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Wall Crossing from Boltzmann Black Hole Halos
, 2011
"... A key question in the study of N = 2 supersymmetric string or field theories is to understand the decay of BPS bound states across walls of marginal stability in the space of parameters or vacua. By representing the potentially unstable bound states as multicentered black hole solutions in N = 2 s ..."
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A key question in the study of N = 2 supersymmetric string or field theories is to understand the decay of BPS bound states across walls of marginal stability in the space of parameters or vacua. By representing the potentially unstable bound states as multicentered black hole solutions in N = 2 supergravity, we provide two fully general and explicit formulæ for the change in the (refined) index across the wall. The first, “Higgs branch” formula relies on Reineke’s results for invariants of quivers without oriented loops, specialized to the Abelian case. The second, “Coulomb branch ” formula results from evaluating the symplectic volume of the classical phase space of multicentered solutions by localization. We provide extensive evidence that these new formulæ agree with each other and with the mathematical results of Kontsevich and Soibelman (KS) and Joyce and Song (JS). The main physical insight behind our results is that the BoseFermi statistics of individual black holes participating in the bound state can be traded for MaxwellBoltzmann statistics, provided the (integer) index Ω(γ) of the internal degrees of freedom carried by each black hole is replaced by an effective (rational) index Ω̄(γ) = mγ Ω(γ/m)/m 2. A similar map also exists for the refined index. This observation provides a physical rationale for the appearance of the rational DonaldsonThomas invariant Ω̄(γ) in the works of KS and JS. The simplicity of the wallcrossing formula for rational invariants allows us to generalize the “semiprimitive wallcrossing formula ” to arbitrary decays of the type γ →Mγ1 +Nγ2 with M = 2, 3.
Nonperturbative black hole entropy and Kloosterman sums,” arXiv:1404.0033 [hepth
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On stable higher spin states in heterotic string theories
 JHEP 1103 (2011) 051, arXiv:1010.1177 [hepth
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2011 String Theory: Perspectives over the last 25 years Class
 Quantum Grav
"... Abstract: This article provides some historical background and then reviews developments in string theory over the last twentyfive years or so. Both perturbative and nonperturbative approaches to string theory are surveyed and their impact on how we view quantum gravity is analysed. * * Invited r ..."
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Abstract: This article provides some historical background and then reviews developments in string theory over the last twentyfive years or so. Both perturbative and nonperturbative approaches to string theory are surveyed and their impact on how we view quantum gravity is analysed. * * Invited review, published in Classical and Quantum Gravity, 28 (2011) 153001. The INSPIRE database continues to show an incorrect title for the published version, despite my best efforts.
Which AdS3 configurations contribute to the SCFT2 elliptic genus?
, 2011
"... According to the AdS/CFT duality, the superconformal index of a superconformal field theory should have an AdS interpretation as a Euclidean functional integral with periodic boundary conditions on the fermions. Unlike the thermal case, the Euclidean continuation of the supersymmetric AdS black ho ..."
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According to the AdS/CFT duality, the superconformal index of a superconformal field theory should have an AdS interpretation as a Euclidean functional integral with periodic boundary conditions on the fermions. Unlike the thermal case, the Euclidean continuation of the supersymmetric AdS black hole does not smoothly fill in these boundary conditions, leading us to ask the title question. In the context of AdS3/CFT2, we show using supersymmetric localization that the gravitational functional integral for the elliptic genus localizes onto asymptotically AdS3 configurations that are annihilated by a certain supercharge, in the relevant offshell supergravity theory. For (0, 4) superconformal field theories, we find such a localizing configuration in the 5d N = 2 offshell supergravity theory that is asymptotically AdS3×S2. This configuration interpolates smoothly between the supersymmetric BTZ black hole in the interior and a constant gauge field configuration at the boundary, thus smoothly filling in the (++) boundary conditions for spinors on the boundary torus. It has an action equal to the supersymmetric BTZ black hole, holomorphic in the complex structure τ of the boundary torus. Our results have interesting implications for the black hole Farey tail in AdS3, as well as for higher dimensional AdS theories.