Mirror symmetry in 2+1 and 1+1 dimensions

Fjrw-rings and Landau-ginzburg Mirror Symmetry in Two Dimensions

For any non-degenerate, quasi-homogeneous hypersurface singularity W and an admissible group of diagonal symmetries G, Fan, Jarvis, and Ruan have constructed a cohomological field theory which is a candidate for the mathematical structure behind the Landau-Ginzburg A-model. When using the orbifold Milnor ring of a singularity W as a B-model, and the Frobenius algebra HW,G constructed by Fan, Ja...

Mirror Symmetry in 2 + 1 and 1 + 1 Dimensions

We study the Coulomb-Higgs duality of N = 2 supersymmetric Abelian Chern-Simons theories in 2 + 1 dimensions, by compactifying dual pairs on a circle of radius R and comparing the resulting N = (2, 2) theories in 1 + 1 dimensions. Below the compactification scale, the theory on the Higgs branch reduces to the non-linear sigma model on a toric manifold. In the dual theory on the Coulomb branch, ...

Monopole Operators and Mirror Symmetry in Three Dimensions

We study vortex-creating, or monopole, operators in 3d CFTs which are the infrared limit of N = 2 and N = 4 supersymmetric QEDs in three dimensions. Using large-Nf expansion, we construct monopole operators which are primaries of short representations of the superconformal algebra. Mirror symmetry in three dimensions makes a number of predictions about such operators, and our results confirm th...

Log Mirror Symmetry and Local Mirror Symmetry

We study Mirror Symmetry of log Calabi-Yau surfaces. On one hand, we consider the number of “affine lines” of each degree in P\B, where B is a smooth cubic. On the other hand, we consider coefficients of a certain expansion of a function obtained from the integrals of dx/x ∧ dy/y over 2chains whose boundaries lie on Bφ, where {Bφ} is a family of smooth cubics. Then, for small degrees, they coin...

Mirror Symmetry and Localization