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Marco Bochicchio

Publications and source records attributed to Marco Bochicchio.

35 records · Page 2Linked to original sources
arXiv2013

Glueball and meson propagators of any spin in large-N QCD

We prove an asymptotic structure theorem for glueball and meson propagators of any spin in large-N QCD and in n=1 SUSY QCD with massless quarks, that determines asymptotically the residues of the poles of the propagators in terms of their anomalous dimensions and of the spectral density of the masses. The asymptotic theorem follows by the severe constraints on the propagators in large-N QCD with massless quarks, or in any large-N confining asymptotically-free gauge theory massless in perturbation theory, that arise by perturbation theory in conjunction with the renormalization group and by the OPE on the ultraviolet side. The asymptotic theorem is inspired by a recently proposed Topological Field Theory (TFT) underlying large-N pure YM, that computes sums of the scalar and of the pseudoscalar correlators satisfying the asymptotic theorem and that implies for the large-N joint scalar and pseudoscalar glueball spectrum exact linearity in the masses squared. On the infrared side we test the prediction of the exact linearity in the TFT by Meyer-Teper lattice numerical computation of the masses of the low-lying glueballs in SU(8) YM, finding accurate agreement. Besides, we employ the aforementioned ultraviolet and infrared constraints in order to compare critically the scalar or pseudoscalar glueball propagators computed in the framework of the AdS String/large-N Gauge Theory correspondence with those of the TFT underlying large-N YM. We find that only the TFT satisfies the ultraviolet and infrared constraints.

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arXiv2012

Glueballs in large-N YM by localization on critical points

By exploiting in large-N YM the change of variables from the gauge connection to the ASD part of its curvature by a non-SUSY version of the Nicolai map, we show that certain twistor Wilson loops supported on a Lagrangian submanifold of twistor space are localized on lattices of surface operators of Z(N) holonomy that form translational invariant sectors labelled by the magnetic charge k=1,2,...,N-1 at a point. The localization is obtained reducing the loop equation in the ASD variables in the holomorphic gauge, regularized by analytic continuation to Minkowski space-time, to a critical equation, by exploiting the invariance of the twistor Wilson loops by deformations for the addition of backtracking arcs ending with cusps on the singular divisor of surface operators. Alternatively localization is obtained contracting the YM measure in the ASD variables on the fixed points of a semigroup that acts on the fiber of the Lagrangian twistor fibration which twistor Wilson loops are supported on and leaves invariant their v.e.v.. The masses squared of the fluctuations of surface operators in the sectors labelled by k, supported on the Lagrangian submanifold analytically continued to Minkowski space-time, form a trajectory linear in k that does not include any massless state. The glueballs propagators in the holomorphic/antiholomorphic sector defined by correlators of a complex combination of the ASD curvature and its adjoint saturate at short distances the logarithms of perturbation theory by a sum of pure poles. In this framework Regge trajectories of higher spins are related to fluctuations of surface operators with pole singularities of any order.

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arXiv2012

Glueballs propagators in large-N YM

We have computed in [arXiv:1107.4320 (hep-th)] the glueballs spectrum in a certain sector of the large-N YM theory by solving by a change of variables the holomorphic loop equation for cusped twistor Wilson loops supported on certain Lagrangian submanifolds and by evaluating the correlators of surface operators supported on these Lagrangian submanifolds. We have shown that the correlators of composite surface operators of length L reproduce in the large-L limit the leading logarithms of perturbation theory of the corresponding glueballs propagators, including the correct anomalous dimensions. In this paper we show that the correlators of surface operators match in the large-L limit the stronger constraints arising by the operator product expansion, according to Migdal technique of computing the spectral sum over the glueballs including the subleading asymptotics given by the Euler formula. Finally, we discuss correlators of surface operators for finite L.

