Little strings, long strings, and fuzzballs

Abstract

At high energy densities, fivebranes are populated by a Hagedorn phase of so-called little strings, whose statistical mechanics underlies black fivebrane thermodynamics. A particular limit of this phase yields BTZ black holes in AdS 3 , leading us to the idea that in this context fuzzballs and highly excited little strings are one and the same. We explore these ideas through an analysis of D-brane probes of fivebrane supertube backgrounds. String theory dynamics on these backgrounds is described by an exactly solvable null-gauged WZW model. We develop the formalism of null gauging on worldsheets with boundaries, and find that D-branes wrapping topology at the bottom of the supertube throat are avatars of the "long string" structure that dominates the thermodynamics of the black hole regime, appearing here as excitations of supertubes lying near but slightly outside the black hole regime.

Stringy structure at the BPS bound

“…In the geometrical description as a null-gauged sigma model on a Lunin-Mathur background, D-branes ending on the fivebranes localize the fivebranes at discrete (relative) positions determined by the quantization of worldvolume JHEP12(2020)135 flux. This phenomenon was first seen in our analysis of D-branes in the null-gauged WZW model in [22]; we verify that this structure continues to hold in the deformation of the circular fivebrane array to an elliptical array, and propose that it holds in general Lunin-Mathur geometries. On the Landau-Ginsburg side, the fivebrane locations are directly coded by the zeros of the holomorphic worldvolume superpotential; we exhibit a precise map between the parameters of the superpotential and those that determine the shape profile F I (v) of the supertube source in the supergravity description.…”

“…Recent work on null-gauged sigma models for fivebrane backgrounds has focused on cosets where the "upstairs" (10+2)-dimensional spacetime contains global AdS 3 × S 3 [14,21,22]. The simplest example of the family of models that can be obtained in this way is the Coulomb branch circular array of fivebranes [11,12,14], where the isometry that is gauged corresponds to the Killing vectors in eq.…”

“…In recent work, the gauging of null isometries of nonlinear sigma models has been applied to study configurations of fivebranes, as well as NS5-F1 and NS5-P supertubes, that are based on circular source profiles [14,21,22]. The null gauging of the SL(2, R)×SU (2) WZW model is the simplest example, one in which the current algebra symmetries enable the exact solution of the worldsheet theory.…”

Pure-Higgs states from the Lefschetz-Sommese theorem

“…Footnote a similar gap has recently been observed in[29] in a closely related context 6. The be precise, in one of the chambers that we consider we face a technical problem in the computation of the holomorphic Euler number via methods of algebraic topology, there we resort to the Abelianization technique of[11].…”

Instant folded strings and black fivebranes

“…[28], for a review), and which appear in the microstates entropy counting done in [29] and more recently in e.g. [30], in terms of strings living on the fivebrane.…”