Do all BPS black hole microstates carry zero angular momentum?

Abstract

From the analysis of the near horizon geometry and supersymmetry algebra it has been argued that all the microstates of single centered BPS black holes with four unbroken supersymmetries carry zero angular momentum in the region of the moduli space where the black hole description is valid. A stronger form of the conjecture would be that the result holds for any sufficiently generic point in the moduli space. In this paper we set out to test this conjecture for a class of black hole microstates in type II string theory on T 6 , represented by four stacks of D-branes wrapped on various cycles of T 6 . For this system the above conjecture translates to the statement that the moduli space of classical vacua must be a collection of points. Explicit analysis of systems carrying a low number of D-branes supports this conjecture.

The full space of BPS multicenter states with pure D-brane charges

“…So it is not very clear whether to count this state as pure-Higgs or not. We have however showed that each of the 12 quivers has only one ground state which hopefully leave the total of 12 states as expected from [10,11].…”

“…Supersymmetry allows for, but does not determine, other interactions preserving 4 supercharges, denoted as L N =1 . In [10,11], the authors considered few terms of L N =1 and argued that higher order terms, although certainly present, do not affect the index computation.…”

“…Such black holes are also known to carry zero angular momentum. In view of these facts, the authors of [11] conjectured that at a generic point of moduli space, all microstates of a single-center BPS black hole carry zero angular momentum.…”

More on microstate geometries of 4d black holes

“…The remaining entries are determined by the conditions that the sum along rows and columns of the matrix k I i should vanish. The number 12 matches the number of apostles and the degeneracy of four-charge black hole micro-states with the minimal unit of charge P 0 = Q I = 1 [36]! Moreover the solutions satisfy 3 I=1 k I 2 = m 2 = 0 and therefore according to (2.19) and (2.20) they carry zero angular momentum and admit a microscopic description in terms of orthogonal intersecting D3-branes along the lines of [32].…”

“…Higher multipole modes are generated by extra insertions of untwisted open string fields on the disk boundaries. The micro-state multiplicities can be computed by counting open strings in the D1-D5-p-KK system or vacua in the quantum mechanics associated to the D0-D2-D4-D6 realisation of the black hole [36,37].…”