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arXiv2011

Large-N Wilsonian beta function in SU(N) Yang-Mills theory by localization on the fixed points of a semigroup contracting the functional measure

In a certain (non-commutative) version of large-N SU(N) Yang-Mills theory there are special Wilson loops, called twistor Wilson loops for geometrical reasons, whose v.e.v. is independent on the parameter that occurs in their operator definition. There is a semigroup that acts on the parameter by rescaling and on the functional measure, resolved into anti-selfdual orbits by a non-supersymmetric version of the Nicolai map, by contracting the support of the measure. As a consequence the twistor Wilson loops are localized on the fixed points of the semigroup of contractions. This localization is a non-supersymmetric analogue of the localization that occurs in the Nekrasov partition function of the n=2 SUSY YM theory on the fixed points of a certain torus action on the moduli space of (non-commutative) instantons. One main consequence of the localization in the large-N YM case, as in the n=2 SUSY YM case, is that the beta function of the Wilsonian coupling constant in the anti-selfdual variables is one-loop exact. Consequently the large-N Yang-Mills canonical beta function has a NSVZ form that reproduces the first two universal perturbative coefficients.

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arXiv2010

Exact beta function and glueball spectrum in large-N Yang Mills theory

In the pure large-N Yang-Mills theory there is a quasi-BPS sector that is exactly solvable at large N. It follows an exact beta function and the glueball spectrum in this sector. The main technical tool is a new holomorphic loop equation for quasi-BPS Wilson loops, that occurs as a non-supersymmetric analogue of Dijkgraaf-Vafa holomorphic loop equation for the glueball superpotential of n=1 SUSY gauge theories. The new holomorphic loop equation is localized, i.e. reduced to a critical equation, by a deformation of the loop that is a vanishing boundary in homology, somehow in analogy with Witten's cohomological localization by a coboundary deformation in SUSY gauge theories.

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arXiv2009

The Yang-Mills String as the A-Model on the Twistor Space of the Complex Two-Dimensional Projective Space with Fluxes and Wilson Loops: the Beta Function

We argue that the string theory dual to a certain sector of the four-dimensional Yang-Mills theory at large-N is the A-model wrapping N-Lagrangian D-branes on the twistor space of the complex two-dimensional projective space, with certain fluxes and Wilson loops, by finding that the target-space beta function of this A-model coincides with the large-N beta function of the Yang-Mills theory

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arXiv2008

Quasi BPS Wilson loops, localization of loop equation by homology and exact beta function in the large N limit of SU(N) Yang-Mills theory

We localize the loop equation of large-N YM theory in the ASD variables on a critical equation for an effective action by means of homological methods as opposed to the cohomological localization of equivariantly closed forms in local field theory. Our localization occurs for some special simple quasi BPS Wilson loops, that have no perimeter divergence and no cusp anomaly for backtracking cusps, in a partial Eguchi-Kawai reduction from four to two dimensions of the non-commutative theory in the limit of infinite non-commutativity and in a lattice regularization in which the ASD integration variables live at the points of the lattice, thus implying an embedding of parabolic Higgs bundles in the YM functional integral. We find that the beta function of the effective action is saturated by the non-commutative ASD vortices of the EK reduction. An exact canonical beta function of NSVZ type that reproduces the universal first and second perturbative coefficients follows by the localization on vortices. Finally we argue that a scheme can be found in which the canonical coupling coincides with the physical charge between static quark sources in the large-N limit and we compare our theoretical calculation with some numerical lattice result.

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arXiv2007

Exact beta function from the holographic loop equation of large-N QCD_4

We construct and study a previously defined quantum holographic effective action whose critical equation implies the holographic loop equation of large-N QCD_4 for planar self-avoiding loops in a certain regularization scheme. We extract from the effective action the exact beta function in the given scheme. For the Wilsonean coupling constant the beta function is exacly one loop and the first coefficient agrees with its value in perturbation theory. For the canonical coupling constant the exact beta function has a NSVZ form and the first two coefficients agree with their value in perturbation theory.

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arXiv2005

Twisted local systems solve the (holographic) loop equation of large-N QCD_4

We construct a holographic map from the loop equation of large-N QCD in d=2 and d=4, for planar self-avoiding loops, to the critical equation of an equivalent effective action. The holographic map is based on two ingredients: an already proposed holographic form of the loop equation, such that the quantum contribution is reduced to a regularized residue; a new conformal map from the region encircled by the based loop to a cuspidal fundamental domain in the upper half-plane, such that the regularized residue vanishes at the cusp. As a check, we study the first coefficient of the beta function and that part of the second coefficient which arises from the rescaling anomaly, in passing from the Wilsonian to the canonically normalised (holographic) effective action.

