박재모 교수

We prove that 3d superconformal index for general $$ \mathcal{N} $$ = 2 U(N) gauge group with fundamentals and anti-fundmentals with/without Chern-Simons terms is factorized into vortex and anti-vortex partition function. We show that for simple cases, 3d vortex partition function coincides with a suitable topological open string partition function. We provide much more elegant derivation at the index level for $$ \mathcal{N} $$ = 2 Seiberg-like dualities of unitary gauge groups with fundamantal

We work out the factorization of the 3d superconformal index for $$ \mathcal{N}=2 $$ U(N c ) gauge theory with one adjoint chiral multiplet as well as N f fundamental, N a anti-fundamental chiral multiplets. Using the factorization, one can prove the Seiberg-like duality for $$ \mathcal{N}=4 $$ U(N c ) theory with N f hypermultiplets at the index level. We explicitly show that monopole operators violating unitarity bound in a bad theory are mapped to free hypermultiplets in the dual side. For $$

We work out boundary conditions for the covariant open string in the type IIA plane wave background, which corresponds to the D-branes in the type IIA theory. We use the kappa symmetric string action and see what kind of boundary conditions should be imposed to retain kappa symmetry. We find half BPS as well as quarter BPS branes and the analysis agrees with the previous work in the light cone gauge if the result is available. Finally we find that D0-brane is non-supersymmetric.

We investigate a deformed matrix model of type 0A theory related to supersymmetric Witten's black hole in two-dimensions, a generalization of bosonic model suggested by Kazakov et al. We find a free field realization of the partition function of the matrix model, which includes Ramond-Ramond perturbations in the type 0A theory. In a simple case, the partition function is factorized into two determinants, which are given by $\ensuremath{\tau}$ function of an integrable system. We work out the gen