Searcharxiv⌕ Search

arXiv subjects

Elisabetta Pallante

Publications and source records attributed to Elisabetta Pallante.

At least 19 recordsLinked to original sources
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.

hep-th↗
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.

hep-th↗
arXiv2021

QNMs of scalar fields on small Reissner-Nordström-AdS$\mathbf{_5}$ black holes

We study the quasinormal modes (QNMs) of a charged scalar field on a Reissner-Nordström-anti-de Sitter (RN-AdS$_{5}$) black hole in the small radius limit by using the isomonodromic method. We also derive the low-temperature expansion of the fundamental QNM frequency. Finally, we provide numerical evidence that instabilities appear in the small radius limit for large values of the charge of the scalar field.

hep-th↗
arXiv2021

Remarks on holographic models of the Kerr-AdS$_{5}$ geometry

We study the low-temperature limit of scalar perturbations of the Kerr-AdS$_{5}$ black-hole for generic rotational parameters. We motivate the study by considering real-time holography of small black hole backgrounds. Using the isomonodromic technique, we show that corrections to the extremal limit can be encoded in the monodromy parameters of the Painlevé V transcendent, whose expansion is given in terms of irregular chiral conformal blocks. After discussing the contribution of the intermediate states to the quasi-normal modes, we perform a numerical analysis of the low-lying frequencies. We find that the fundamental mode is perturbatively stable at low temperatures for small black holes and that excited perturbations are superradiant, as expected from thermodynamical considerations. We close by considering the holographic interpretation of the unstable modes and the decaying process.

hep-th↗
arXiv2020

Conserved vector current in QCD-like theories and the gradient flow

We present analytical results for the Euclidean 2-point correlator of the flavor-singlet vector current evolved by the gradient flow at next-to-leading order ($O(g^2)$) in perturbatively massless QCD-like theories. We show that the evolved 2-point correlator requires multiplicative renormalization, in contrast to the nonevolved case, and confirm, in agreement with other results in the literature, that such renormalization ought to be identified with a universal renormalization of the evolved elementary fermion field in all evolved fermion-bilinear currents, whereas the gauge coupling renormalizes as usual. We explicitly derive the asymptotic solution of the Callan-Symanzik equation for the connected 2-point correlators of these evolved currents in the limit of small gradient-flow time $\sqrt{t}$, at fixed separation $|x-y|$. Incidentally, this computation determines the leading coefficient of the operator-product expansion (OPE) in the small $t$ limit for the evolved currents in terms of their local nonevolved counterpart. Our computation also implies that, in the evolved case, conservation of the vector current, hence transversality of the corresponding 2-point correlator, is no longer related to the nonrenormalization, in contrast to the nonevolved case. Indeed, for small flow time the evolved vector current is conserved up to $O(t)$ softly violating effects, despite its $t$-dependent nonvanishing anomalous dimension.

hep-th↗
arXiv2020

Vector perturbations of Kerr-AdS$_5$ and the Painlevé VI transcendent

We analyze the Ansatz of separability for Maxwell equations in generically spinning, five-dimensional Kerr-AdS black holes. We find that the parameter μintroduced in a previous work by O. Lunin can be interpreted as apparent singularities of the resulting radial and angular equations. Using isomonodromy deformations, we describe a non-linear symmetry of the system, under which μis tied to the Painlevé VI transcendent. By translating the boundary conditions imposed on the solutions of the equations for quasinormal modes in terms of monodromy data, we find a procedure to fix μand study the behavior of the quasinormal modes in the limit of fast spinning small black holes.

hep-th↗
arXiv2019

Scalar quasinormal modes of Kerr-AdS$\mathbf{_5}$

An analytic expression for the scalar quasinormal modes of the generic, spinning Kerr-$\mathrm{AdS_5}$ black holes was previously proposed by the authors in ref. 1, in terms of transcendental equations involving the Painlevé VI (PVI) $τ$ function. In this work, we carry out a numerical investigation of the modes for generic rotation parameters, comparing implementations of expansions for the PVI $τ$ function both in terms of conformal blocks (Nekrasov functions) and Fredholm determinants. We compare the results with standard numerical methods for the subcase of Schwarzschild black holes. We then derive asymptotic formulas for the angular eigenvalues and the quasinormal modes in the small black hole limit for generic scalar mass and discuss, both numerically and analytically, the appearance of superradiant modes.

