Holography for Nonperturbative Study of QFT
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olography for Nonperturbative Study of QFT I. Aref’eva* Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991 Russia *e-mail: [email protected] Received December 20, 2019; revised January 16, 2020; accepted January 29, 2020
Abstract—In this talk the following issues are discussed: (1) holography for quantum field theory (QCD) in general and for quantum chromodynamics (QCD) (so called holographic QCD (HQCD)) in particular; (2) holography for HIC (Heavy-Ions Collisions); (3) results from holography for HIC (there are two types of results: the results confirming experimental data and the results predicting new effects). For the most part we are going to discuss what is special for NICA. Our general presentation is in the line of review of papers and previous talks [1]. DOI: 10.1134/S1063779620040097
1. INTRODUCTION 1.1. Few Remarks on Holography (AdS/CFT) Holography is nowadays one of the most effective tools to study quantum non-equilibrium physics of strongly interacting many body systems. These systems include ultrarelativistic heavy-ion collisions (HIC), cold atom systems, quantum simulators, “ultrafast” techniques in condensed matter physics, etc. Holography translates the physics of quantum many body systems into a dual classical gravitational problem in a space-time with an extra dimension. Holographic description of strong coupling regime first was concerned to a very special model, 1 = 4 supersymmetric Yang–Mills theory. Now it is widely applied for a very large class of quantum field models including QCD in the strong coupling regime. One can say that holography is a new type of phenomenology. In particular, this theory has to fit the following experimental data: transport coefficients, thermalization time, multiplicity, direct-photon spectra etc. We also expect that it predicts new data: detailed form of QCD phase diagram, dependence of energy lost and jet quenching parameters on the parameters specified the HIC, etc. 2. FEW REMARKS ON HOLOGRAPHIC QCD (HQCD) Three important achievements in HQCD are: • HQCD reproduces transport coefficients in high temperature gauge theories. Perturbation theory doesn’t reproduce experimental value of η s . Namely, 2 −1 perturbative calculations give s η = gYM [2], log gYM
that is faraway from the experimental data, meanwhile they are almost reproduced by AdS/CFT result s η = 4π [3]. • HQCD reproduces the Cornell potential obtained previously by lattice data for zero chemical potential [4]. • AHQCD (anisotropic holographic QCD) reproduces the energy dependence of total particle multiplicity produced in HIC [5],
} ∼ s 0.15(5).
(1) • More precisely, the AHQCD with a parameter of anisotropy ν > 1 gives [6] 1 (2 +ν)
}∼s
(2)
• that reproduces (1) for ν = 4.5. Let us remind that the Landau theory [7] predicts } Landau ∼ s 0.25, AdS background predicts [8] } AdS ∼ s 0.33, and the best isotropic HQCD result is [9] } IHQCD ∼ s 0.22(1 + log), see also [10] and refs therein. 2. 5-DIM BACKGROUND FOR HQCD The starting point of HQCD is a 5-dim action having a s
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