Holographic renormalization of cascading gauge theories

Abstract

We perform a holographic renormalization of cascading gauge theories. Specifically, we find the counter-terms that need to be added to the gravitational action of the backgrounds dual to the cascading theory of Klebanov and Tseytlin, compactified on an arbitrary four-manifold, in order to obtain finite correlation functions (with a limited set of sources). We show that it is possible to truncate the action for deformations of this background to a five dimensional system coupling together the metric and four scalar fields. Somewhat surprisingly, despite the fact that these theories involve an infinite number of high-energy degrees of freedom, we find finite answers for all one-point functions (including the conformal anomaly). We compute explicitly the renormalized stress tensor for the cascading gauge theories at high temperature and show how our finite answers are consistent with the infinite number of degrees of freedom. Finally, we discuss ambiguities appearing in the holographic renormalization we propose for the cascading gauge theories; our finite results for the one-point functions have some ambiguities in curved space (including the conformal anomaly) but not in flat space.Comment: 65 pages (46 pages + appendix), latex. v2: added references. v3: added a reference and a footnot

Gauge-String Dualities and some Applications

“…This identification is legitimate since in the cascading theory, which is nearAdS in the UV, equation (7.19) holds modulo powers of ln r [110,111]. Due to the absence of sources for baryonic operators we again have ϕ0 = 0, and e −S D5 (r) gives the dimensions of the baryon operators, and the values of their condensates.…”

Effective action of the baryonic branch in string theory flux throats

“…This action includes five dimensional metric coupled to four bulk scalar fields. It was used to prove the renomalizability of cascading gauge theory [7], and detailed studies of thermodynamics and hydrodynamics of chirally symmetric phase of cascading gauge theory plasma [8][9][10]. In [9] it was shown that cascading gauge theory undergoes the first order confinementdeconfinement phase transition at a certain critical temperature T c .…”

“…Furthermore, there is a critical point at T u = 0.8749(0)T c where the chirally symmetric phase becomes perturbatively unstable towards condensation of hydrodynamic (sound) modes [10]. To understand chiral symmetry breaking in cascading gauge theory plasma, in [11] we derived effective action corresponding to SU(2) × SU(2) × Z 2 invariant sector of the warped deformed conifold -here, three additional scalar fields are included compare to [7]. This effective action 1 was used to establish that chiral symmetry breaking fluctuations in cascading gauge theory plasma become tachyonic at T χSB = 0.882503(0)T c ; as a result, both confinement and the chiral symmetry breaking in cascading plasma occur simultaneously via the first-order phase transition at T c .…”

“…Likewise, given the prominent role the KS warped throat geometries play in constructing de-Sitter vacua in string theory [6], one needs to understand generic nonsupersymmetric deformations of BGMPZ resolved warped deformed conifolds. The first step in this direction was taken in [7], where a five dimensional effective action describing the SU(2) × SU(2) × U(1) invariant sector of the warped conifold was constructed. This action includes five dimensional metric coupled to four bulk scalar fields.…”

Shear viscosity of CFT plasma at finite coupling

“…To leading order in γ we further parameterize 6) where the asymptotic normalizable components of gravitational modes ν 1 and ν 2 are dual to KW plasma operators of dimension-eight and dimension-six correspondingly [28].…”