8 research outputs found
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
Non-Perturbative Topological Strings And Conformal Blocks
We give a non-perturbative completion of a class of closed topological string
theories in terms of building blocks of dual open strings. In the specific case
where the open string is given by a matrix model these blocks correspond to a
choice of integration contour. We then apply this definition to the AGT setup
where the dual matrix model has logarithmic potential and is conjecturally
equivalent to Liouville conformal field theory. By studying the natural
contours of these matrix integrals and their monodromy properties, we propose a
precise map between topological string blocks and Liouville conformal blocks.
Remarkably, this description makes use of the light-cone diagrams of closed
string field theory, where the critical points of the matrix potential
correspond to string interaction points.Comment: 36 page
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
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