The QCD trace anomaly at strong coupling from M-theory

Aalok Misra,Charles Gale

doi:10.1140/epjc/s10052-020-8174-5

Abstract

Obtaining a lattice-consistent result for the temperature dependence of the QCD conformal anomaly from a top-down M-theory dual (valid) for all temperatures – both, T<T_c and T>T_c – of thermal QCD at intermediate gauge coupling, has been missing in the literature. We fill this gap by addressing this issue from the M-theory uplift of the SYZ type IIA mirror at intermediate gauge/string coupling [both obtained in Dhuria et al. (JHEP 1311:001, 2013)] of the UV-complete type IIB holographic dual of large-N thermal QCD of Mia et al. (Nucl Phys B 839:187, 2010), and comparing with the very recent lattice results of Bazavov et al. (Phys Rev D 97(1):014510, 2018). Estimates of the mathcal{O}(R^4) higher derivative corrections in the D=11 supergravity action relevant to considering the aforementioned M theory uplift in the intermediate ’t Hooft coupling (in addition to gauge coupling) limit, are also presented. We also show that after a tuning of the (small) Ouyang embedding parameter and radius of a blown-up S^2 when expressed in terms of the horizon radius, a QCD deconfinement temperature T_c=150 MeV from a Hawking–Page phase transition at vanishing baryon chemical potential consistent with lattice QCD in the heavy-quark limit, can be obtained.

Highlights

The equation of state (EOS) is an integral part of the energy–momentum tensor, T μν
To the best of our knowledge, there is no precedence of studying the QCD conformal/trace anomaly from a top-down M theory dual (inclusive of higher derivative (O(R4)) corrections corresponding to considering the intermediate ’t-Hooft coupling limit) at low and high temperatures consistent with recent lattice results
We showed that for Tc = 150 MeV, N f = 3, our M theory results for the variation of the QCD conformal anomaly with temperature can be made to be consistent with

Summary

Introduction

The EOS is an integral part of the energy–momentum tensor, T μν. In a classical theory without any dimentionful parameters, a scale transformation leaves the action invariant, and leads to a traceless energy momentum tensor: Tμμ = 0. We provide a short review of a UV complete type IIB holographic dual (the only one we are aware of) of large-N thermal QCD constructed in [2], its Strominger– Yau–Zaslow (SYZ) type IIA mirror at intermediate string coupling and its subsequent M-theory uplift constructed in [1, 34]. The type IIB model of [2] make it an ideal holographic dual of thermal QCD because: (i) it is UV conformal (Landau poles are absent), (ii) it is IR confining, (iii) the quarks transform in the fundamental representation of flavor and color groups, and (iv) it is defined for the full range of temperature – both low and high. The SU (3)/G2 structure torsion classes (which measure the deviation of a six/sevenfold from having SU (3)/G2 holonomy) are denoted respectively by Wi=1,2,3,4,5/ Wi=1,2,3,4 (with superscripts in the G2structure torsion classes denoting the respective dimensionalities) therein

Lattice-compatible Tc

QCD trace anomaly from M theory

N 4 MUV

Summary and discussion