121271536
Four-dimensional superconformal index reloaded
We consider the four-dimensional N≥1 superconformal index and its generalization to the lens space. We discuss reductions of the latter to the three-dimensional N≥2 sphere partition function, the threedimensional N≥2 superconformal index, and the two-dimensional N≥(2, 2) sphere partition function. We apply these reductions to a class of four-dimensional N=1 superconformal field theories dual to toric Calabi-Yau manifolds, and we find surprising connections with integrable spin chains and hyperbolic geometry. We comment on the problem of classifying infrared fixed points of four-dimensional and threedimensional supersymmetric gauge theories.
118488616
String theory origin of bipartite SCFTs
A bstractWe provide a string theory embedding for $ \mathcal{N} $ = 1 superconformal field theories defined by bipartite graphs inscribed on a disk. We realize these theories by exploiting the close connection with related $ \mathcal{N} $ = 2 generalized (Ak−1, An−1) Argyres-Douglas theories. The $ \mathcal{N} $ = 1 theory is obtained from spacetime filling D5-branes wrapped on an algebraic curve and NS5-branes wrapped on special Lagrangians of $ {{\mathbb{C}}^2} $ which intersect along the BPS flow lines of the corresponding $ \mathcal{N} $ = 2 Argyres-Douglas theory. Dualities of the $ \mathcal{N} $ = 1 field theory follow from geometric deformations of the brane configuration which leave the UV boundary conditions fixed. In particular we show how to recover the classification of IR fixed points from cells of the totally non-negative Grassmannian $ \mathrm{Gr}_{k,n+k}^{\mathrm{tnn}} $. Additionally, we present evidence that in the 3D theory obtained from dimensional reduction on a circle, VEVs of line operators given by D3-branes wrapped over faces of the bipartite graph specify a coordinate system for $ \mathrm{Gr}_{k,n+k}^{\mathrm{tnn}} $.
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).
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.
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.
55014255
The Non-commutative Topological Vertex and Wall Crossing Phenomena
We propose a generalization of the topological vertex, which we call the "non-commutative topological vertex". This gives open BPS invariants for a toric Calabi-Yau manifold without compact 4-cycles, where we have D0/D2/D6-branes wrapping holomorphic 0/2/6-cycles, as well as D2-branes wrapping disks whose boundaries are on D4-branes wrapping non-compact Lagrangian 3-cycles. The vertex is defined combinatorially using the crystal melting model proposed recently, and depends on the value of closed string moduli at infinity. The vertex in one special chamber gives the same answer as that computed by the ordinary topological vertex. We prove an identify expressing the non-commutative topological vertex of a toric Calabi-Yau manifold X as a specialization of the closed BPS partition function of an orbifold of X, thus giving a closed expression for our vertex. We also clarify the action of the Weyl group of an affine A_L Lie algebra on chambers, and comment on the generalization of our results to the case of refined BPS invariants.
125828668
High-Energy Proton Proton Elastic Scattering and Multiple Scattering Effect in Fresnel Approximation