Kazutoshi Ohta

Non-Abelian vortices on a cylinder : Duality between vortices and walls

We investigate vortices on a cylinder in supersymmetric non-Abelian gauge theory with hypermultiplets in the fundamental representation. We identify moduli space of periodic vortices and find that a pair of wall-like objects appears as the vortex moduli is varied. Usual domain walls also can be obtained from the single vortex on the cylinder by introducing a twisted boundary condition. We can understand these phenomena as a T duality among D-brane configurations in type II superstring theories. Using this T-duality picture, we find a one-to-one correspondence between the moduli space of non-Abelian vortices and that of kinky D-brane configurations for domain walls.

D-brane construction for non-Abelian walls

Supersymmetric U(NC) gauge theory with NF massive hypermultiplets in the fundamental representation is given by the brane configuration made of NC fractional Dp-branes stuck at the Z2 orbifold singularity on NF separated D(p+4)-branes. We show that non-Abelian walls in this theory are realized as kinky fractional Dp-branes interpolating between D(p+4)branes. Wall solutions and their duality between NC and NF − NC imply extensions of the s-rule and the Hanany-Witten effect in brane dynamics. We also find that the reconnection of fractional D-branes occurs in this system. Diverse phenomena in non-Abelian walls found in field theory can be understood very easily by this brane configuration.

Global structure of moduli space for BPS walls

We study the global structure of the moduli space of BPS walls in the Higgs branch of supersymmetric theories with eight supercharges. We examine the structure in the neighborhood of a special Lagrangian submanifold M, and find that the dimension of the moduli space can be larger than that naively suggested by the index theorem, contrary to previous examples of BPS solitons. We investigate BPS wall solutions in an explicit example of M using Abelian gauge theory. Its Higgs branch turns out to contain several special Lagrangian submanifolds including M. We show that the total moduli space of BPS walls is the union of these submanifolds. We also find interesting dynamics between BPS walls as a by-product of the analysis. Namely, mutual repulsion and attraction between BPS walls sometimes forbid a movement of a wall and lock it in a certain position; we also find that a pair of walls can transmute to another pair of walls with different tension after they pass through.

Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold

We derive non-Abelian localization formulae for supersymmetric Yang-Mills- Chern-Simons theory with matters on a Seifert manifold M, which is the three- dimensional space of a circle bundle over a two-dimensional Riemann surface �, by using the cohomological approach introduced by Kallen. We find that the partition function and the vev of the supersymmetric Wilson loop reduces to a finite dimen- sional integral and summation over classical flux configurations labeled by discrete integers. We also find the partition function reduces further to just a discrete sum over integers in some cases, and evaluate the supersymmetric index (Witten in- dex) exactly on S 1 × �. The index completely agrees with the previous prediction from field theory and branes. We discuss a vacuum structure of the ABJM theory

Statistical mechanics of vortices from D-branes and T-duality

We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We there use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on a torus, our results agree with exact results which are geometrically derived by an explicit integration over the moduli space of vortices. The equation of state for U(N) gauge theory deviates from van der Waals one, and the second virial coefficient is proportional to 1 / p N, implying that non-Abelian vortices are “softer” than Abelian vortices. Vortices on a sphere are also briefly discussed.

D‐brane Configurations for Domain Walls and Their Webs

Supersymmetric U(NC) gauge theory with NF massive hypermultiplets in the fundamental representation admits various BPS solitons like domain walls and their webs. In the first part we show as a review of the previous paper that domain walls are realized as kinky fractional D3‐branes interpolating between separated D7‐branes. In the second part we discuss brane configurations for domain wall webs. This is a contribution to the conference based on the talk given by MN.

Non-Abelian Gauge Field Localized on Walls with Four-Dimensional World Volume

A mechanism using the position-dependent gauge coupling is proposed to localize non-Abelian gauge fields on domain walls in five-dimensional space-time. Low-energy effective theory posseses a massless vector field, and a mass gap. The four-dimensional gauge invariance is maintained intact. We obtain perturbatively the four-dimensional Coulomb law for static sources on the domain wall. BPS domain wall solutions with the localization mechanism are explicitly constructed in the U(1)xU(1) supersymmetric gauge theory coupling to the non-Abelian gauge fields only through the cubic prepotential, which is consistent with the general principle of supersymmetry in five-dimensional space-time.

On Relationships among Chern-Simons Theory, BF Theory and Matrix Model

Chern-Simons theory on a U(1) bundle over a Riemann surface \Sigma_g of genus g is dimensionally reduced to BF theory with a mass term, which is equivalent to the two-dimensional Yang-Mills on \Sigma_g. We show that the former is inversely obtained from the latter by the extended matrix T-duality developed in hep-th/0703021. For the case of g=0 (i.e. S^2), the U(1) bundle represents the lens space S^3/Z_p. We find that in this case both the Chern-Simons theory and the BF theory with the mass term are realized in a matrix model. We also construct Wilson loops in the matrix model that correspond to those in the Chern-Simons theory on S^3.

Volume of Moduli Space of Vortex Equations and Localization

We evaluate volume of moduli space of BPS vortices on a compact genus h Riemann surface Σh by using topological field theory and localization technique developed by Moore, Nekrasov and Shatashvili. We apply this technique to Abelian (ANO) vortex and show that the volume of moduli space agrees with the previous results obtained by integrating over the moduli space metric. We extend the evaluation to non-Abelian gauge groups and multi

Exact results in quiver quantum mechanics and BPS bound state counting

A bstractWe exactly evaluate the partition function (index) of N