Mitsuhiro Kato

D-Branes on Group Manifolds

Abstract Possible Dirichlet boundary states for WZW models with untwisted affine super Kac-Moody symmetry are classified for all compact simple Lie groups. They are obtained by inner- and outerautomorphisms of the group. The D-brane world-volume turns out to be a group manifold of a symmetric subgroup, so that the moduli space of D-branes is locally isomorphic to an irreducible Riemannian symmetric space. It is also clarified how these D-branes are transformed into each other under abelian T-duality of the WZW model. Our result implies, for example, that there is no D-particle on the compact simple group manifold. When the D-brane world-volume contains an S1 factor, the D-brane moduli space becomes locally isomorphic to a hermitian symmetric space and open string world-sheet instantons are allowed.

Hybrid Monte Carlo on Lefschetz thimbles — A study of the residual sign problem

A bstractWe consider a hybrid Monte Carlo algorithm which is applicable to lattice theories defined on Lefschetz thimbles. In the algorithm, any point (field configuration) on a thimble is parametrized uniquely by the flow-direction and the flow-time defined at a certain asymptotic region close to the critical point, and it is generated by solving the gradient flow equation downward. The associated complete set of tangent vectors is also generated in the same manner. Molecular dynamics is then formulated as a constrained dynamical system, where the equations of motion with Lagrange multipliers are solved by the second-order constraint-preserving symmetric integrator. The algorithm is tested in the λϕ4 model at finite density, by choosing the thimbles associated with the classical vacua for subcritical and supercritical values of chemical potential. For the lattice size L = 4, we find that the residual sign factors average to not less than 0.99 and are safely included by reweighting and that the results of the number density are consistent with those obtained by the complex Langevin simulations.

Taming the Leibniz rule on the lattice

We study a product rule and a difference operator equipped with Leibniz rule in a general framework of lattice field theory. It is shown that the difference operator can be determined by the product rule and some initial data through the Leibniz rule. This observation leads to a no-go theorem that it is impossible to construct any difference operator and product rule on a lattice with the properties of (i) translation invariance, (ii) locality and (iii) Leibniz rule. We present a formalism to overcome the difficulty by an infinite flavor extension or a matrix expression of a lattice field theory.

Null field construction and KAC formulae of N = 2 superconformal algebras in two dimensions

Abstract The oscillator representation of the N = 2 superconformal algebras in two dimensions is investigated. The null field construction is given in terms of singular vertex operators with a focus on the degenerate primary superconformal properties of the constructed null fields. We present our derivation of the Kac formulae for the N = 2 case.

Topological matrix model

Starting from the primal principle based on the noncommutative nature of (9+1)-dimensional spacetime, we construct a topologically twisted version of the supersymmetric reduced model with a certain modification. Our formulation automatically provides extra 1+1 dimensions, thereby the dimensions of spacetime are promoted to 10+2. With a suitable gauge choice, we can reduce the model with (10+2)-dimensional spacetime to the one with (9+1)-dimensions and thus we regard this gauge as the light-cone gauge. It is suggested that the model so obtained would describe the light-cone F-theory. From this viewpoint we argue the relation of the reduced model to the matrix model of M-theory and the SL(2,Z) symmetry of type IIB string theory. We also discuss the general covariance of the matrix model in a broken phase, and make some comments on the background independence.

New Covariant Gauges in String Field Theory

A single-parameter family of covariant gauge fixing conditions in bosonic string field theory is proposed. It is a natural string field counterpart of the covariant gauge in the conventional gauge theory, which includes the Landau gauge as well as the Feynman (Siegel) gauge as special cases. The action in the Landau gauge is largely simplified in such a way that numerous component fields have no derivatives in their kinetic terms and appear in at most quadratic in the vertex.

NOTE ON N = 0 STRING AS N = 1 STRING

A similarity transformation, which brings a particular class of the

Toward a Super Yang-Mills Theory on the Lattice

N=1

General Linear Gauges and Amplitudes in Open String Field Theory

string to the

Level truncated tachyon potential in various gauges

N=0