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arXiv2003

Solving loop equations by Hitchin systems via holography in large-N QCD_4

For (planar) closed self-avoiding loops we construct a "holographic" map from the loop equations of large-N QCD_4 to an effective action defined over infinite rank Hitchin bundles. The effective action is constructed densely embedding Hitchin systems into the functional integral of a partially quenched or twisted Eguchi-Kawai model, by means of the resolution of identity into the gauge orbits of the microcanonical ensemble and by changing variables from the moduli fields of Hitchin systems to the moduli of the corresponding holomorphic de Rham local systems. The key point is that the contour integral that occurs in the loop equations for the de Rham local systems can be reduced to the computation of a residue in a certain regularization. The outcome is that, for self-avoiding loops, the original loop equations are implied by the critical equation of an effective action computed in terms of the localisation determinant and of the Jacobian of the change of variables to the de Rham local systems. We check, at lowest order in powers of the moduli fields, that the localisation determinant reproduces exactly the first coefficient of the beta function.

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arXiv1999

The Abelian projection versus the Hitchin fibration of K(D) pairs in four-dimensional QCD

We point out that the concept of Abelian projection gives us a physical interpretation of the role that the Hitchin fibration of parabolic K(D) pairs plays in the large-N limit of four-dimensional QCD. This physical interpretation furnishes also a simple criterium for the confinement of electric fluxes in the large-N limit of QCD. There is also an alternative, compatible interpretation, based on the QCD string.

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arXiv1999

The confining branch of QCD

We show that, as a consequence of a physical interpretation based on the Abelian projection and on the QCD string, four-dimensional QCD confines the electric flux if and only if the functional integral in the fiberwise-dual variables admits a hyper-Kahler reduction under the action of the gauge group.

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arXiv1999

Four-dimensional QCD and fiberwise duality

We transform, by means of a fiberwise duality, the partition function of QCD on a product of two two-tori, into a four-dimensional sigma-model, whose target space is the cotangent space of unitary connections on the fiber torus fiberwise.

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arXiv1999

The large-N limit of QCD and the collective field of the Hitchin fibration

By means of a certain exact non-abelian duality transformation, we show that there is a natural embedding, dense in the sense of the distributions in the large-N limit, of parabolic Higgs bundles of rank N on a fiber two-dimensional torus into the QCD functional integral, fiberwise over the base two-dimensional torus of the trivial elliptic fibration on which the four-dimensional theory is defined. The moduli space of parabolic Higgs bundles of rank N is an integrable Hamiltonian system, that admits a foliation by the moduli of holomorphic line bundles over N-sheeted spectral covers (or, what is the same, over a space of N gauge-invariant polynomials), the Hitchin fibration. According to Hitchin, the Higgs bundles can be recovered from the spectral covers and the line bundles. If the N invariant polynomials together with the abelian connection on the line bundles are chosen as the N+1 collective fields of the Hitchin fibration, all the entropy of the functional integration over the moduli of the Higgs bundles is absorbed, in the large-N limit, into the Jacobian determinant of the change of variables to the collective fields of the Hitchin fibration. Hence, the large-N limit is dominated by the saddle-point of the effective action as in vector-like models.

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arXiv1999

Some comments on S-duality in four-dimensional QCD

We show that a necessary condition, for the partition function of four-dimensional Yang-Mills theory to satisfy a S-duality property, is that certain functional determinants, generated by the dual change of variables, cancel each other. This result holds up to non-topological boundary terms in the dual action and modulo the problem of field-strength copies for the Bianchi identity constraint.

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arXiv1996

Large-N limit and contact terms in unbroken YM_4

I characterize the structure of the master field for $F^{0}_{z \bar z}$ in $SU(\infty)$-$YM_4$ on a product of two Riemann surfaces $Z \times W$ in the gauge $F^{ch}_{z \bar z}=0$ as the sum of a `bulk' constant term and of delta-like `contact' terms.\\ The contact terms may occur because the localization of the functional integral at $N=\infty$ on a master orbit of a constant connection under the action of singular gauge transformations is still compatible with the large-$N$ factorization and translational invariance.\\ In addition I argue that if the gauge group is unbroken and there is a mass gap, that is if the theory confines, the functional measure at $N=\infty$, in the gauge $F^{ch}_{z \bar z}=0$, must be localized on the moduli space of flat connections with punctures on $Z \times W$.

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