - which may or may not coincide with the IR/UV limit of the aforementioned conformal scaling - for $Λ_{\scriptscriptstyle{IR/UV}}$ fixed. In the conformal case we also discuss how the LET for bare correlators is the rationale for the existence in massless QCD of the mysterious divergent contact term in the OPE of $Tr\,F^2$ with itself discovered in perturbation theory in arXiv:1209.1516, arXiv:1407.6921 and computed to all orders in arXiv:1601.08094. Specifically, if $γ_{F^2}$ does not vanish, the divergent contact term in the rhs of the LET for the 2-point correlator of $Tr\,F^2$ has to match - and we verify by direct computation that it actually does - the divergence in the lhs due to the nontrivial anomalous dimension of $Tr\,F^2$. Hence, remarkably, the additive renormalization due to the divergent contact term in the rhs is related by the LET to the multiplicative renormalization in the lhs, in such a way that a suitably renormalized version of the LET has no ambiguity for additive renormalization.

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arXiv2021

Operator mixing in massless QCD-like theories and Poincare'-Dulac theorem

Recently, a geometric approach to operator mixing in massless QCD-like theories -- that involves canonical forms based on the Poincare'-Dulac theorem for the linear system that defines the renormalized mixing matrix in the coordinate representation $Z(x,μ)$ -- has been advocated in arXiv:2103.15527 . As a consequence, a classification of operator mixing in four cases -- depending on the canonical forms of $- \frac{γ(g)}{β(g)}$, with $γ(g)=γ_0 g^2+\cdots$ the matrix of the anomalous dimensions and $β(g)=-β_0 g^3 + \cdots$ the beta function -- has been proposed: (I) nonresonant $\frac{γ_0}{β_0}$ diagonalizable, (II) resonant $\frac{γ_0}{β_0}$ diagonalizable, (III) nonresonant $\frac{γ_0}{β_0}$ nondiagonalizable, (IV) resonant $\frac{γ_0}{β_0}$ nondiagonalizable. In particular, in arXiv:2103.15527 a detailed analysis of the case (I) -- where operator mixing reduces to all orders of perturbation theory to the multiplicatively renormalizable case -- has been provided. In the present paper, following the aforementioned approach, we work out in the remaining three cases the canonical forms for $- \frac{γ(g)}{β(g)}$ to all orders of perturbation theory, the corresponding UV asymptotics of $Z(x,μ)$, and the physics interpretation. We also work out in detail physical realizations of the cases (I) and (II).

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arXiv2021

$n$-point correlators of twist-$2$ operators in $SU(N)$ Yang-Mills theory to the lowest perturbative order

We compute, to the lowest perturbative order in $SU(N)$ Yang-Mills theory, $n$-point correlators in the coordinate and momentum representation of the gauge-invariant twist-$2$ operators with maximal spin along the $p_+$ direction, both in Minkowskian and -- by analytic continuation -- Euclidean space-time. We also construct the corresponding generating functionals. Remarkably, they have the structure of the logarithm of a functional determinant of the identity plus a term involving the effective propagators that act on the appropriate source fields.

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arXiv2021

On the geometry of operator mixing in massless QCD-like theories

We revisit the operator mixing in massless QCD-like theories. In particular, we address the problem of determining under which conditions a renormalization scheme exists where the renormalized mixing matrix in the coordinate representation, $Z(x, μ)$, is diagonalizable to all perturbative orders. As a key step, we provide a differential-geometric interpretation of renormalization that allows us to apply the Poincaré-Dulac theorem to the problem above: We interpret a change of renormalization scheme as a (formal) holomorphic gauge transformation, $-\frac{γ(g)}{β(g)}$ as a (formal) meromorphic connection with a Fuchsian singularity at $g=0$, and $Z(x,μ)$ as a Wilson line, with $γ(g)=γ_0 g^2 + \cdots$ the matrix of the anomalous dimensions and $β(g)=-β_0 g^3 +\cdots$ the beta function. As a consequence of the Poincaré-Dulac theorem, if the eigenvalues $λ_1, λ_2, \cdots $ of the matrix $\frac{γ_0}{β_0}$, in nonincreasing order $λ_1 \geq λ_2 \geq \cdots$, satisfy the nonresonant condition $λ_i -λ_j -2k \neq 0$ for $i\leq j$ and $k$ a positive integer, then a renormalization scheme exists where $-\frac{γ(g)}{β(g)} = \frac{γ_0}{β_0} \frac{1}{g}$ is one-loop exact to all perturbative orders. If in addition $\frac{γ_0}{β_0}$ is diagonalizable, $Z(x, μ)$ is diagonalizable as well, and the mixing reduces essentially to the multiplicatively renormalizable case. We also classify the remaining cases of operator mixing by the Poincaré-Dulac theorem.

