Dissecting the string theory dual to QCD

Abstract

Input from QCD and string theory is used in order to elucidate basic features of the string theory dual of QCD, It is argued that the relevant string theory is a five-dimensional version of the type-0 superstring. The vacuum solution is asymptotically AdS5, and the geometry near the boundary is stringy. The structure of YM perturbation theory however emerges near the boundary. In the IR, the theory is argued to be wellapproximated by a two-derivative truncation that takes into account strong coupling effects. This explains the success of previously proposed five-dimensional Eistein-dilaton gravity with an appropriate potential to describe salient features of the strong YM dynamics.Fortschr. Phys. 57, No. 5 -7 (2009) 397 that changed our perception of the description of strongly-coupled large-N c gauge theories, [2][3][4]. The prototype example has been the AdS/CFT correspondence as exemplified by the (well studied by now) duality of N = 4 super Yang-Mills theory and IIB string theory on AdS 5 × S 5 . Further studies focused on providing examples that are closer to real world QCD, [5,6]. It is fair to say that we now have a good holographic understanding of phenomena like confinement, chiral symmetry and its breaking as well as several related issues. The finite temperature dynamics of gauge theories, has a natural holographic counterpart in the thermodynamics of black-holes on the gravity side, and the thermal properties of various holographic constructions have been widely studied, [5,[7][8][9][10], exhibiting the holographic version of deconfinement and chiral restoration transitions.The simplest top-down string theory model of QCD involves D 4 branes with supersymmetry breaking boundary conditions for fermions [5], as well as a flavor sector that involves pairs of D 8 − D 8 probe branes inserted in the bulk, [11]. The qualitative thermal properties of this model closely mimic what we expect in QCD, [8]. Although such theories reproduced the qualitative features of IR QCD dynamics, they contain Kaluza-Klein modes, not expected in QCD, with KK masses of the same order as the dynamical scale of the gauge theory. Above this scale the theories deviate from QCD. Therefore, although the qualitative features of the relevant phenomena are correct, a quantitative matching to real QCD is difficult.Despite the hostile environment of non-critical theory, several attempts have been made to understand holographic physics in lower dimensions in order to avoid the KK contamination, based on two-derivative gravitational actions, [12,13]. Indeed, large N c QCD is expected to be described by a 5-dimensional theory. The alternative problem in non-critical theories is that curvatures are of string scale size and the truncation of the theory to the zero mode sector is subtle and may be misleading.A different and more phenomenological bottom-up approach was developed and is now known as AdS/QCD. The original idea described in [14] was successfully applied to the meson sector in [15], and its thermodynamics was analyzed in [9]. The...

On finite-temperature holographic QCD in the Veneziano limit

“…The starting point of our finite temperature analysis is the T = 0 holographic model introduced in [26], based on previous theoretical ideas in [30][31][32][33][34][35][36][37][38][39][40]. Moving to finite T implies studying black hole solutions of the action in [26].…”

“…The other scalar, the "tachyon" τ , is dual to the quark mass operatorqq. The potentials and interactions were modeled along successful bottomup models for YM, namely Improved Holographic QCD (IHQCD) [30][31][32][33][34][35][36] and the idea that string theory tachyon condensation describes chiral symmetry breaking [37][38][39][62][63][64][65].…”

“…The notion of regularity is tricky even in the case of IHQCD (pure glue), as there is a naked singularity in the far IR. For the dilaton this has been settled in [30][31][32][33][34][35]. For the tachyon the notion of regularity is different and has been studied in detail in [38,39].…”

“…These terms do not affect the thermodynamics of the models. The background solution of the dilaton λ(r) and the warp factor A(r) are identified as the 't Hooft coupling and the logarithm of the energy scale of the dual field theory, respectively [30][31][32]. As a matter of convention, we shall fix the normalisation of λ(r) so that its relation to the perturbative QCD coupling is…”

“…Then the dilaton profile can be linked to the effective potential [26] by using Einstein's equations [30][31][32].…”