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Jun 29, 2018
06/18

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Matteo Giordano; Sandor D. Katz; Tamas G. Kovacs; Ferenc Pittler

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We study the problems of deconfinement, chiral symmetry restoration and localisation of the low Dirac eigenmodes in a toy model of QCD, namely unimproved staggered fermions on lattices of temporal extension $N_T=4$. This model displays a genuine deconfining and chirally-restoring first-order phase transition at some critical value of the gauge coupling. Our results indicate that the onset of localisation of the lowest Dirac eigenmodes takes place at the same critical coupling where the system...

Topic: High Energy Physics - Lattice

Source: http://arxiv.org/abs/1611.03284

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4.0

Jun 29, 2018
06/18

by
Falk Bruckmann; Gergely Endrodi; Matteo Giordano; Sandor D. Katz; Tamas G. Kovacs; Ferenc Pittler; Jacob Wellnhofer

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The spectrum of the two-dimensional continuum Dirac operator in the presence of a uniform background magnetic field consists of Landau levels, which are degenerate and separated by gaps. On the lattice the Landau levels are spread out by discretization artefacts, but a remnant of their structure is clearly visible (Hofstadter butterfly). If one switches on a non-Abelian interaction, the butterfly structure will be smeared out, but the lowest Landau level (LLL) will still be separated by a gap...

Topic: High Energy Physics - Lattice

Source: http://arxiv.org/abs/1611.05747

4
4.0

Jun 30, 2018
06/18

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Matteo Giordano; Tamas G. Kovacs; Ferenc Pittler; Laszlo Ujfalusi; Imre Varga

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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...

Topics: High Energy Physics - Phenomenology, High Energy Physics - Lattice, Disordered Systems and Neural...

Source: http://arxiv.org/abs/1410.8308

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2.0

Jun 29, 2018
06/18

by
Matteo Giordano; Tamas G. Kovacs; Ferenc Pittler

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The Dirac operator in finite temperature QCD is equivalent to the Hamiltonian of an unconventional Anderson model, with on-site noise provided by the fluctuations of the Polyakov lines. The main features of its spectrum and eigenvectors, concerning the density of low modes and their localization properties, are qualitatively reproduced by a toy-model random Hamiltonian, based on an Ising-type spin model mimicking the dynamics of the Polyakov lines. Here we study the low modes of this toy model...

Topic: High Energy Physics - Lattice

Source: http://arxiv.org/abs/1612.05059

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13

Jun 26, 2018
06/18

by
Matteo Giordano; Tamas G. Kovacs; Ferenc Pittler

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We discuss a possible mechanism leading to localisation of the low-lying Dirac eigenmodes in high-temperature lattice QCD, based on the spatial fluctuations of the local Polyakov lines in the partially ordered configurations above $T_c$. This mechanism provides a qualitative explanation of the dependence of localisation on the temperature and on the lattice spacing, and also of the phase diagram of QCD with an imaginary chemical potential. To test the viability of this mechanism we propose a...

Topic: High Energy Physics - Lattice

Source: http://arxiv.org/abs/1502.02532

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2.0

Jun 29, 2018
06/18

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Matteo Giordano; Tamas G. Kovacs; Ferenc Pittler

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We discuss chiral symmetry restoration and eigenmode localisation in finite-temperature QCD by looking at the lattice Dirac operator as a random Hamiltonian. We argue that the features of QCD relevant to both phenomena are the presence of order in the Polyakov line configuration, and the correlations that this induces between spatial links across time slices. This ties the fate of chiral symmetry and of localisation of the lowest Dirac eigenmodes to the confining properties of the theory. We...

Topic: High Energy Physics - Lattice

Source: http://arxiv.org/abs/1610.07412

2
2.0

Jun 30, 2018
06/18

by
Matteo Giordano; Tamas G. Kovacs; Ferenc Pittler

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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...

Topics: High Energy Physics - Theory, High Energy Physics - Phenomenology, High Energy Physics - Lattice,...

Source: http://arxiv.org/abs/1409.5210

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3.0

Jun 30, 2018
06/18

by
Matteo Giordano; Sandor D. Katz; Tamas G. Kovacs; Ferenc Pittler

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At low temperature the low-lying QCD Dirac spectrum obeys random matrix statistics. Recently we found that above $T_{c}$ the lowest part of the spectrum consists of localized modes that obey Poisson statistics. An interesting implication of this is that as the system crosses $T_{c}$ from above, the spectral statistics at $\lambda=0$ changes from Poisson to random matrix. Here we study this transition and its possible implications for the finite temperature transition of QCD-like theories.

Topic: High Energy Physics - Lattice

Source: http://arxiv.org/abs/1410.8392

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Sep 19, 2013
09/13

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Enrico Meggiolaro; Matteo Giordano

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We will discuss how the problem of high-energy hadron-hadron (dipole-dipole) scattering at low momentum transfer can be approached from the point of view of lattice QCD, by means of Monte Carlo numerical simulations.