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arXiv2021

Operator mixing, UV asymptotics of nonplanar/planar $2$-point correlators, and nonperturbative large-$N$ expansion of QCD-like theories

We work out the interplay between lowest-order perturbative computations in the 't Hooft coupling, $g^2=g^2_{YM} N$, operator mixing, renormalization-group (RG) improved ultraviolet (UV) asymptotics of leading-order (LO) nonplanar/planar contributions to $2$-point correlators, and nonperturbative large-$N$ expansion of perturbatively massless QCD-like theories. As concrete examples, we compute to the lowest perturbative order in $SU(N)$ YM theory the ratios, $r_i$, of LO-nonplanar to planar contributions to the $2$-point correlators in the orthogonal basis in the coordinate representation of the gauge-invariant dimension-$8$ scalar operators and all the twist-$2$ operators. We demonstrate that -- if $\frac{γ_0}{β_0}$ has no LO-nonplanar contribution, with $γ_0$ and $β_0$ the one-loop coefficients of the anomalous-dimension matrix and beta function respectively -- $r_i$ actually coincides with the corresponding ratio in the large-$N$ expansion of the RG-improved UV asymptotics of the $2$-point correlators, provided that a certain canonical nonresonant diagonal renormalization scheme exists for the corresponding operators. Contrary to the aforementioned scalar operators, for the first $10^3$ twist-$2$ operators we actually verify the above conditions, and we get the universal value $r_i=-\frac{1}{N^2}$. Hence, nonperturbatively such $r_i$ must coincide with the UV asymptotics of the ratio of the glueball self-energy loop to the glueball tree contribution to the $2$-point correlators above. As a consequence, the universality of $r_i$ reflects the universality of the effective coupling in the nonperturbative large-$N$ YM theory for the twist-$2$ operators in the coordinate representation.

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arXiv2019

OPE and a low-energy theorem in QCD-like theories

We verify, both perturbatively and nonperturbatively asymptotically in the ultraviolet (UV), a special case of a low-energy theorem of the NSVZ type in QCD-like theories, recently derived in arXiv:1701.07833, that relates the logarithmic derivative with respect to the gauge coupling, or the logarithmic derivative with respect to the renormalization-group (RG) invariant scale, of an $n$-point correlator of local operators in one side to an $n+1$-point correlator with the insertion of $Tr F^2$ at zero momentum in the other side. Our computation involves the operator product expansion (OPE) of the scalar glueball operator, $Tr F^2$, in massless QCD, worked out perturbatively in arXiv:1209.1516 -- and in its RG-improved form in the present paper -- by means of which we extract both the perturbative divergences and the nonperturbative UV asymptotics in both sides. We also discuss the role of the contact terms in the OPE, both finite and divergent, discovered some years ago in arXiv:1209.1516, in relation to the low-energy theorem. Besides, working the other way around by assuming the low-energy theorem for any 2-point correlator of a multiplicatively renormalizable gauge-invariant operator, we compute in a massless QCD-like theory the corresponding perturbative OPE to the order of $g^2$ and nonperturbative asymptotics. The low-energy theorem has a number of applications: to the renormalization in asymptotically free QCD-like theories, both perturbatively and nonperturbatively in the large-$N$ 't Hooft and Veneziano expansions, and to the way the open/closed string duality may or may not be realized in the would-be solution by canonical string theories for QCD-like theories, both perturbatively and in the 't Hooft large-$N$ expansion. Our computations will also enter further developments based on the low-energy theorem.

