BPS Fivebrane Stars and BTZ Black Holes

TL;DR

This work constructs and analyzes a broad class of 1/8-BPS geometries sourced by arbitrarily chiral left-moving profiles on NS5-branes and fundamental strings, in a regime where fivebranes sit on the Coulomb branch and are slightly separated. By coupling a bulk Type II supergravity action to the worldvolume actions of NS5-branes and F1 strings, the authors derive a layered set of BPS equations and a joint effective action that captures near-BPS dynamics and the interactions between brane clouds. A key result is that many three-charge solutions exhibit ultracompact, BTZ-like AdS_2 throats with caps set by fivebrane separation, while quantum/non-abelian dynamics (little strings) become important near the non-abelian scale, signaling a transition toward black hole physics and a bulk realization of Hawking-Page deconfinement. The circular/single-mode analyses connect these backgrounds to known superstrata, reveal Schwarzian-like collective modes controlling throat depth, and illuminate how horizonless fivebrane stars can mimic several black-hole features, offering a concrete framework to study black hole microstructure and information-transport mechanisms in string theory.

Abstract

We construct a large new class of BPS supergravity solutions parametrized by arbitrary chiral wave profiles on fundamental string and Neveu-Schwarz fivebrane sources. The effective action approach we employ describes the regime where the brane sources are slightly separated. String probes see these backgrounds as smooth and effectively capped off at the scale of that separation. Within the space of solutions is a large ensemble of ultracompact objects exhibiting many of the features of extremal BTZ black holes, in particular having a deep $AdS_2$ throat. We present the details of solutions with circular source profiles, and compare them to known superstratum geometries. The separation of the sources makes them structurally more like BPS fivebrane stars than like extremal black hole microstates. When evaluated on the supergravity background, the brane effective action governs (chaotic) near-BPS dynamics, and exhibits a collective mode analogous to the Schwarzian mode of $AdS_2$ black holes. Finally, we discuss the approach to the black hole phase as the sources coalesce, in which the semiclassical approximation breaks down due to the appearance of light D-brane excitations; this bulk realization of the fivebrane deconfinement transition connects directly to the Hawking-Page transition.

Figures (5)

• Figure 1: A highly excited BPS fivebrane multiply wrapping the y-circle ($v=t+y$) executes a random walk in its transverse space. The hues of the fivebrane strands evolve around the color wheel (ROYGBIV) to indicate their connectivity.
• Figure 2: Proper size of ${\mathbb S}^1_y$ as a function of radius in the typical three-charge BPS state we construct, in the regime of weak string coupling and large $R_y$.
• Figure 3: Sketch of the $(\ell,0,n)$ superstratum geometry. The geometry has an $AdS_2$ throat beginning at $r\sim \sqrt{n/\ell}\,b$, supported by a momentum wave at $r\sim \sqrt{n/\ell}\,a$; inside the momentum wave, the geometry is approximately $AdS_3$ again down to $r=0$, where it caps off smoothly.
• Figure 4: A fivebrane source coherently spinning in a transverse plane. The BPS condition is satisfied if the net momentum is locally perpendicular to the brane; the brane thus carries both momentum along $y$ and angular momentum in the ${\mathsf x}^1$- ${\mathsf x}^2$ plane, which dynamically determines the radius ${\mathfrak a}$.
• Figure 5: Even amounts of spectral flow relate extremal weights in the affine weight diagram of ${SU(2)}$ spin $j'$ (the blue polygon). Allowed weights lie on or within the polygonal bound. Odd amounts of spectral flow map an extremal weight of spin $j'$ to an extremal weight of spin $\frac{{n_5}}{2}-j'$ (the red polygon). The conformal dimensions of the ground states are $h_0=\frac{j'(j'+1)}{{n_5}}$ and $\tilde{h}_0 = \frac{\tilde{j}'(\tilde{j}'+1)}{{n_5}}$, where $\tilde{j}'=\frac{{n_5}}{2}-j'$. The dashed purple curve is the trajectory of the extremal weights under continuous spectral flow.