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Matteo Giordano

Publications and source records attributed to Matteo Giordano.

At least 91 records · Page 5Linked to original sources
arXiv2014

Dirac eigenmodes at the QCD Anderson transition

Recently we found an Anderson-type localization-delocalization transition in the QCD Dirac spectrum at high temperature. Using spectral statistics we obtained a critical exponent compatible with that of the corresponding Anderson model. Here we study the spatial structure of the eigenmodes both in the localized and the transition region. Based on previous studies in the Anderson model, at the critical point, the eigenmodes are expected to have a scale invariant multifractal structure. We verify the scale invariance of Dirac eigenmodes at the critical point.

hep-lat↗
arXiv2014

Understanding localisation in QCD through an Ising-Anderson model

Above the QCD chiral crossover temperature, the low-lying eigenmodes of the Dirac operator are localised, while moving up in the spectrum states become extended. This localisation/delocalisation transition has been shown to be a genuine second-order phase transition, in the same universality class as that of the 3D Anderson model. The existence of localised modes and the effective dimensional reduction can be tentatively explained as a consequence of local fluctuations of the Polyakov loop, that provide 3D on-site disorder, in analogy to the on-site disorder of the Anderson model. To test the viability of this explanation we study a 3D effective, Anderson-like model, with on-site disorder provided by the spins of a spin model, which mimics the Polyakov loop dynamics. Our preliminary results show that localised modes are present in the ordered phase, thus supporting the proposed mechanism for localisation in QCD.

hep-lat↗
arXiv2014

Hadronic total cross sections, Wilson loop correlators and the QCD spectrum

We show how to obtain rising hadronic total cross sections in QCD, in the framework of the nonperturbative approach to soft high-energy scattering based on Wilson-loop correlators. Total cross sections turn out to be of "Froissart"-type, i.e., the leading energy dependence is of the form $σ_{\rm tot} \sim B \log^2 s$, in agreement with experiments. The observed universality of the prefactor $B$ is obtained rather naturally in this framework. In this case, $B$ is entirely determined by the stable spectrum of QCD, and predicted to be $B_{th} = 0.22\, {\rm mb}$, in fair agreement with experiments.

hep-ph↗
arXiv2014

Anderson localization in QCD-like theories

We review the present status of the Anderson transition in the spectrum of the Dirac operator of QCD-like theories on the lattice. Localized modes at the low-end of the spectrum have been found in SU(2) Yang-Mills theory with overlap and staggered valence fermions as well as in Nf=2+1 QCD with staggered quarks. We draw an analogy between the transition from localized to delocalized modes in the Dirac spectrum and the Anderson transition in electronic systems. The QCD transition turns out to be in the same universality class as the transition in the corresponding Anderson model. We also speculate on the possible physical relevance of this transition to QCD at high temperature and the possible finite temperature phase transition in QCD-like models with different fermion contents.

hep-lat↗
arXiv2014

Universality and the QCD Anderson Transition

We study the Anderson-type transition previously found in the spectrum of the QCD quark Dirac operator in the high temperature, quark-gluon plasma phase. Using finite size scaling for the unfolded level spacing distribution, we show that in the thermodynamic limit there is a genuine mobility edge, where the spectral statistics changes from Poisson to Wigner-Dyson statistics in a non-analytic way. We determine the correlation length critical exponent, $ν$, and find that it is compatible with that of the unitary Anderson model.

hep-lat↗
arXiv2014

Hadronic total cross sections at high energy and the QCD spectrum

We show how to obtain the leading energy dependence of hadronic total cross sections, in the framework of the nonperturbative approach to soft high-energy scattering based on Wilson-loop correlation functions, if certain nontrivial analyticity assumptions are satisfied. The total cross sections turn out to be of "Froissart" type, $σ_{\rm tot}^{(hh)}(s) \mathop\sim B\log^2 s$ for ${s \to \infty}$. We also discuss under which conditions the coefficient $B$ is universal, i.e., independent of the hadrons involved in the scattering process. In the most natural scenarios for universality, $B$ can be related to the stable spectrum of QCD, and is predicted to be $B_{\rm th}\simeq 0.22~{\rm mb}$, in fair agreement with experimental results. If we consider, instead, the stable spectrum of the quenched (i.e., pure-gauge) theory, we obtain a quite larger value $B^{(Q)}_{\rm th} \ge 0.42~{\rm mb}$, suggesting (quite surprisingly) large unquenching effects due to the sea quarks.

hep-ph↗
arXiv2013

Critical statistics at the mobility edge of QCD Dirac spectra

We examine statistical fluctuation of eigenvalues from the near-edge bulk of QCD Dirac spectra above the critical temperature. For completeness we start by reviewing on the spectral property of Anderson tight-binding Hamiltonians as described by nonlinear sigma models and random matrices, and on the scale-invariant intermediate spectral statistics at the mobility edge. By fitting the level spacing distributions, deformed random matrix ensembles which model multifractality of the wave functions typical of the Anderson localization transition, are shown to provide an excellent effective description for such a critical statistics. Next we carry over the above strategy for the Anderson Hamiltonians to the Dirac spectra. For the staggered Dirac operators of QCD with 2+1 flavors of dynamical quarks at the physical point and of SU(2) quenched gauge theory, we identify the precise location of the mobility edge as the scale-invariant fixed point of the level spacing distribution. The eigenvalues around the mobility edge are shown to obey critical statistics described by the aforementioned deformed random matrix ensembles of unitary and symplectic classes. The best-fitting deformation parameter for QCD at the physical point turns out to be consistent with the Anderson Hamiltonian in the unitary class. Finally, we propose a method of locating the mobility edge at the origin of QCD Dirac spectrum around the critical temperature, by the use of individual eigenvalue distributions of deformed chiral random matrices.

