Sergei Gukov

CFT's from Calabi–Yau four-folds

We consider F/M/Type IIA theory compactified to four, three, or two dimensions on a Calabi–Yau four-fold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes. We analyze the vacuum and soliton structure of these models, and show that near an isolated singularity, one often generates massless chiral superfields and a superpotential, and in many instances in two or three dimensions one obtains nontrivial superconformal field theories. In the case of two dimensions, we identify some of these theories with certain Kazama–Suzuki coset models, such as the N=2 minimal models.

Loop and surface operators in N=2 gauge theory and Liouville modular geometry

Recently, a duality between Liouville theory and four dimensional

Vortex Counting and Lagrangian 3-Manifolds

\mathcal{N} = 2

Solitons, superpotentials and calibrations

gauge theory has been uncovered by some of the authors. We consider the role of extended objects in gauge theory, surface operators and line operators, under this correspondence. We map such objects to specific operators in Liouville theory. We employ this connection to compute the expectation value of general supersymmetric ’t Hooft-Wilson line operators in a variety of

The Superpolynomial for knot homologies

\mathcal{N} = 2

Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial

gauge theories.

Khovanov-Rozansky Homology and Topological Strings

To every 3-manifold M one can associate a two-dimensional

2d index and surface operators

{\mathcal{N}=(2, 2)}