Emerging AdS from Extremally Rotating NS5-branes

TL;DR

The paper addresses holographic duals for extremally rotating NS5-branes by analyzing the near-horizon geometry, which exhibits an $AdS_2$ structure with two chiral Virasoro algebras and, in a special limit where one angular momentum vanishes, an $AdS_3$ enhancement. It embeds this setup into an exact string-theory background described by the $SL(2,\mathbb{R})_N/U(1)$ coset and the $SU(2)_N$ WZW models, realizing the duality through a null-Melvin twist and T-duality in an $O(3,3)$ framework. The paper computes central charges $c^{(1)}$ and $c^{(2)}$, temperatures $T_{\phi_1}$ and $T_{\phi_2}$, and shows that the Cardy entropy reproduces the bulk Bekenstein-Hawking entropy, providing a microscopic string-theory perspective on the dual boundary theory. It also discusses the interpretation of these Virasoro symmetries within the extreme corner of Little String Theory, highlighting how emergent infinite symmetries can arise in a $(1+5)$-dimensional nonlocal theory.

Abstract

We investigate the near-horizon limit of extremally rotating NS5-branes. The resulting geometry has SL(2,R) \times U(1)^2 isometry. The asymptotic symmetry group contains a chiral Virasoro algebra, and we obtain two different realizations depending on the boundary conditions we impose. When one of the two angular momenta vanishes, the symmetry is enhanced to AdS_3. The entropy of the boundary theory can be estimated from the Cardy formula and it agrees with the Bekenstein-Hawking entropy of the bulk theory. We can embed the extremally rotating NS5-brane geometry in an exactly solvable string background, which may yield microscopic understanding of this duality, especially about the mysterious enhancement of the symmetry from AdS_2 to AdS_3. The construction suggests emerging Virasoro symmetries in the extreme corner of the (1+5) dimensional little string theory.