164 research outputs found

    Single-centered black hole microstate degeneracies from instantons in supergravity

    Get PDF
    We obtain holographic constraints on the microscopic degeneracies of black holes by computing the exact macroscopic quantum entropy using localization, including the effects of string worldsheet instantons in the supergravity effective action. For 14\frac14-BPS black holes in type II string theory on K3×T2K3 \times T^{2}, the constraints can be explicitly checked against expressions for the microscopic BPS counting functions that are known in terms of certain mock modular forms. We find that the effect of including the infinite sum over instantons in the holomorphic prepotential of the supergravity leads to a sum over Bessel functions with successively sub-leading arguments as in the Rademacher expansion of Jacobi forms -- but begins to disagree with such a structure near an order where the mock modular nature becomes relevant. This leads to a systematic method to recover the polar terms of the microscopic degeneracies from the degeneracy of instantons (the Gromov-Witten invariants). We check explicitly that our formula agrees with the known microscopic answer for the first seven values of the magnetic charge invariant.Comment: 32 pages, comments added in v2, submitted to JHE

    On the positivity of black hole degeneracies in string theory

    Full text link
    Certain helicity trace indices of charged states in N=4 and N=8 superstring theory have been computed exactly using their explicit weakly coupled microscopic description. These indices are expected to count the exact quantum degeneracies of black holes carrying the same charges. In order for this interpretation to be consistent, these indices should be positive integers. We prove this positivity property for a class of four/five dimensional black holes in type II string theory compactified on T^6/T^5 and on K3 \times T^2/S^1. The proof relies on the mock modular properties of the corresponding generating functions.Comment: v2: Typos correcte

    Twisting and localization in supergravity: equivariant cohomology of BPS black holes

    Full text link
    We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in arxiv:1806.03690. The gravitational functional integral localizes onto the cohomology of a global supercharge QeqQ_\text{eq}, obeying Qeq2=HQ_\text{eq}^2=H, where HH is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N=2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the QeqVQ_\text{eq} \mathcal{V} deformation operator for the off-shell fluctuations of the Weyl multiplet around the AdS2×S2AdS_2 \times S^2 saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy.Comment: V2: subsection 4.3 added, typo corrected, accepted version in JHEP; V3: typos correcte

    Quantum black hole entropy and the holomorphic prepotential of N=2 supergravity

    Get PDF
    Supersymmetric terms in the effective action of N=2 supergravity in four dimensions are generically classified into chiral-superspace integrals and full-superspace integrals. For a theory of N=2 vector multiplets coupled to supergravity, a special class of couplings is given by chiral-superspace integrals that are governed by a holomorphic prepotential function. The quantum entropy of BPS black holes in such theories depends on the prepotential according to a known integral formula. We show, using techniques of localization, that a large class of full-superspace integrals in the effective action of N=2 supergravity do not contribute to the quantum entropy of BPS black holes at any level in the derivative expansion. Our work extends similar results for semi-classical supersymmetric black hole entropy, and goes towards providing an explanation of why the prepotential terms capture the exact microscopic quantum black hole entropy.Comment: 22 page

    Functional determinants, index theorems, and exact quantum black hole entropy

    Get PDF
    The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the QVQ\mathcal{V} operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around QQ-invariant off-shell configurations in four-dimensional N=2\mathcal{N}=2 supergravity with AdS2×S2AdS_{2} \times S^{2} boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in N=2\mathcal{N}=2 supergravity. We explain cancellations concerning 18\frac18-BPS black holes in N=8\mathcal{N}=8 supergravity that were observed in arXiv:1111.1161. We also make comments about the interpretation of a logarithmic term in the topological string partition function in the low energy supergravity theory.Comment: 47 pages; v3 accepted for publication in JHE

    Moonshine in Fivebrane Spacetimes

    Get PDF
    We consider type II superstring theory on K3×S1×R1,4K3 \times S^1 \times \mathbb{R}^{1,4} and study perturbative BPS states in the near-horizon background of two Neveu-Schwarz fivebranes whose world-volume wraps the K3×S1K3 \times S^1 factor. These states are counted by the spacetime helicity supertrace χ2(τ)\chi_2(\tau) which we evaluate. We find a simple expression for χ2(τ)\chi_2(\tau) in terms of the completion of the mock modular form H(2)(τ)H^{(2)}(\tau) that has appeared recently in studies of the decomposition of the elliptic genus of K3 surfaces into characters of the N=4 superconformal algebra and which manifests a moonshine connection to the Mathieu group M24M_{24}.Comment: 32 page

    Localization & Exact Holography

    Full text link
    We consider the AdS_2/CFT_1 holographic correspondence near the horizon of big four-dimensional black holes preserving four supersymmetries in toroidally compactified Type-II string theory. The boundary partition function of CFT_1 is given by the known quantum degeneracies of these black holes. The bulk partition function is given by a functional integral over string fields in AdS_2. Using recent results on localization we reduce the infinite-dimensional functional integral to a finite number of ordinary integrals over a space of localizing instantons. Under reasonable assumptions about the relevant terms in the effective action, these integrals can be evaluated exactly to obtain a bulk partition function. It precisely reproduces all terms in the exact Rademacher expansion of the boundary partition function as nontrivial functions of charges except for the Kloosterman sum which can in principle follow from an analysis of phases in the background of orbifolded instantons. Our results can be regarded as a step towards proving `exact holography' in that the bulk and boundary partition functions computed independently agree for finite charges. Since the bulk partition function defines the quantum entropy of the black hole, our results enable the evaluation of perturbative as well as nonperturbative quantum corrections to the Bekenstein-Hawking-Wald entropy of these black holes
    • …
    corecore