Related papers: A Note on q-Deformed Two-Dimensional Yang-Mills an…
The topological string partition function for the neighbourhood of three spheres meeting at one point in a Calabi-Yau threefold, the so-called 'closed topological vertex', is shown to be reproduced by a simple Calabi-Yau crystal model which…
These notes are a writeup of lectures given at the twelfth Oporto meeting on ``Geometry, Topology, and Physics,'' and at the Adelaide workshop ``Strings and Mathematics 2003,'' primarily geared towards a physics audience. We review current…
In this paper, we review the construction and large $N$ study of the continuous two-dimensional Yang--Mills theory with gauge group $\mathrm{U}(N)$ through probability, combinatorics and representation theory. In the first part, we define…
We obtain exact results in \alpha' for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five dimensional gauge theories. The toric Calabi-Yau's that we…
We show that refined Chern-Simons theory and large N duality can be used to study the refined topological string with and without branes. We derive the refined topological vertex of hep-th/0701156 and hep-th/0502061 from a link invariant of…
We consider freely acting orbifold compactifications, which interpolate in two possible decompactification limits between the supersymmetric type II string and the non-supersymmetric type 0 string. In particular we discuss how D-branes are…
This is the first of a series of three papers on open string field theories based on Witten star product deformed with a gauge invariant open/closed coupling. This deformation is a tree-level tadpole which destabilizes the initial…
We calculate the partition function of the $SU(N)$ ( and $U(N)$) generalized $YM_2$ theory defined on an arbitrary Riemann surface. The result which is expressed as a sum over irreducible representations generalizes the Rusakov formula for…
D-brane configurations containing fundamental strings are constructed as classical solutions of Yang-Mills theory. The fundamental strings in these systems stretch between D-branes. In the case of D1-branes, this construction gives smooth…
We construct a novel orientifold of type IIB string theory that breaks all supersymmetries. It is a closed string theory without open sector and it can be understood as a Scherk-Schwarz deformation in which supersymmetry is restored at…
We study certain properties of six-dimensional tensionless E-strings (arising from zero size $E_8$ instantons). In particular we show that $n$ E-strings form a bound string which carries an $E_8$ level $n$ current algebra as well as a…
This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a…
We derive the analog of the large $N$ Gross-Taylor holomorphic string expansion for the refinement of $q$-deformed $U(N)$ Yang-Mills theory on a compact oriented Riemann surface. The derivation combines Schur-Weyl duality for quantum groups…
We study the topological string partition function of a class of toric, double elliptically fibered Calabi-Yau threefolds $X_{N,M}$ at a generic point in the K\"ahler moduli space. These manifolds engineer little string theories in five…
We construct a supermanifold ST which turns to be an open subset of a superquadric Q(5|6) subset P^{3|3}times P^{3|3}. The Dolbeault algebra Omega^{0*}(ST) is quasiisomorphic to N=3, D=4 YM algebra in Batalin-Vilkovisky formulation. We…
In this paper we construct complete macroscopic operators in two dimensional type 0 string theory. They represent D-branes localized in the time direction. We give another equivalent description of them as deformed Fermi surfaces. We also…
We show that a general solution to the extended holomorphic anomaly equations for the open topological string on D-branes in a Calabi-Yau manifold, recently written down by Walcher in arXiv:0705.4098, is obtained from the general solution…
In this work we verify consistency of refined topological string theory from several perspectives. First, we advance the method of computing refined open amplitudes by means of geometric transitions. Based on such computations we show that…
The integrable structure of open--closed string theories in the $(p,q)$ conformal minimal model backgrounds is presented. The relation between the $\tau$--function of the closed string theory and that of the open--closed string theory is…
We study the q-deformed oscillator algebra acting on the wavefunctions of non-compact D-branes in the topological string on conifold. We find that the mirror B-model curve of conifold appears from the commutation relation of the q-deformed…