6 research outputs found
Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
We survey recent results on quantum corrections to the hypermultiplet moduli
space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or,
equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our
main focus lies on the problem of resumming the infinite series of D-brane and
NS5-brane instantons, using the mathematical machinery of automorphic forms. We
review the proposal that whenever the low-energy theory in D=3 exhibits an
arithmetic "U-duality" symmetry G(Z) the total instanton partition function
arises from a certain unitary automorphic representation of G, whose Fourier
coefficients reproduce the BPS-degeneracies. For D=4, N=2 theories on R^3 x S^1
we argue that the relevant automorphic representation falls in the quaternionic
discrete series of G, and that the partition function can be realized as a
holomorphic section on the twistor space Z over M. We also offer some comments
on the close relation with N=2 wall crossing formulae.Comment: 25 pages, contribution to the proceedings of the workshop "Algebra,
Geometry and Mathematical Physics", Tjarno, Sweden, 25-30 October, 201
Massless black holes and black rings as effective geometries of the D1-D5 system
We compute correlation functions in the AdS/CFT correspondence to study the
emergence of effective spacetime geometries describing complex underlying
microstates. The basic argument is that almost all microstates of fixed charges
lie close to certain "typical" configurations. These give a universal response
to generic probes, which is captured by an emergent geometry. The details of
the microstates can only be observed by atypical probes. We compute two point
functions in typical ground states of the Ramond sector of the D1-D5 CFT, and
compare with bulk two-point functions computed in asymptotically AdS_3
geometries. For large central charge (which leads to a good semiclassical
limit), and sufficiently small time separation, a typical Ramond ground state
of vanishing R-charge has the M=0 BTZ black hole as its effective description.
At large time separation this effective description breaks down. The CFT
correlators we compute take over, and give a response whose details depend on
the microstate. We also discuss typical states with nonzero R-charge, and argue
that the effective geometry should be a singular black ring. Our results
support the argument that a black hole geometry should be understood as an
effective coarse-grained description that accurately describes the results of
certain typical measurements, but breaks down in general.Comment: 47 pages, 4 figures. v2: references added. v3: minor corrections to
Appendix A, references adde
Non-supersymmetric Black Holes and Topological Strings
We study non-supersymmetric, extremal 4 dimensional black holes which arise
upon compactification of type II superstrings on Calabi-Yau threefolds. We
propose a generalization of the OSV conjecture for higher derivative
corrections to the non-supersymmetric black hole entropy, in terms of the one
parameter refinement of topological string introduced by Nekrasov. We also
study the attractor mechanism for non-supersymmetric black holes and show how
the inverse problem of fixing charges in terms of the attractor value of CY
moduli can be explicitly solved.Comment: 47 pages, harvmac. v2: footnote(4) expanded, references adde
Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
In these lecture notes, we review some recent developments on the relation
between the macroscopic entropy of four-dimensional BPS black holes and the
microscopic counting of states, beyond the thermodynamical, large charge limit.
After a brief overview of charged black holes in supergravity and string
theory, we give an extensive introduction to special and very special geometry,
attractor flows and topological string theory, including holomorphic anomalies.
We then expose the Ooguri-Strominger-Vafa (OSV) conjecture which relates
microscopic degeneracies to the topological string amplitude, and review
precision tests of this formula on ``small'' black holes. Finally, motivated by
a holographic interpretation of the OSV conjecture, we give a systematic
approach to the radial quantization of BPS black holes (i.e. quantum
attractors). This suggests the existence of a one-parameter generalization of
the topological string amplitude, and provides a general framework for
constructing automorphic partition functions for black hole degeneracies in
theories with sufficient degree of symmetry.Comment: 103 pages, 8 figures, 21 exercises, uses JHEP3.cls; v5: important
upgrade, prepared for the proceedings of Frascati School on Attractor
Mechanism; Sec 7 was largely rewritten to incorporate recent progress; more
figures, more refs, and minor changes in abstract and introductio