hep-th↗
arXiv2018

On the gradient flow of the Lagrangian density in non-Abelian gauge theories

We observe that the would-be running coupling on the lattice defined by means of the gradient-flow method in order to identify the conformal window of QCD is not renormalization-group invariant (RGI). Indeed, we show that the would-be running coupling, $g_{wb}^2(t)\propto t^2\langle E(t)\rangle$, -- with $\langle E(t)\rangle$ the expectation value of the Lagrangian density smeared by means of the gradient flow -- has an anomalous dimension associated to the multiplicative renormalization factor of $t^2\langle E(t)\rangle$. As a consequence, at a nontrivial infrared (IR) fixed point with nonvanishing anomalous dimension, $γ_*$, in the conformal window, the would-be running coupling vanishes asymptotically as $g_{wb}^2(t)\propto t^2\langle E(t)\rangle\sim t^{-γ_*/2}$ and does not scale as $g_{wb}^2(t)\propto t^2\langle E(t)\rangle\sim g_{wb}^{*2}\neq 0$, with $g_{wb}^{*}$ the nonvanishing would-be coupling at the nontrivial fixed point, as postulated in the literature. The associated would-be beta function, $β_{wb}({g}_{wb}^2(t))$, is not proportional to a true RGI beta function, and it also vanishes asymptotically in the IR for nonvanishing $γ_*$ at the IR fixed point. Moreover, $β_{wb}$ violates two-loop universality and may develop spurious zeroes both in the confined and the conformal phase, despite $g_{wb}^2(t)$ is asymptotic to a true RGI running coupling in a neighborhood of the asymptotically free fixed point. Our analysis allows us to reinterpret the contradictory lattice results based on this method, specifically those for the $N_f$=12 theory, explain the origin of their discrepancies and suggest a new strategy to discriminate between the confined phase and the conformal window. In this respect, we disagree with a recent claim that attributes the same contradictory results to staggered fermions being in the wrong universality class.

hep-th↗
arXiv2018

The scalar glueball operator, the a-theorem, and the onset of conformality

We show that the anomalous dimension $γ_G$ of the scalar glueball operator contains information on the mechanism that leads to the onset of conformality at the lower edge of the conformal window in a non-Abelian gauge theory. In particular, it distinguishes whether the merging of an UV and an IR fixed point -- the simplest mechanism associated to a conformal phase transition and preconformal scaling -- does or does not occur. At the same time, we shed light on new analogies between QCD and its supersymmetric version. In SQCD, we derive an exact relation between $γ_G$ and the mass anomalous dimension $γ_m$, and we prove that the SQCD exact beta function is incompatible with merging as a consequence of the $a$-theorem; we also derive the general conditions that the latter imposes on the existence of fixed points, and prove the absence of an UV fixed point at nonzero coupling above the conformal window of SQCD. Perhaps not surprisingly, we then show that an exact relation between $γ_G$ and $γ_m$, fully analogous to SQCD, holds for the massless Veneziano limit of large-N QCD. We argue, based on the latter relation, the $a$-theorem, perturbation theory and physical arguments, that the incompatibility with merging may extend to QCD.

hep-th↗
arXiv2017

On the Kerr-AdS/CFT correspondence

We review the relation between four-dimensional global conformal blocks and field propagation in ${\rm AdS_5}$. Following the standard argument that marginal perturbations should backreact in the geometry, we turn to the study of scalar fields in the generic Kerr-${\rm AdS_5}$ geometry. On one hand, the result for scattering coefficients can be obtained exactly using the isomonodromy technique, giving exact expressions in terms of $c=1$ chiral conformal blocks. On the other hand, one can use the analogy between the scalar field equations to the Level 2 null field Ward identity in two dimensional Liouville field theory to write approximate expressions for the same coefficients in terms of semi-classical chiral Liouville conformal blocks. Surprisingly, the conformal block thus constructed has a well-behaved interpretation in terms of Liouville vertex operators.

hep-th↗
arXiv2016

Conformal or Confining

We present a lattice study of the phase transitions at zero and nonzero temperature for the $SU(3)$ gauge theory with a varying number of flavours $N_f$ in the fundamental representation of the gauge group. We show that all results are consistent with a lower edge of the conformal window between $N_f=8$ and $N_f=6$. A lower edge in this interval is in remarkable agreement with perturbation theory and recent large-$N$ arguments. .

hep-th↗
arXiv2014

Approaching Conformality

We investigate the preconformal region of the phase diagram of SU(3) theories with fundamental flavors. We have simulated SU(3) theories with six and eight fundamental flavors at volumes 32^3 x 64. We use the generated configurations to measure the string tension σand the w0 scale setting quantity extracted from the gradient flow. We show preliminary results on the ratios Tc/\sqrtσ and Tc w0. We compare them to the behavior obtained at smaller Nf and discuss the implications of our results.

