Related papers: On explicit formulae of LMOV invariants
The superconformal index of quiver gauge theories realized on D3-branes in toric Calabi-Yau cones is investigated. We use the AdS/CFT correspondence and study D3-branes wrapped on supersymmetric cycles. We focus on brane configurations in…
R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. The calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the…
Updated rerefences and introduction. Given a knot in an integer homology sphere, one can construct a family of closed 3-manifolds (parametrized by the positive integers), namely the cyclic branched coverings of the knot. In this paper we…
This is a companion paper of a long work appeared in [1] discussing the super-Chern-Simons theory on supermanifolds. Here, it is emphasized that the BV formalism is naturally formulated using integral forms for any supersymmetric and…
A version of Kirby calculus for spin and framed three-manifolds is given and is used to construct invariants of spin and framed three-manifolds in two situations. The first is ribbon *-categories which possess odd degenerate objects. This…
We consider compactifications of type I supergravity on manifolds with SU(3) structure, in the presence of RR fluxes and magnetized D9-branes, and analyze the generalized Dirac and Laplace-Beltrami operators associated to the D9-brane…
The study of open/closed string duality and large $N$ duality suggests a Gromov-Witten theory for conifolds that sits on the border of both a closed Gromov-Witten theory and an open Gromov-Witten theory. In this work we employ the result of…
We study topological strings on non-commutative resolutions of singular Calabi-Yau threefolds that are double covers of $\mathbb{P}^3$, ramified over determinantal octic surfaces. Using conifold transitions to complete intersections in…
A new infinite class of Chern-Simons theories is presented using brane tilings. The new class reproduces all known cases so far and introduces many new models that are dual to M2 brane theories which probe a toric non-compact CY 4-fold. The…
Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. The tension of the domainwall between the two vacua on the brane, which is the generating function for the open…
In this letter we study topological open string field theory on D--branes in a IIB background given by non compact CY geometries ${\cal O}(n)\oplus{\cal O}(-2-n)$ on $\P1$ with a singular point at which an extra fiber sits. We wrap $N$…
We derive topological string amplitudes on local Calabi-Yau manifolds in terms of polynomials in finitely many generators of special functions. These objects are defined globally in the moduli space and lead to a description of mirror…
Fractional branes added to a large stack of D3-branes at the singularity of a Calabi-Yau cone modify the quiver gauge theory breaking conformal invariance and leading to different kinds of IR behaviors. For toric singularities admitting…
Brane tilings provide the most general framework in string and M-theory for matching toric Calabi-Yau singularities probed by branes with superconformal fixed points of quiver gauge theories. The brane tiling data consists of a bipartite…
We give a precise definition and produce a path-integral computation of the normalized partition function of the abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne-Beilinson formalism,…
We consider the geometric transition and compute the all-genus topological string amplitudes expressed in terms of Hopf link invariants and topological vertices of Chern-Simons gauge theory. We introduce an operator technique of…
We add fundamental flavors to N=2 Chern-Simons-matter theories living on M2 branes probing a Calabi-Yau four-fold singularity. This is dual, in the 't Hooft limit described by IIA string theory, to the introduction of supersymmetric D6…
% A new, formal, non-combinatorial approach to invariants of % three-dimensional manifolds of Reshetikhin, Turaev and % Witten in the framework of non-perturbative topological % quantum Chern-Simons theory, corresponding to an arbitrary %…
The $\hat{Z}$ invariants of three-manifolds introduced by Gukov-Pei-Putrov-Vafa have influenced many areas of mathematics and physics. However, their TQFT structure remains poorly understood. In this work, we develop a framework of…
Motivated by recent developments in the AdS/CFT correspondence, we provide several alternative bulk descriptions of an arbitrary Wilson loop operator in Chern-Simons theory. Wilson loop operators in Chern-Simons theory can be given a…