New Phases of Near-Extremal Branes on a Circle

TL;DR

This paper constructs a precise boost/U-duality map from static, neutral Kaluza-Klein black holes on $\mathcal{M}^d \times S^1$ to near-extremal branes on a circle, translating the $(\mu,n)$ phase diagram into a $(\epsilon,r)$ diagram and thereby transferring known KK black hole phases to brane phases. It shows that each KK branch (uniform, non-uniform, and black hole on cylinder) yields corresponding non-extremal and near-extremal brane phases, including a new non-uniform phase and a localized phase with calculable thermodynamics. The authors derive explicit relations, such as $\epsilon = \frac{d+n}{2(d-1)}\mu$ and $r = 2\frac{(d-1)n}{d+n}$, and they compute leading corrections to entropy and free energy for localized and non-uniform phases, with applications to dual theories like SYM on a circle and $(2,0)$ LST. The results provide new insights into finite-temperature behavior of these non-gravitational theories and suggest potential counterexamples to the Gubser–Mitra conjecture, while offering a framework to explore further phases (including bubbles) via the gravity-brane correspondence.

Abstract

We study the phases of near-extremal branes on a circle, by which we mean near-extremal branes of string theory and M-theory with a circle in their transverse space. We find a 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 x S^1, and map it to a corresponding solution for a near-extremal brane on a circle. The map is derived using first a combined boost and U-duality transformation on the Kaluza-Klein black hole, transforming it to a solution for a non-extremal brane on a circle. The resulting solution for a near-extremal brane on a circle is then obtained by taking a certain near-extremal limit. As a consequence of the map, we can transform the neutral non-uniform black string branch into a new non-uniform phase of near-extremal branes on a circle. Furthermore, we use recently obtained analytical results on small black holes in Minkowski-space times a circle to get new information about the localized phase of near-extremal branes on a circle. This gives in turn predictions for the thermal behavior of the non-gravitational theories dual to these near-extremal branes. In particular, we give predictions for the thermodynamics of supersymmetric Yang-Mills theories on a circle, and we find a new stable phase of (2,0) Little String Theory in the canonical ensemble for temperatures above its Hagedorn temperature.

Figures (5)

• Figure 1: Phase diagram for $d=5$ in the region $n \leq 1/3$.
• Figure 2: Phase diagram for near-extremal M5-branes on a circle.
• Figure 3: The entropy $\hat{\mathfrak{s}}(\epsilon)$ as a function of energy for near-extremal M5-branes on a circle.
• Figure 4: The free energy $\hat{\mathfrak{f}}(\hat{\mathfrak{t}})$ as a function of temperature for the non-uniform phase of near-extremal M5-branes on a circle, and for the copies of the non-uniform phase.
• Figure 5: The heat capacity $c$ as function of the temperature $\hat{\mathfrak{t}}$ for the non-uniform phase of near-extremal M5-branes on a circle.