Related papers: Refined Wall-Crossing, Free Fermions and Crystal M…
We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli…
We consider two different physical systems for which the basis of the Hilbert space can be parametrized by Young diagrams: free complex fermions and the phase model of strongly correlated bosons. Both systems have natural, well-known…
We introduce a class of new algebras, the shifted quiver Yangians, as the BPS algebras for type IIA string theory on general toric Calabi-Yau three-folds. We construct representations of the shifted quiver Yangian from general subcrystals…
A refinement of the stable pair invariants of Pandharipande and Thomas for non-compact Calabi-Yau spaces is introduced based on a virtual Bialynicki-Birula decomposition with respect to a C* action on the stable pair moduli space, or…
We introduce a new wall-crossing formula which combines and generalizes the Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d systems respectively. This 2d-4d wall-crossing formula governs the wall-crossing of BPS…
It was known that the ABJM matrix model is dual to the topological string theory on a Calabi-Yau manifold. Using this relation it was possible to write down the exact instanton expansion of the partition function of the ABJM matrix model.…
We consider the spectrum of open strings for non-BPS D-brane configuration in type II string theory on a Calabi-Yau threefold. In general, there is no degeneracy between bosonic and fermionic states. However we find special values for the…
We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric Calabi-Yau threefold, the D-branes wrapping holomorphic…
We investigate BPS states in 4d N=4 supersymmetric Yang-Mills theory and the corresponding (p, q) string networks in Type IIB string theory. We propose a new interpretation of the algebra of line operators in this theory as a tensor product…
Motivated by studies on 4d black holes and q-deformed 2d Yang Mills theory, and borrowing ideas from compact geometry of the blowing up of affine ADE singularities, we build a class of local Calabi-Yau threefolds (CY^{3}) extending the…
We study the topological B-model on a deformed $\Z_2$ orbifolded conifold by investigating variation of complex structures via quantum Kodaira-Spencer theories. The fermionic/brane formulation together with systematic utilization of…
We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main…
Three-manifolds can be obtained through surgery of framed links in $S^3$. We study the meaning of surgery procedures in the context of topological strings. We obtain U(N) three-manifold invariants from U(N) framed link invariants in…
We formulate large $N$ duality of $\mathrm{U}(N)$ refined Chern-Simons theory with a torus knot/link in $S^3$. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string…
It is known that the large N expansion of the partition function in ABJM theory on a three-sphere is completely determined by the topological string on local Hirzebruch surface F_0. In this note, we investigate the ABJM partition function…
The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related…
We present the partition function of Chern-Simons theory with the exceptional gauge group on three-sphere in the form of a partition function of the refined closed topological string with relation $2\tau=g_s(1-b) $ between single K\"ahler…
We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper arXiv:0811.2801. In particular, the thermodynamic partition…
In a previous paper, we presented a matrix model reproducing the topological string partition function on an arbitrary given toric Calabi-Yau manifold. Here, we study the spectral curve of our matrix model and thus derive, upon imposing…
The number of BPS bound states of D-branes on a Calabi-Yau manifold depends on two sets of data, the BPS charges and the stability conditions. For D0 and D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold X, both are…