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.
Exact results for the BPS index are known for a class of BPS dyons in type II string theory compactified on a six dimensional torus. In this paper we set up the problem of counting the same BPS states in a duality frame in which the states carry only Ramond-Ramond charges. We explicitly count the number of states carrying the lowest possible charges and find agreement with the result obtained in other duality frames. Furthermore, we find that after factoring out the supermultiplet structure, each of these states carry zero angular momentum. This is in agreement with the prediction obtained from a representation of these states as supersymmetric black holes.
In quiver quantum mechanics with 4 supercharges, supersymmetric ground states are known to be in one-to-one correspondence with Dolbeault cohomology classes on the moduli space of stable quiver representations. Using supersymmetric localization, the refined Witten index can be expressed as a residue integral with a specific contour prescription, originally due to Jeffrey and Kirwan, depending on the stability parameters. On the other hand, the physical picture of quiver quantum mechanics describing interactions of BPS black holes predicts that the refined Witten index of a non-Abelian quiver can be expressed as a sum of indices for Abelian quivers, weighted by 'single-centered invariants'. In the case of quivers without oriented loops, we show that this decomposition naturally arises from the residue formula, as a consequence of applying the Cauchy-Bose identity to the vector multiplet contributions. For quivers with loops, the same procedure produces a natural decomposition of the single-centered invariants, which remains to be elucidated. In the process, we clarify some under-appreciated aspects of the localization formula. Part of the results reported herein have been obtained by implementing the Jeffrey-Kirwan residue formula in a public Mathematica code.
The Sachdev-Ye-Kitaev is a quantum mechanical model of N Majorana fermions which displays a number of appealing features -solvability in the strong coupling regime, nearconformal invariance and maximal chaos -which make it a suitable model for black holes in the context of the AdS/CFT holography. In this paper we show for the colored SYK model and several of its tensor model cousins that the next-to-leading order in the N expansion preserves the conformal invariance of the 2-point function in the strong coupling regime, up to the contribution of the Goldstone bosons leading to the spontaneous breaking of the symmetry and which are already seen in the leading order 4-point function. We also comment on the composite field approach for computing correlation functions in colored tensor models.
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