9 research outputs found
The Refined Topological Vertex
We define a refined topological vertex which depends in addition on a
parameter, which physically corresponds to extending the self-dual graviphoton
field strength to a more general configuration. Using this refined topological
vertex we compute, using geometric engineering, a two-parameter (equivariant)
instanton expansion of gauge theories which reproduce the results of Nekrasov.
The refined vertex is also expected to be related to Khovanov knot invariants.Comment: 70 Pages, 23 Figure
Instantons and the 5D U(1) gauge theory with extra adjoint
In this paper we compute the partition function of 5D supersymmetric U(1)
gauge theory with extra adjoint matter in general -background. It is
well known that such partition functions encode very rich topological
information. We show in particular that unlike the case with no extra matter,
the partition function with extra adjoint at some special values of the
parameters directly reproduces the generating function for the Poincare
polynomial of the moduli space of instantons. Comparing our results with those
recently obtained by Iqbal et. al., who used the refined topological vertex
method, we present our comments on apparent discrepancies.Comment: 9 page
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
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
G2 Hitchin functionals at one loop
We consider the quantization of the effective target space description of
topological M-theory in terms of the Hitchin functional whose critical points
describe seven-manifolds with G2 structure. The one-loop partition function for
this theory is calculated and an extended version of it, that is related to
generalized G2 geometry, is compared with the topological G2 string. We relate
the reduction of the effective action for the extended G2 theory to the Hitchin
functional description of the topological string in six dimensions. The
dependence of the partition functions on the choice of background G2 metric is
also determined.Comment: 58 pages, LaTeX; v2: Acknowledgments adde
Matrix Models, Geometric Engineering and Elliptic Genera
We compute the prepotential of N=2 supersymmetric gauge theories in four
dimensions obtained by toroidal compactifications of gauge theories from 6
dimensions, as a function of Kahler and complex moduli of T^2. We use three
different methods to obtain this: matrix models, geometric engineering and
instanton calculus. Matrix model approach involves summing up planar diagrams
of an associated gauge theory on T^2. Geometric engineering involves
considering F-theory on elliptic threefolds, and using topological vertex to
sum up worldsheet instantons. Instanton calculus involves computation of
elliptic genera of instanton moduli spaces on R^4. We study the
compactifications of N=2* theory in detail and establish equivalence of all
these three approaches in this case. As a byproduct we geometrically engineer
theories with massive adjoint fields. As one application, we show that the
moduli space of mass deformed M5-branes wrapped on T^2 combines the Kahler and
complex moduli of T^2 and the mass parameter into the period matrix of a genus
2 curve.Comment: 90 pages, Late
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
Challenges of beta-deformation
A brief review of problems, arising in the study of the beta-deformation,
also known as "refinement", which appears as a central difficult element in a
number of related modern subjects: beta \neq 1 is responsible for deviation
from free fermions in 2d conformal theories, from symmetric omega-backgrounds
with epsilon_2 = - epsilon_1 in instanton sums in 4d SYM theories, from
eigenvalue matrix models to beta-ensembles, from HOMFLY to super-polynomials in
Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras
etc. The main attention is paid to the context of AGT relation and its possible
generalizations.Comment: 20 page