D1-D5-P microstates at the cap

Abstract

The geometries describing D1-D5-P bound states in string theory have three regions: flat asymptotics, an anti-de Sitter throat, and a 'cap' region at the bottom of the throat. We identify the CFT description of a known class of supersymmetric D1-D5-P microstate geometries which describe degrees of freedom in the cap region. The class includes both regular solutions and solutions with conical defects, and generalizes configurations with known CFT descriptions: a parameter related to spectral flow in the CFT is generalized from integer to fractional values. We provide strong evidence for this identification by comparing the massless scalar excitation spectrum between gravity and CFT and finding exact agreement

Non-BPS multi-bubble microstate geometries

“…A similar analysis to the above can be performed in the five-dimensional bubbling black hole microstate solutions [12,[25][26][27][28][29][30], where one can find that each additional GibbonsHawking center gives rise to an additional two-cycle.…”

“…These microstate geometries have no horizon or singularities, but have nontrivial topology supported by fluxes, such that the solutions have the mass and charges of a black hole. For large supersymmetric black holes a very large number of such microstate geometries have been constructed (see for example [12,[25][26][27][28][29][30]) and their entropy has been argued to reproduce the growth with charges of the Bekenstein-Hawking entropy of the black hole [31]. Similarly, one can also construct microstate geometries for extremal non-BPS black holes by starting from almost-BPS multi-center solutions [32] and performing certain duality transformations [33].…”

Instability of supersymmetric microstate geometries

“…D is proportional to α ν 1 ; in the decoupling limit ν 1 → 1 and α → 0 so we see that the imaginary part vanishes in this limit, as expected. The real part reduces to the expression for certain normal modes in AdS 3 × S 3 , as given in [55].…”

Hair-brane ideas on the horizon

“…Indeed, these light degrees of freedom are typically branes wrapping a vanishing cycle [20,21]. The differences here are that there is a macroscopic number of light brane states associated to the relevant cycles, and that the proper spatial volume of 11 When gcd(q, k 3 ) = r > 1, the ambient 6d spacetime has a Zr orbifold singularity at the corresponding pole [52].…”

“…Indeed, a proposal for the "missing" entropy of geometrical solutions has been explored in [8,9,58]. But even if microstate geometries turn out not to be the main contributors to the density of states, the macroscopic entropy already found from geometrical constructions [18], the matching of certain low-energy black hole emission spectra [59][60][61], the possibility of perturbing them slightly to become black holes, and the increasingly precise duality map (see for example [9,10,52,62]) make these objects particularly worthy of further study.…”