Source: http://arxiv.org/abs/1010.0914v1

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2.0

Jun 30, 2018
06/18

by
Matteo Giordano; Enrico Meggiolaro

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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 $\sigma_{\rm tot} \sim B \log^2 s$, in agreement with experiments. The observed universality of the prefactor $B$ is obtained rather naturally in this framework. In this case, $B$ is entirely...

Topic: High Energy Physics - Phenomenology

Source: http://arxiv.org/abs/1409.7376

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36

Sep 23, 2013
09/13

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Matteo Giordano; Robi Peschanski; Shigenori Seki

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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...

Source: http://arxiv.org/abs/1110.3680v2

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2.0

Jun 30, 2018
06/18

by
Matteo Giordano; Enrico Meggiolaro

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We discuss how hadronic total cross sections at high energy depend on the details of QCD, namely on the number of colours $N_c$ and the quark masses. We find that while a "Froissart"-type behaviour $\sigma_{\rm tot}\sim B\log^2s$ is rather general, relying only on the presence of higher-spin stable particles in the spectrum, the value of $B$ depends quite strongly on the quark masses. Moreover, we argue that $B$ is of order ${\cal O}(N_c^0)$ at large $N_c$, and we discuss a bound for...

Topics: High Energy Physics - Phenomenology, Nuclear Theory

Source: http://arxiv.org/abs/1411.0553

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34

Sep 19, 2013
09/13

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Matteo Giordano

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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...

Source: http://arxiv.org/abs/1009.2971v1

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2.0

Jun 30, 2018
06/18

by
Matteo Giordano; Tamas G. Kovacs; Ferenc Pittler

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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,...

Topic: High Energy Physics - Lattice

Source: http://arxiv.org/abs/1410.6378

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4.0

Jun 29, 2018
06/18

by
Matteo Giordano; Tamas G. Kovacs; Ferenc Pittler

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We study the problems of chiral symmetry breaking and eigenmode localisation in finite-temperature QCD by looking at the lattice Dirac operator as a random Hamiltonian. We recast the staggered Dirac operator into an unconventional three-dimensional Anderson Hamiltonian ("Dirac-Anderson Hamiltonian") carrying internal degrees of freedom, with disorder provided by the fluctuations of the gauge links. In this framework, we identify the features relevant to chiral symmetry restoration and...

Topic: High Energy Physics - Lattice

Source: http://arxiv.org/abs/1603.09548

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40

Sep 18, 2013
09/13

by
Matteo Giordano

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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.

Source: http://arxiv.org/abs/1209.5940v1

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39

Sep 21, 2013
09/13

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Matteo Giordano

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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...

Source: http://arxiv.org/abs/1204.3772v3

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149

Sep 17, 2013
09/13

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Matteo Giordano; Robi Peschanski

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Using the AdS/CFT correspondence, we study the high-energy behavior of colorless dipole elastic scattering amplitudes in N=4 SYM gauge theory through the Wilson loop correlator formalism and Euclidean to Minkowskian analytic continuation. The purely elastic behavior obtained at large impact-parameter L, through duality from disconnected AdS_5 minimal surfaces beyond the Gross-Ooguri transition point, is combined with unitarity and analyticity constraints in the central region. In this way we...

Source: http://arxiv.org/abs/1003.2309v2

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10.0

Jun 28, 2018
06/18

by
Matteo Giordano; Enrico Meggiolaro

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We determine the large-distance behaviour of the static dipole-dipole potential for a wide class of gauge theories on nonperturbative grounds, exploiting only general properties of the theory. In the case of QCD, we recover the known results in the regime of small dipole sizes, and discuss recent nonperturbative calculations. Moreover, we discuss the case of pure-gauge theories, and compare our prediction with the available lattice results.

Topics: High Energy Physics - Phenomenology, High Energy Physics - Lattice, High Energy Physics - Theory

Source: http://arxiv.org/abs/1507.07215

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91

Jul 20, 2013
07/13

by
Matteo Giordano; Enrico Meggiolaro; Niccolò Moretti

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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...

Source: http://arxiv.org/abs/1203.0961v2

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Jun 28, 2018
06/18

by
Matteo Giordano

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We study the renormalisation of $SU(N_c)$ gauge theories on general anisotropic lattices, to one-loop order in perturbation theory, employing the background field method. The results are then applied in the context of two different approaches to hadronic high-energy scattering. In the context of the Euclidean nonperturbative approach to soft high-energy scattering based on Wilson loops, we refine the nonperturbative justification of the analytic continuation relations of the relevant...

Topics: High Energy Physics - Phenomenology, High Energy Physics - Lattice

Source: http://arxiv.org/abs/1506.04529

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46

Sep 20, 2013
09/13

by
Vicente Azcoiti; Giuseppe Di Carlo; Eduardo Follana; Matteo Giordano

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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...

Source: http://arxiv.org/abs/1207.4905v2