16,445 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
On Dyson's crank conjecture and the uniform asymptotic behavior of certain inverse theta functions
In this paper we prove a longstanding conjecture by Freeman Dyson concerning
the limiting shape of the crank generating function. We fit this function in a
more general family of inverse theta functions which play a key role in
physics.Comment: Some error bounds have been fixe
BPS Microstates and the Open Topological String Wave Function
It has recently been conjectured that the closed topological string wave
function computes a grand canonical partition function of BPS black hole states
in 4 dimensions: Z_BH=|psi_top|^2. We conjecture that the open topological
string wave function also computes a grand canonical partition function, which
sums over black holes bound to BPS excitations on D-branes wrapping cycles of
the internal Calabi-Yau: Z^open_BPS=|psi^open_top|^2. This conjecture is
verified in the case of Type IIA on a local Calabi-Yau threefold involving a
Riemann surface, where the degeneracies of BPS states can be computed in
q-deformed 2-dimensional Yang-Mills theory.Comment: 50 pages, LaTe
Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
We study three-dimensional Chern-Simons theory with complex gauge group
SL(2,C), which has many interesting connections with three-dimensional quantum
gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence
of a single knotted Wilson loop in an infinite-dimensional representation of
the gauge group, the classical and quantum properties of such theory are
described by an algebraic curve called the A-polynomial of a knot. Using this
approach, we find some new and rather surprising relations between the
A-polynomial, the colored Jones polynomial, and other invariants of hyperbolic
3-manifolds. These relations generalize the volume conjecture and the
Melvin-Morton-Rozansky conjecture, and suggest an intriguing connection between
the SL(2,C) partition function and the colored Jones polynomial.Comment: 67 pages, 13 figures, harvma
On the Mullineux involution for Ariki-Koike algebras
This note is concerned with a natural generalization of the Mullineux
involution for Ariki-Koike algebras. Using a result of Fayers together with
previous results by the authors, we give an efficient algorithm for computing
this generalized Mullineux involution. Our algorithm notably does not involve
the determination of paths in affine crystals.Comment: 17 page
The Gravity Dual of the Ising Model
We evaluate the partition function of three dimensional theories of gravity
in the quantum regime, where the AdS radius is Planck scale and the central
charge is of order one. The contribution from the AdS vacuum sector can - with
certain assumptions - be computed and equals the vacuum character of a minimal
model CFT. The torus partition function is given by a sum over geometries which
is finite and computable. For generic values of Newton's constant G and the AdS
radius L the result has no Hilbert space interpretation, but in certain cases
it agrees with the partition function of a known CFT. For example, the
partition function of pure Einstein gravity with G=3L equals that of the Ising
model, providing evidence that these theories are dual. We also present
somewhat weaker evidence that the 3-state and tricritical Potts models are dual
to pure higher spin theories of gravity based on SL(3) and E_6, respectively.Comment: 42 page
A Holographic View on Matrix Model of Black Hole
We investigate a deformed matrix model proposed by Kazakov et.al. in relation
to Witten's two-dimensional black hole. The existing conjectures assert the
equivalence of the two by mapping each to a deformed c=1 theory called the
sine-Liouville theory. We point out that the matrix theory in question may be
naturally interpreted as a gauged quantum mechanics deformed by insertion of an
exponentiated Wilson loop operator, which gives us more direct and holographic
map between the two sides. The matrix model in the usual scaling limit must
correspond to the bosonic SL(2,R)/U(1) theory in genus expansion but exact in
\alpha'. We successfully test this by computing the Wilson loop expectation
value and comparing it against the bulk computation. For the latter, we employ
the \alpha'-exact geometry proposed by Dijkgraaf, Verlinde, and Verlinde, which
was further advocated by Tseytlin. We close with comments on open problems.Comment: LaTeX, 19 page
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