19 research outputs found
S-duality and Topological Strings
In this paper we show how S-duality of type IIB superstrings leads to an
S-duality relating A and B model topological strings on the same Calabi-Yau as
had been conjectured recently: D-instantons of the B-model correspond to
A-model perturbative amplitudes and D-instantons of the A-model capture
perturbative B-model amplitudes.
Moreover this confirms the existence of new branes in the two models.
As an application we explain the recent results concerning A-model
topological strings on Calabi-Yau and its equivalence to the statistical
mechanical model of melting crystal.Comment: 13 page
Link Homologies and the Refined Topological Vertex
We establish a direct map between refined topological vertex and sl(N)
homological invariants of the of Hopf link, which include Khovanov-Rozansky
homology as a special case. This relation provides an exact answer for
homological invariants of the of Hopf link, whose components are colored by
arbitrary representations of sl(N). At present, the mathematical formulation of
such homological invariants is available only for the fundamental
representation (the Khovanov-Rozansky theory) and the relation with the refined
topological vertex should be useful for categorifying quantum group invariants
associated with other representations (R_1, R_2). Our result is a first direct
verification of a series of conjectures which identifies link homologies with
the Hilbert space of BPS states in the presence of branes, where the physical
interpretation of gradings is in terms of charges of the branes ending on
Lagrangian branes.Comment: 38 pages, 5 figure
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
Refined topological amplitudes in N=1 flux compactification
We study the implication of refined topological string amplitudes in the
supersymmetric N=1 flux compactification. They generate higher derivative
couplings among the vector multiplets and graviphoton with generically
non-holomorphic moduli dependence. For a particular term, we can compute them
by assuming the geometric engineering. We claim that the Dijkgraaf-Vafa large N
matrix model with the beta-ensemble measure directly computes the higher
derivative corrections to the supersymmetric effective action of the
supersymmetric N=1$ gauge theory.Comment: 16 pages, v2: reference adde
Gravitational corrections in supersymmetric gauge theory and matrix models
Gravitational corrections in N=1 and N=2 supersymmetric gauge theories are
obtained from topological string amplitudes. We show how they are recovered in
matrix model computations. This provides a test of the proposal by Dijkgraaf
and Vafa beyond the planar limit. Both, matrix model and topological string
theory, are used to check a conjecture of Nekrasov concerning these
gravitational couplings in Seiberg-Witten theory. Our analysis is performed for
those gauge theories which are related to the cubic matrix model, i.e. pure
SU(2) Seiberg-Witten theory and N=2 U(N) SYM broken to N=1 via a cubic
superpotential. We outline the computation of the topological amplitudes for
the local Calabi-Yau manifolds which are relevant for these two cases.Comment: 27 pages, one eps figur
Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces
We perform a study of the moduli space of framed torsion-free sheaves on
Hirzebruch surfaces by using localization techniques. We discuss some general
properties of this moduli space by studying it in the framework of
Huybrechts-Lehn theory of framed modules. We classify the fixed points under a
toric action on the moduli space, and use this to compute the Poincare
polynomial of the latter. This will imply that the moduli spaces we are
considering are irreducible. We also consider fractional first Chern classes,
which means that we are extending our computation to a stacky deformation of a
Hirzebruch surface. From the physical viewpoint, our results provide the
partition function of N=4 Vafa-Witten theory on total spaces of line bundles on
P1, which is relevant in black hole entropy counting problems according to a
conjecture due to Ooguri, Strominger and Vafa.Comment: 17 pages. This submission supersedes arXiv:0809.0155 [math.AG
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
Five-dimensional gauge theory and compactification on a torus
We study five-dimensional minimally supersymmetric gauge theory compactified
on a torus down to three dimensions, and its embedding into string/M-theory
using geometric engineering. The moduli space on the Coulomb branch is
hyperkaehler equipped with a metric with modular transformation properties. We
determine the one-loop corrections to the metric and show that they can be
interpreted as worldsheet and D1-brane instantons in type IIB string theory.
Furthermore, we analyze instanton corrections coming from the solitonic BPS
magnetic string wrapped over the torus. In particular, we show how to compute
the path-integral for the zero-modes from the partition function of the M5
brane, or, using a 2d/4d correspondence, from the partition function of N=4 SYM
theory on a Hirzebruch surface.Comment: 30 pages, 2 figures; v2: typos corrected, added references, JHEP
versio
M5-branes, toric diagrams and gauge theory duality
In this article we explore the duality between the low energy effective
theory of five-dimensional N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge
theories compactified on S^1. The theories we study are the five-dimensional
uplifts of four-dimensional superconformal linear quivers. We study this
duality by comparing the Seiberg-Witten curves and the Nekrasov partition
functions of the two dual theories. The Seiberg-Witten curves are obtained by
minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov
partition functions are computed using topological string theory. The result of
our study is a map between the gauge theory parameters, i.e., Coulomb moduli,
masses and UV coupling constants, of the two dual theories. Apart from the
obvious physical interest, this duality also leads to compelling mathematical
identities. Through the AGTW conjecture these five-dimentional gauge theories
are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The
duality we study implies the relations between Liouville and Toda correlation
functions through the map we derive.Comment: 58 pages, 17 figures; v2: minor corrections, references adde
3d-3d Correspondence Revisited
In fivebrane compactifications on 3-manifolds, we point out the importance of
all flat connections in the proper definition of the effective 3d N=2 theory.
The Lagrangians of some theories with the desired properties can be constructed
with the help of homological knot invariants that categorify colored Jones
polynomials. Higgsing the full 3d theories constructed this way recovers
theories found previously by Dimofte-Gaiotto-Gukov. We also consider the
cutting and gluing of 3-manifolds along smooth boundaries and the role played
by all flat connections in this operation.Comment: 43 pages + 1 appendix, 6 figures Version 2: new appendix on flat
connections in the 3d-3d correspondenc