Holographic dual of hot Polchinski-Strassler quark-gluon plasma

Abstract

We construct the supergravity dual of the hot quark-gluon plasma in the massdeformed N = 4 Super-Yang-Mills theory (also known as N = 1 * ). The full ten-dimensional type IIB holographic dual is described by 20 functions of two variables, which we determine numerically, and it contains a black hole with S 5 horizon topology. As we lower the temperature to around half of the mass of the chiral multiplets, we find evidence for (most likely a first-order) phase transition, which could lead either to one of the Polchinski-Strassler confining, screening, or oblique vacua with polarized branes, or to an intermediate phase corresponding to blackened polarized branes with an S 2 × S 3 horizon topology. This phase transition is a feature that could in principle be seen by putting the theory on the lattice, and thus our result for the ratio of the chiral multiplet mass to the phase transition temperature, m c /T = 2.15467491205(6), constitutes the first prediction of string theory and AdS/CFT that could be independently checked via four-dimensional super-QCD lattice computation. We also construct the black-hole solution in certain five-dimensional gauged supergravity truncations and, without directly using uplift/reduction formulae, we find strong evidence that the five-and ten-dimensional solutions are the same. This indicates that five-dimensional gauged supergravity is powerful enough to capture the physics of the high-temperature deconfined phase of the Polchinski-Strassler quark-gluon plasma. Dedicated to the memory of Joe Polchinski arXiv:1805.06463v1 [hep-th] 16 May 2018 Contents 1 Introduction 1 2 N = 1 * super-Yang-Mills and its holographic dual 5 2.1 The vacua of the N = 1 * theory and their supergravity duals 5 2.2 Five-dimensional gauged supergravity and GPPZ flow 7 2.3 The uplift of the supersymmetric GPPZ solution to ten dimensions 10 2.4 The 5D-10D connection 11 3 The SO(3)-invariant flows at finite temperature in 5d 12 3.1 The 2-scalar GPPZ subsector 12 3.2 Constructing finite-temperature flows in the 2-scalar GPPZ subsector 13 3.3 Thermal phases of the 2-scalar GPPZ subsector: results 17 4 The SO(3)×U (1)-invariant finite-temperature flows in type IIB supergravity 23 4.1 The type IIB equations of motion 23 4.2 The cohomogeneity-2 ansatz 25 4.3 Numerical scheme 28 4.4 Energy and a Smarr relation 30 4.5 IIB description of the deconfined high-temperature phase: results 33 5 Conclusion 35These are equivalent to the commutation relations of SU (2), and thus the (classical) vacua are classified by homomorphisms of SU (2) into the gauge group SU (N ). These have a nice combinatoric structure, which we will not detail here (but we refer the reader to [28]). In particular, there exist special vacua for each positive integer d that divides N , which have (classically) an unbroken SU (d) gauge symmetry. Quantum mechanically, these vacua split into d separate vacua with totally broken gauge symmetry and a mass gap [5]. They can be described as Higgs or screening (d = 1), confining (d = N ), or oblique confining (1 < d...

Phase transitions in a three-dimensional analogue of Klebanov-Strassler

“…Yet, the UV of our models, which are asymptotically free, is simpler than the infinite cascade of their four-dimensional cousins in [15,16]. It would also be interesting to compare to the phase structure of the N = 1 * super Yang-Mills theory, the high temperature deconfined phase of which was studied in [33].…”

A holographic kaleidoscope for $$ \mathcal{N} $$ = 1*

“…Putting the field theory at finite temperature is a natural physical choice. Indeed, this was studied for the N = 1 * theory in [46], see also [47] for recent work. While this is certainly one way to remedy the naked singularity of the GPPZ solutions, the lack of supersymmetry complicates the analysis of this set-up significantly.…”

Crossing a large-N phase transition at finite volume

“…Recall that, before imposing boundary conditions, we have 6 integration constants at the UV and another 6 in the IR. A power-law Taylor expansion about the asymptotic boundary, 25) concludes that, after imposing the boundary conditions (2.23) that fix a 1(0) = 1, a 3(0) = 1 and a 4(0) = Λ (a 2(0) is not a free parameter since it is fixed by the equations of motion), we are left with three free UV parameters, namely a 1(2) (x), a 2(2) (x), a 4(1) (x). Note that we will give Λ as an input parameter so the boundary-value problem will not have to determine 6 The notation q (p,q) j (x, y) refers to partial derivative p times with respect to the first variable and q times with respect to the second variable.…”

“…These methods are reviewed and explained in detail in the review [20] and used in e.g. [21][22][23][24][25]. As explained in sections 2.1 and 2.2 (see in particular footnote 2 and the associated discussion) our gauge was judiciously chosen to guarantee that our solutions have analytical polynomial expansions at all the boundaries of the integration domain.…”