12 research outputs found
Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
We review and extend recent attempts to find a precise relation between
extremal black hole entropy and degeneracy of microstates using AdS_2/CFT_1
correspondence. Our analysis leads to a specific relation between degeneracy of
black hole microstates and an appropriately defined partition function of
string theory on the near horizon geometry, -- named the quantum entropy
function. In the classical limit this reduces to the usual relation between
statistical entropy and Wald entropy.Comment: LaTeX file, 27 pages, A modified and extended version of the talk
given at Strings 200
How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?
Single centered supersymmetric black holes in four dimensions have
spherically symmetric horizon and hence carry zero angular momentum. This leads
to a specific sign of the helicity trace index associated with these black
holes. Since the latter are given by the Fourier expansion coefficients of
appropriate meromorphic modular forms of Sp(2,Z) or its subgroup, we are led to
a specific prediction for the signs of a subset of these Fourier coefficients
which represent contributions from single centered black holes only. We
explicitly test these predictions for the modular forms which compute the index
of quarter BPS black holes in heterotic string theory on T^6, as well as in Z_N
CHL models for N=2,3,5,7.Comment: LaTeX file, 17 pages, 1 figur
Dying Dyons Don't Count
The dyonic 1/4-BPS states in 4D string theory with N=4 spacetime
supersymmetry are counted by a Siegel modular form. The pole structure of the
modular form leads to a contour dependence in the counting formula obscuring
its duality invariance. We exhibit the relation between this ambiguity and the
(dis-)appearance of bound states of 1/2-BPS configurations. Using this insight
we propose a precise moduli-dependent contour prescription for the counting
formula. We then show that the degeneracies are duality-invariant and are
correctly adjusted at the walls of marginal stability to account for the
(dis-)appearance of the two-centered bound states. Especially, for large black
holes none of these bound states exists at the attractor point and none of
these ambiguous poles contributes to the counting formula. Using this fact we
also propose a second, moduli-independent contour which counts the "immortal
dyons" that are stable everywhere.Comment: 27 pages, 2 figures; one minus sign correcte
Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions
We show that various holomorphic quantities in supersymmetric gauge theories
can be conveniently computed by configurations of D4-branes and D6-branes.
These D-branes intersect along a Riemann surface that is described by a
holomorphic curve in a complex surface. The resulting I-brane carries
two-dimensional chiral fermions on its world-volume. This system can be mapped
directly to the topological string on a large class of non-compact Calabi-Yau
manifolds. Inclusion of the string coupling constant corresponds to turning on
a constant B-field on the complex surface, which makes this space
non-commutative. Including all string loop corrections the free fermion theory
is elegantly formulated in terms of holonomic D-modules that replace the
classical holomorphic curve in the quantum case.Comment: 67 pages, 6 figure
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