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arXiv2018

Renormalization in large-$N$ QCD is incompatible with open/closed string duality

Solving by a canonical string theory, of closed strings for the glueballs and open strings for the mesons, the 't Hooft large-$N$ expansion of QCD is a long-standing problem that resisted all the attempts despite the advent of the celebrated gauge/gravity duality in the framework of string theory. We demonstrate that in the canonical string framework such a solution does not actually exist because an inconsistency arises between the renormalization properties of the QCD S matrix at large $N$ -- a consequence of the asymptotic freedom (AF) -- and the open/closed duality of the would-be string solution. Specifically, the would-be open-string one-loop corrections to the tree glueball amplitudes must be ultraviolet (UV) divergent. Hence, naively, the inconsistency arises because these amplitudes are dual to tree closed-string diagrams, which are universally believed to be both UV finite -- since they are closed-string tree diagrams -- and infrared finite because of the glueball mass gap. In fact, the inconsistency follows from a low-energy theorem of the NSVZ type that controls the renormalization in QCD-like theories. The inconsistency extends to the would-be canonical string for a vast class of 't Hooft large-$N$ QCD-like theories including $\mathcal{N}=1$ SUSY QCD. We also demonstrate that the presently existing SUSY string models with a mass gap -- such as Klebanov-Strassler, Polchinski-Strassler (PS) and certain PS variants -- cannot contradict the above-mentioned results since they are not asymptotically free. Moreover, we shed light on the way the open/closed string duality may be perturbatively realized in these string models compatibly with a mass gap in the 't Hooft-planar closed-string sector and the low-energy theorem because of the lack of AF. Finally, we suggest a noncanonical way-out for QCD-like theories based on topological strings on noncommutative twistor space.

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arXiv2016

Asymptotic Freedom versus Open/Closed Duality in Large-N QCD

The solution of the large-N 't Hooft limit of QCD is universally believed to be a String Theory of Closed Strings in the Glueball Sector and of Open Strings in the Meson Sector. Yet, we prove a no-go theorem, that the large-N limit of QCD with massless quarks, or more generally, that the large-N limit of a vast class of confining, i.e. with a Mass Gap in the Glueball Sector, asymptotically-free Gauge Theories coupled to matter fields with no mass scale in perturbation theory cannot be a canonically-defined String Theory of Closed and Open Strings, i.e. admitting Open/Closed Duality. The no-go theorem occurs because Open/Closed Duality, implying that the ultraviolet divergences of annulus diagrams in the Open Sector arise from infrared divergences of tadpoles of massless particles in the Closed Sector, turns out to be incompatible with the existence of the Mass Gap in the Glueball Sector of confining asymptotically-free theories with no mass scale in perturbation theory in which, as for example in QCD, the first coefficient of the beta function for 't Hooft gauge coupling gets $1/N$ corrections due to the matter fields. Moreover, we suggest a way-out to the no-go theorem on the basis of a new non-canonical construction of the String S-matrix for asymptotically-free Gauge Theories such as large-N QCD, involving Topological Strings on Non-Commutative Twistor Space.

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arXiv2015

An asymptotic solution of large-$N$ $QCD$, and of large-$N$ $\mathcal{N}=1$ $SUSY$ $YM$

We find an asymptotic solution for two- and three-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$, in terms of glueball and meson propagators, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap. The asymptotically-free bootstrap exploits the lowest-order conformal invariance of connected correlators of gauge invariant composite operators in perturbation theory, the renormalization-group improvement, and a recently-proved asymptotic structure theorem for glueball and meson propagators, that involves the unknown particle spectrum and the anomalous dimension of operators for fixed spin. In principle the asymptotically-free bootstrap extends to all the higher-spin two- and three-point correlators whose lowest-order conformal limit is non-vanishing in perturbation theory, and by means of the operator product expansion to the corresponding asymptotic multi-point correlators as well. Besides, the asymptotically-free bootstrap provides asymptotic $S$-matrix amplitudes in massless large-$N$ $QCD$ in terms of glueball and meson propagators as opposed to perturbation theory. Remarkably, the asymptotic $S$-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions. Moreover, the asymptotically-free bootstrap applies to large-$N$ $\mathcal{N}=1$ $SUSY$ $YM$ as well. Practically, as just a few examples among many more, it follows the structure of the light by light scattering amplitude, of the pion form factor, and the associated vector dominance. Theoretically, the asymptotic solution sets the strongest constraints on any actual solution of large-$N$ $QCD$ (and of large-$N$ $\mathcal{N}=1$ $SUSY$ $YM$), and in particular on any string solution.

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arXiv2014

An asymptotic solution of large-$N$ $QCD$

We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic $S$-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic $S$-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the $LSZ$ reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-$N$ $QCD$, and in particular on any string solution.