hep-lat↗
arXiv2012

The strong coupling regime of twelve flavors QCD

We summarize the results recently reported in Ref.[1] [A. Deuzeman, M.P. Lombardo, T. Nunes da Silva and E. Pallante,"The bulk transition of QCD with twelve flavors and the role of improvement"] for the SU(3) gauge theory with Nf=12 fundamental flavors, and we add some numerical evidence and theoretical discussion. In particular, we study the nature of the bulk transition that separates a chirally broken phase at strong coupling from a chirally restored phase at weak coupling. When a non-improved action is used, a rapid crossover is observed at small bare quark masses. Our results confirm a first order nature for this transition, in agreement with previous results we obtained using an improved action. As shown in Ref.[1], when improvement of the action is used, the transition is preceded by a second rapid crossover at weaker coupling and an exotic phase emerges, where chiral symmetry is not yet broken. This can be explained [1] by the non hermiticity of the improved lattice Transfer matrix, arising from the competition of nearest-neighbor and non-nearest neighbor interactions, the latter introduced by improvement and becoming increasingly relevant at strong coupling and coarse lattices. We further comment on how improvement may generally affect any lattice system at strong coupling, be it graphene or non abelian gauge theories inside or slightly below the conformal window.

hep-lat↗
arXiv2012

The bulk transition of QCD with twelve flavors and the role of improvement

We study the SU(3) gauge theory with Nf=12 flavors in the fundamental representation by use of lattice simulations with staggered fermions. With a non-improved action we observe a chiral zero-temperature (bulk) transition separating a region at weak coupling, where chiral symmetry is realized, from a region at strong coupling where chiral symmetry is broken. With improved actions, a more complicated pattern emerges, and in particular two first order transitions in the chiral limit appear. We observe that at sufficiently strong coupling the next-to-nearest neighbor terms of the improved lattice action are no longer irrelevant and can indeed modify the pattern observed without improvement. Baryon number conservation can be realized in an unusual way, allowing for an otherwise prohibited oscillating term in the pseudoscalar channel. We discuss the phenomenon by means of explicit examples borrowed from statistical mechanics. Finally, these observations can also be useful when simulating other strongly coupled systems on the lattice, such as graphene.

hep-lat↗
arXiv2012

Slinky evolution of domain wall brane cosmology

Invoking an initial symmetry between the time $ t $ and some extra spatial dimension $ y $, we discuss a novel scenario where the dynamical formation of the 4-dim brane and its cosmological evolution are induced simultaneously by a common $ t<->y $ symmetry breaking mechanism. The local maximum of the underlying scalar potential is mapped onto a 'watershed' curve in the $ (t,y) $ plane; the direction tangent to this curve is identified as the cosmic time, whereas the perpendicular direction serves locally as the extra spatial dimension. Special attention is devoted to the so-called slinky configurations, whose brane cosmology is characterized by a decaying cosmological constant along the watershed curve. Such a slinky solution is first constructed within a simplified case where the watershed is constrained by $ y = 0 $. The physical requirements for a slinky configuration to generate a realistic model of cosmological evolution are then discussed in a more elaborated framework.

hep-th↗
arXiv2012

Chiral phase transition at finite temperature and conformal dynamics in large Nf QCD

We investigate the chiral phase transition at finite temperature (T) in colour SU(Nc=3) Quantum Chromodynamics (QCD) with six species of fermions (Nf=6) in the fundamental representation by using lattice QCD with improved staggered fermions. By considering lattices with several temporal extensions Nt, we observe asymptotic scaling for Nt > 4. We then extract the dimensionless ratio Tc/Lambda_L (Lambda_L = Lattice Lambda-parameter) for Nf = 6 and Nf = 8, the latter relying on our earlier results. Further, we collect the critical couplings beta^c for the chiral phase transition at Nf = 0 (quenched), and Nf = 4 at a fixed Nt = 6. The results are consistent with enhanced fermionic screening at larger Nf. The Tc/Lambda_L depends very mildly on Nf in the Nf = 0 - 4 region, starts increasing at Nf = 6, and becomes significantly larger at Nf = 8, close to the edge of the conformal window. We discuss interpretations of these results as well as their possible interrelation with preconformal dynamics in the light of a functional renormalization group analysis.

hep-lat↗
arXiv2012

On the spectrum of QCD-like theories and the conformal window

We report on the spectrum of the SU(3) gauge theory with twelve flavours in the fundamental representation of the gauge group. We isolate distinctive features of the hadronic phase - the one proper of QCD at zero temperature - and the so called conformal phase. The latter should emerge at sufficiently large Nf and before the loss of asymptotic freedom. In particular, we analyse available lattice data for the spectrum of Nf=12 and include a comparison with results with Nf=16; the latter theory, predicted by the perturbative beta-function to develop an IRFP and therefore be in the conformal phase, can serve as a paradigm for the study of theories in the conformal window. Our analysis suggests that the theory with twelve flavours is in the conformal window, possibly close to its lower boundary.

hep-lat↗