New phases of thermal SYM and LST from Kaluza‐Klein black holes

Abstract

We review the recently found map that takes any static and neutral Kaluza-Klein black hole, i.e. any static and neutral black hole on Minkowski-space times a circle M d × S 1 , and maps it to a corresponding solution for a non-and near-extremal brane on a circle. This gives a precise connection between phases of Kaluza-Klein black holes and the thermodynamic behavior of the non-gravitational theories dual to near-extremal branes on a circle. In particular, for the thermodynamics of strongly-coupled supersymmetric Yang-Mills theories on a circle we predict the existence of a new non-uniform phase and find new information about the localized phase. We also find evidence for the existence of a new stable phase of (2, 0) Little String Theory in the canonical ensemble for temperatures above its Hagedorn temperature.

Instabilities of black strings and branes

“…36 In this section we discuss gauge/gravity duals in which the gravity side exhibits a Gregory-Laflamme instability. The presence of this classical gravitational instability in the bulk has important consequences for the gauge theory on the boundary, which we review following [56,57,155,66,58]. Focusing on a set of examples that are closely connected to the material of this review we will consider first D-branes on a circle, where the relevant gauge theory is super-Yang-Mills theory on a circle.…”

“…In this limit the dynamics of the theory is believed to reduce to a string theory without gravity called Little String Theory (LST), or more precisely (2, 0) LST of type A N −1 [166,167,168,169,170]. 45 In this subsection (see also [155,58]) we will consider the thermodynamics of the near-extremal NS5-brane in type IIA string theory using as a starting point the S-dual description as a near-extremal M5-brane on a transverse circle and the input of the phases obtained from six-dimensional neutral Kaluza-Klein black holes in Section 3. Other interesting work on the thermodynamics of LST can be found in [171,164,172,173,174,175,176,177,178,179,180].…”

Supersymmetric Yang–mills Theories With Exact Supersymmetry on the Lattice

“…In particular, for the strongly coupled region, the dual D1-brane system can be described by certain black holes in supergravity, with a compact spatial circle. Then arguments from the dual gravity model indicate a first order Gregory-Laflamme 82,83 phase transition between the black hole solutions localized on the circle and uniform black hole solutions which wrap the circle 80,81,84,85,86,87,88,89 . Translating back to the SYM, the dual gravity model predicts the parametric dependence of the transition temperature against dimensionless circle coupling -a dependence that seemingly cannot be deduced by simple SYM considerations.…”

Simulations of black holes in compactified spacetimes

“…In this work, we wish to study how the compactness of extra dimensions changes the dynamics of such higher-dimensional gravity scenarios. There is considerable literature on Kaluza-Klein BHs and BHs on cylinders [19][20][21][22], but, to the best of our knowledge, the full non-linear dynamics of BHs on such spacetimes remains unexplored.…”