hep-lat↗
arXiv2013

Critical behaviour in the QCD Anderson transition

We study the Anderson-type localisation-delocalisation transition found previously in the QCD Dirac spectrum at high temperature. Using high statistics QCD simulations with $N_f=2+1$ flavours of staggered quarks, we discuss how the change in the spectral statistics depends on the volume, the temperature and the lattice spacing, and we speculate on the possible universality of the transition from Poisson to Wigner-Dyson in the spectral statistics. Moreover, we show that the transition is a genuine phase transition: at the mobility edge, separating localised and delocalised modes, quantities characterising the spectral statistics become non-analytic in the thermodynamic limit. Using finite size scaling we also determine the critical exponent of the correlation length, and we speculate on possible extensions of the universality of Anderson transitions.

hep-lat↗
arXiv2013

Quark localization in QCD above $T_c$

It was previously found that at high temperature the lowest part of the QCD Dirac spectrum consists of localized modes obeying Poisson statistics. Higher up in the spectrum, modes become delocalized and their statistics can be described by random matrix theory. The transition from localized to delocalized modes is analogous to the Anderson metal-insulator transition. Here we use dynamical QCD simulations with staggered quarks to study this localization phenomenon. We show that the "mobility edge", separating localized and delocalized modes, scales properly in the continuum limit and rises steeply with the temperature. Using very high statistics simulations in large volumes we find that the density of localized modes scales precisely with the spatial volume and even at $T=2.6T_{c}$ the lowest part of the spectrum extends all the way down to zero with no evidence of a spectral gap.

hep-lat↗
arXiv2012

Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations

We investigate the critical behaviour at theta=pi of the two-dimensional O(3) nonlinear sigma model with topological term on the lattice. Our method is based on numerical simulations at imaginary values of theta, and on scaling transformations that allow a controlled analytic continuation to real values of theta. Our results are compatible with a second order phase transition, with the critical exponent of the SU(2)_1 Wess-Zumino-Novikov-Witten model, for sufficiently small values of the coupling.

hep-lat↗
arXiv2012

Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

We derive a nonperturbative expression for the non-vacuum, qqbar-Reggeon-exchange contribution to the meson-meson elastic scattering amplitude at high energy and low momentum transfer, in the framework of QCD. Describing the mesons in terms of colourless qqbar dipoles, the problem is reduced to the two-fermion-exchange contribution to the dipole-dipole scattering amplitudes, which is expressed as a path integral, over the trajectories of the exchanged fermions, of the expectation value of a certain Wilson loop. We also show how the resulting expression can be reconstructed from a corresponding quantity in the Euclidean theory, by means of analytic continuation. Finally, we make contact with previous work on Reggeon exchange in the gauge/gravity duality approach.

hep-ph↗
arXiv2012

Asymptotic Energy Dependence of Hadronic Total Cross Sections from Lattice QCD

The nonperturbative approach to soft high-energy hadron-hadron scattering, based on the analytic continuation of Wilson-loop correlation functions from Euclidean to Minkowskian theory, allows to investigate the asymptotic energy dependence of hadron-hadron total cross sections in lattice QCD. In this paper we will show, using best fits of the lattice data with proper functional forms satisfying unitarity and other physical constraints, how indications emerge in favor of a universal asymptotic high-energy behavior of the kind B log^2 s for hadronic total cross sections.

hep-ph↗
arXiv2012

Wilson-loop formalism for Reggeon exchange at high energy

I will discuss how the non-vacuum, quark-antiquark Reggeon-exchange contribution to meson-meson elastic scattering, at high energy and low tranferred momentum, can be related to the path-integral of a certain Wilson-loop expectation value over the trajectories of the exchanged fermions. Making use of this representation, I will show how a linear Regge trajectory is obtained through gauge/gravity duality and the use of minimal surfaces.

hep-ph↗
arXiv2012

Eikonal Approach to N=4 SYM Regge Amplitudes in the AdS/CFT Correspondence

The high-energy behavior of N=4 SYM elastic amplitudes at strong coupling is studied by means of the AdS/CFT correspondence. We consider the eikonal method proposed by Janik and one of the authors, where the relevant minimal surface is a "generalized helicoid" in hyperbolic space ("Euclidean AdS_5"), from which the physical amplitude is obtained after an appropriate analytic continuation. We then compare our results with those obtained, using a minimal surface in AdS_5 momentum space, by Alday and Maldacena for gluon-gluon scattering, and by Barnes and Vaman for quark-quark scattering ("Alday-Maldacena approach"). Exploiting a conformal transformation, we show that the eikonal amplitudes are dominated by the Euclidean version of the cusp contribution found in the Alday-Maldacena approach. The amplitudes in the two approaches are of Regge type at high-energy and with the same logarithmic Regge trajectory independently of the kind of colliding particles, in agreement with the expected universality of Regge trajectories.

hep-th↗
arXiv2010

High-energy bounds on total cross sections in N=4 SYM from AdS/CFT

Using the AdS/CFT correspondence, we study the high-energy behavior of scattering amplitudes in N=4 SYM gauge theory for dipole-dipole soft elastic scattering, described in the Wilson-loop correlator formalism. The amplitudes are evaluated in the dual picture, at large impact-parameter, by considering the exchange of supergravity fields between certain minimal surfaces in Euclidean AdS_5, and performing the appropriate analytic continuation to Minkowskian signature. The purely elastic behavior at large impact-parameter is then combined with the unitarity constraint in the central region, in order to derive an absolute bound on the high-energy behavior of the dipole-dipole total cross section. The possibility to obtain a stronger bound by assuming a larger domain of validity for the AdS/CFT result is also discussed.

hep-ph↗