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arXiv2014

Yang-Mills mass gap, Floer homology, glueball spectrum, and conformal window in large-N QCD

Morse-Smale-Floer homology associates the critical points of the action functional of a classical field theory over a manifold to its homology. We associate to the intersection homology of certain Lagrangian submanifolds of R^4 the critical points of a quantum effective action of large-N SU(N) YM. For this purpose we construct in YM a trivial Topological Field Theory defined by twistor Wilson loops whose v.e.v. is 1 in the large-N limit for any shape of the loops supported on certain punctured Lagrangian submanifolds. We derive a new holomorphic loop equation for the twistor Wilson loops, that involves the change of variables in the YM functional integral from the connection to the anti-selfdual part of the curvature and the choice of a holomorphic gauge. Employing the holomorphic loop equation, and viewing Floer homology the other way around, we associate to arcs asymptotic in both directions to the cusps of the Lagrangian submanifolds the critical points of an effective action, that turn out to be surface operators of Z(N) holonomy. At the next-to-leading 1/N order a certain correlator of surface operators is non-topological and non-trivial, controls the mass gap of YM theory, and is saturated by an infinite sum of pure poles of scalar and pseudoscalar glueballs with positive charge conjugation. It satisfies asymptotically for large momentum fundamental universal constraints arising from the asymptotic freedom and the renormalization group. We predict at large-N the ratio of the masses of the two lower-mass scalar glueballs r=\sqrt 2=1.414, to be compared with the measure in lattice SU(8) YM by Meyer-Teper r=1.42(11), and with the value implied by PDG(2014) r=1.397(008). The construction extends to massless Veneziano large-N limit of QCD, for which we determine the lower edge of the conformal window N_f/N=5/2 and the corresponding quark-mass anomalous dimension gamma=-4/5.

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arXiv2014

Yang-Mills mass gap at large-N, non-commutative YM theory, topological quantum field theory and hyperfiniteness

We review a number of old and new concepts in quantum gauge theories, some of which are well established but not widely appreciated, some are most recent. Such concepts involve non-commutative gauge theories and their relation to the large-N limit, loop equations and the change to the anti-selfdual variables also known as Nicolai map, topological field theory (TFT) and its relation to localization and Morse-Smale-Floer homology, with an emphasis both on the mathematical aspects and the physical meaning. These concepts, assembled in a new way, enter a line of attack to the problem of the mass gap in large-N SU(N) YM, that is reviewed as well. In the large-N limit of pure SU(N) YM the ambient algebra of Wilson loops is known to be a type II_1 non-hyperfinite factor. Nevertheless, for the mass gap problem at the leading 1/N order, only the subalgebra of local gauge-invariant single-trace operators matters. The connected two-point correlators in this subalgebra must be an infinite sum of propagators of free massive fields, a vast simplification. It is an open problem, determined by the grow of the degeneracy of the spectrum, whether the aforementioned local subalgebra is in fact hyperfinite. For the mass-gap problem, in the search of a hyperfinite subalgebra containing the scalar sector of large-N YM, a major role is played by the existence of a TFT underlying the large-N limit of YM, with twisted boundary conditions on a torus or, what is the same by Morita duality, on a non-commutative torus.

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arXiv2013

Glueball and meson spectrum in large-N massless QCD

We provide outstanding numerical evidence that in large-N massless QCD the joint spectrum of the masses squared, for fixed integer spin s and unspecified parity and charge conjugation, obeys exactly the following laws: m_k^2 = (k+s/2) Lambda_QCD^2 for s even, m_k^2 = 2(k+s/2) Lambda_QCD^2 for s odd, k = 1,2,... for glueballs, and m_n^2 = 1/2 (n+s/2) Lambda_QCD^2, n = 0,1,... for mesons. One of the striking features of these laws is that they imply that the glueball and meson masses squared form exactly-linear Regge trajectories in the large-N limit of massless QCD, all the way down to the low-lying states: A fact unsuspected so far. The numerical evidence is based on lattice computations by Meyer-Teper in SU(8) YM for glueballs, and by Bali et al. in SU(17) quenched massless QCD for mesons, that we analyze systematically. The aforementioned spectrum for spin-0 glueballs is implied by a Topological Field Theory underlying the large-N limit of YM, whose glueball propagators satisfy as well fundamental universal constraints arising from the asymptotic freedom and the renormalization group. No other presently existing model meets both the infrared spectrum and the ultraviolet constraints. We argue that some features of the aforementioned spectrum of glueballs and mesons of any spin could be explained by the existence of a Topological String Theory dual to the Topological Field Theory.

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