164 research outputs found
Single-centered black hole microstate degeneracies from instantons in supergravity
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 -BPS black holes in type II string theory on , 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
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
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
, obeying , where 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 deformation operator for
the off-shell fluctuations of the Weyl multiplet around the
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
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
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 operator). We compute
the fluctuation determinant for vector multiplets and hyper multiplets around
-invariant off-shell configurations in four-dimensional
supergravity with 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 supergravity. We explain cancellations concerning
-BPS black holes in 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
We consider type II superstring theory on and study perturbative BPS states in the near-horizon
background of two Neveu-Schwarz fivebranes whose world-volume wraps the factor. These states are counted by the spacetime helicity
supertrace which we evaluate. We find a simple expression for
in terms of the completion of the mock modular form
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
.Comment: 32 page
Localization & Exact Holography
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
- …