119132888
Semiclassical Analysis of the 3d/3d Relation
We provide quantitative evidence for our previous conjecture which states an equivalence of the partition function of a 3d N=2 gauge theory on a duality wall and that of the SL(2,R) Chern-Simons theory on a mapping torus, for a class of examples associated with once-punctured torus. In particular, we demonstrate that a limit of the 3d N=2 partition function reproduces the hyperbolic volume and the Chern-Simons invariant of the mapping torus. This is shown by analyzing the classical limit of the trace of an element of the mapping class group in the Hilbert space of the quantum Teichmuller theory. We also show that the subleading correction to the partition function reproduces the Reidemeister torsion.
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.
33443115
Wall Crossing as Seen by Matrix Models
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 naturally related to the Kähler moduli space $${{\mathcal M}(X)}$$ . We construct unitary one-matrix models which count such BPS states for a class of toric Calabi-Yau manifolds at infinite ’t Hooft coupling. The matrix model for the BPS counting on X turns out to give the topological string partition function for another Calabi-Yau manifold Y, whose Kähler moduli space $${{\mathcal M}(Y)}$$ contains two copies of $${{\mathcal M}(X)}$$ , one related to the BPS charges and another to the stability conditions. The two sets of data are unified in $${{\mathcal M}(Y)}$$ . The matrix models have a number of other interesting features. They compute spectral curves and mirror maps relevant to the remodeling conjecture. For finite ’t Hooft coupling they give rise to yet more general geometry $${\widetilde{Y}}$$ containing Y.
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.
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).
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.
125828668
High-Energy Proton Proton Elastic Scattering and Multiple Scattering Effect in Fresnel Approximation