15310503
Homological mirror symmetry for toric orbifolds of toric del Pezzo surfaces
Abstract We formulate a conjecture which describes the Fukaya category of an exact Lefschetz fibration defined by a Laurent polynomial in two variables in terms of a pair consisting of a consistent dimer model and a perfect matching on it. We prove this conjecture in some cases, and obtain homological mirror symmetry for quotient stacks of toric del Pezzo surfaces by finite subgroups of the torus as a corollary.
120626368
COMMENTS ON ORIENTIFOLD OF BRANE TILINGS
The relation between brane charge conservation law in fivebrane system described by orientifolded brane tilings and the gauge anomaly cancellation in the corresponding gauge theories is summarized.
10042817
Crystal Melting and Toric Calabi-Yau Manifolds
We construct a statistical model of crystal melting to count BPS bound states of D0 and D2 branes on a single D6 brane wrapping an arbitrary toric Calabi-Yau threefold. The three-dimensional crystalline structure is determined by the quiver diagram and the brane tiling which characterize the low energy effective theory of D branes. The crystal is composed of atoms of different colors, each of which corresponds to a node of the quiver diagram, and the chemical bond is dictated by the arrows of the quiver diagram. BPS states are constructed by removing atoms from the crystal. This generalizes the earlier results on the BPS state counting to an arbitrary non-compact toric Calabi-Yau manifold. We point out that a proper understanding of the relation between the topological string theory and the crystal melting involves the wall crossing in the Donaldson-Thomas theory.
10146807
Octonions, G2 and generalized Lie 3-algebras
Abstract We construct an explicit example of a generalized Lie 3-algebra from the octonions. In combination with the result of [S. Cherkis, C. Saemann, arXiv: 0807.0808 [hep-th]], this gives rise to a three-dimensional N = 2 Chern–Simons-matter theory with exceptional gauge group G 2 and with global symmetry SU ( 4 ) × U ( 1 ) . This gives a possible candidate for the theory on multiple M2-branes with G 2 gauge symmetry.
119639562
Quivers, YBE and 3-manifolds
A bstractWe study 4d superconformal indices for a large class of $ \mathcal{N} = 1 $ superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of “zig-zag paths” on a two-dimensional torus T2. An exchange of loops, which we call a “double Yang-Baxter move”, gives the Seiberg duality of the gauge theory, and the invariance of the index under the duality is translated into the Yang-Baxter-type equation of a spin system defined on a “Z-invariant” lattice on T2. When we compactify the gauge theory to 3d, Higgs the theory and then compactify further to 2d, the superconformal index reduces to an integral of quantum/classical dilogarithm functions. The saddle point of this integral unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The 3-manifold is obtained by gluing hyperbolic ideal polyhedra in $ {\mathbb{H}^3} $, each of which could be thought of as a 3d lift of the faces of the 2d bipartite graph. The same quantity is also related with the thermodynamic limit of the BPS partition function, or equivalently the genus 0 topological string partition function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also comment on brane realization of our theories. This paper is a companion to another paper summarizing the results [1].
119669187
A Note on Dimer Models and McKay Quivers
We give one formulation of a procedure of Hanany and Vegh (J High Energy Phys 0710(029):35, 2007) which takes a lattice polygon as an input and produces a set of isoradial dimer models. We study the case of lattice triangles in detail and discuss the relation with coamoebas following Feng et al. (Adv Theor Math Phys 12(3):489–545, 2008).
125828668
High-Energy Proton Proton Elastic Scattering and Multiple Scattering Effect in Fresnel Approximation