Finite discrete symmetries are attractive especially for flavor symmetry of quarks and leptons. However, some classical symmetries can be broken by quantum anomaly effects. I will discuss anomaly free and anomalous structure of a finite discrete group $G$ generally.

We study a systematic derivation of four dimensional N = 1 supersymmetric effective theory

(EFT) from ten dimensional non-Abelian Dirac-Born-Infeld (DBI) action compactified on

a six dimensional torus with magnetic fluxes on the D9-branes. We find a new type of

matter Kahler metric while gauge kinetic function and superpotential are consistent with

previous studies. For the ten dimensional...

We study possibilities to realize a nonvanishing finite Wilson line (WL) scalar mass in flux compactification. Generalizing loop integrals in the quantum correction to WL mass at one-loop, we derive the conditions for the loop integrals and mode sums in one-loop corrections to WL scalar mass to be finite. We further guess and classify the four-point and three-point interaction terms satisfying...

We study the pair production of fermions in a time dependent axion background with and without an electric background. We construct the adiabatic mode functions which incorporate the gauge field and the axion velocity dependence of the dispersion relation. The semiclassical approach using this adiabatic basis shows two types of pair production. One is axion-assisted pair production: the...

We investigate the relation perturbative unitarity and renormalizablility in quantum gravity. In particle theories point of view, Llewellyn Smith conjectured that renormalizablility and tree-unitarity at high energy give the same conditions for theories. If we apply this conjecture to gravity theory, it is shown that Einstein gravity is not renormalizable and does not hold perturbative...

We study nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from a linearly realized theory, we integrate out heavy modes without neglecting derivative terms to obtain constraints on superfields. Thanks to the supersymmetry breaking contribution by the kinetic energy, the validity of constrained...

We investigate whether a class of models describing F-theory compactifications admits a specific type of flux vacua with an exponentially small vacuum expectation value of the superpotential, by generalizing a method recently developed in Type IIB flux compactifications. First we clarify that a restricted choice of G4-flux components reduces a general flux superpotential into a simple form,...

In F-theory, if a fiber type of an elliptic fibration involves a condition that requires an exceptional curve to split into two irreducible components, it is called “split” or “non-split” type depending on whether it is globally possible or not. In the latter case, the gauge symmetry is reduced to a non-simply-laced Lie algebra due to monodromy. We show that the transition from a split to a...

We calculate the superconformal indices of the $¥mathcal N=2$ superconformal field theories realized on $N$ coincident D3-branes in 7-brane backgrounds with constant axiodilaton via the AdS/CFT correspondence. We include the finite-$N$ corrections as the contribution of D3-branes wrapped around 3-cycles in the internal space. We take only single-wrapping contributions into account for...

In this talk, I consider the quantum entanglement in the momentum space for scalar field theory on noncommutative spaces. In an interacting quantum field theory, the degrees of freedom in momentum space show entanglement; it quantifies the correlation between the high/low momentum modes. In noncommutative spaces, it is known that the UV and IR degrees of freedom show a characteristic...

We consider gauge/gravity correspondence between maximally supersymmetric Yang-Mills theory in (p+1) dimensions and superstring theory on the near-horizon limit of the Dp-brane solution. The string-frame metric is AdS_{p+1}\times S^{8-p} times a Weyl factor, and there is no conformal symmetry except for p=3. We consider states which have angular momenta in the AdS directions. We first show...

We propose when and why symmetry enhancements happen in massless renormalization group (RG) flows to two-dimensional rational conformal field theories (RCFTs). We test our proposal against known RG flows from unitary minimal models. We also suggest which sign of the relevant coupling triggers the massless RG flow. The other sign triggers massive RG flows to topological quantum field theories...

I will discuss perturbation theory of supersymmetric gradient flow in four-dimensional N = 1 SQCD and show one-loop calculations to the flowed fields. In flow theory, the perturbation theory consists of a perturbative expansion of the 4D gauge theory and an iterative expansion of the flow equations. We apply the same technique to SQCD in the Wess-Zumino gauge. Once the boundary theory is...

Gradient Flow Exact Renormalization Group (GFERG) is a framework of Exact Renormalization

Group and defines the Wilson action via Gradient Flow equation. We study the fixed

point structure of the GFERG equation associated with the general Gradient Flow equation

for scalar fields and show that it is almost the same as that of the Wilson-Polchinski

(WP) equation. Furthermore, we discuss that...

We study higher derivative extension of the functional renormalization group (FRG).We consider the general form of the FRG equations for a scalar field that include higher functional derivatives with respect to the field. We show that the epsilon expansion around the Wilson-Fisher fixed point is indeed reproduced by the local potential approximation of the general FRG equations.

In the early days of QCD, the axial U(1) anomaly was considered to trigger the breaking of the SU(2)_L ×SU(2)_R symmetry through topological excitations of gluon fields. However, it has been a challenge for lattice QCD to quantify the effect. In this work, we simulate QCD at high temperatures with the overlap Dirac operator. The exact chiral symmetry enables us to separate the contribution...

We consider a massive fermion system having a curved domain-wall embedded in a square

lattice. As already reported in condensed matter physics, the massless chiral edge modes

appearing at the domain-wall feel “gravity” through the induced spin connections. In this

work, we embed S^1 and S^2 domain-wall into a Euclidean space and show how the gravity is

detected from the spectrum of the...

The Monte Carlo simulation of the gauge theory with a theta term is extremely difficult due to the sign problem. The complex Langevin method (CLM) is one of the approaches which allow us to avoid the problem. Recently the analytic study of 't Hooft anomaly matching condition predicted some nontrivial phase structures around θ=π. We use CLM to study 4D SU(2) gauge theory with a theta term....

The tensor renormalization group method is a promising approach to lattice field theories, which is free from the sign problem unlike standard Monte Carlo methods. In this work, we apply the method to two dimensional U(N) and SU(N) gauge theories, where we propose a practical strategy to restrict the number of representations in the character expansion when constructing the fundamental tensor....

All colored particles including dynamical quarks and gluons are confined if the color confinement

criterion proposed by Kugo and Ojima is satisfied. The criterion was obtained under

the gauge fixing of the Lorenz type. However, it was pointed out that the Kugo-Ojima criterion

breaks down for the Maximal Abelian gauge, which is quite strange in view of the fact

that quark confinement has...

We discuss four-dimensional (4d) N=1 superconformal field theories (SCFTs) obtained as deformations of 4d N=2 SCFTs on S-folds by tilting 7-branes. Geometric compatibility with the structures of S-folds constrains the forms of T-branes.

We perform numerical studies of the type IIB matrix model, which was proposed as a

nonperturbative formulation of superstring theory in 1996. In our study, we apply the

complex Langevin method in order to overcome the sign problem, which occurs in Monte

Carlo simulations. In particular, we investigate a scenario on how the signature of space-time

could be determined dynamically in this...

One perturbative string theory is defined on one fixed background. On the other hand, it is necessary that a non-perturbative formulation of string theory includes all the perturbatively stable vacuum and perturbative string theories on various curved backgrounds are derived from the single theory. In this talk, we derive perturbative string theories on various curved backgrounds from the...