The 4D Chern-Simons (CS) theory is a unifying framework of 2D integrable field theories and lattice models. Derivations of integrable field theories from 4D CS theories are based on two classes: order and disorder defects. We develop the aspect of order defects, and derive integrable field theories such as the Faddeev-Reshetikhin model. This approach further admits integrable deformations of...
Recently, a unified picture to describe integrable systems has been established by Costello, Witten and Yamazaki. In the case of 2D integrable field theories, Costello and Yamazaki proposed that by starting from a certain 4D Chern-Simons (CS) theory, one can construct classically integrable field theories systematically by taking a meromorphic 1-form and adopting an appropriate boundary...
The Atiyah-Singer(AS) index theorem on a closed manifold is well understood and appreciated in physics. On the other hand, the Atiyah-Patodi-Singer(APS) index, which is an extension to a manifold with boundary, is physicist-unfriendly, in that it is formulated with a nonlocal boundary condition. Recently we (3 physicists and 3 mathematicians) proved that the same index as APS is obtained from...
Recently, Arutyunov, Bassi and Lacroix have shown that 2D non-linear sigma model with a deformed T1,1 background is classically integrable. This background includes a Kalb-Ramond two-form with a critical value. Then the sigma model has been conjectured to be non-integrable when the two-form is off critical. With a winding string ansatz, the system is reduced to a dynamical system described...
Recently, there are many studies about expanding concepts of symmetries and its applications. One of the directions is to treat non-invertible objects as ""symmetry"". We explicitly constructed a non-invertible defect of duality and a 1-form center symmetry defect in 4D lattice pure Z2 gauge theory. In this talk, we will describe the junction that occurs where the two defects overlap. The...
In this talk, I will talk about the Post-Newtonian expansion of the gravitational three-body effective potential at the 2nd Post-Minkowskian order. At order 2PM a formal result is given in terms of a differential operator acting on the maximal generalized cut of the one-loop triangle integral. We perform the PN expansion unambiguously at the level of the integrand. Finding agreement with the...
We will discuss the compatibility between the conformal symmetry together with the unitarity and the continuous higher-form symmetries. We show that the d-dimensional unitary conformal field theories are not consistent with continuous p-form symmetries for certain (d,p), assuming that the corresponding conserved current is a conformal primary operator. We further discuss several dynamical...
We study dynamics of multi-soliton solutions of anti-self-dual Yang-Mills equations for G = GL(2, C) in four-dimensional spaces. The one-soliton solution can be interpreted as a codimension-one soliton in four-dimensional spaces because the principal peak of action density localizes on a three-dimensional hyperplane. We call it the soliton wall. We prove that in the asymptotic region, the...
We study a holographic construction of conformal blocks in the Regge limit of four-point scalar correlation functions by using coordinates of the two-sided Rindler-AdS black hole. As a generalization of geodesic Witten diagrams, we construct diagrams with four external scalar fields in the Rindler-AdS black hole by integrating over two half-geodesics between the centers of Penrose diagrams and...
We study the 5D N=1 Yang-Mills theory compactified on a circle, focusing on the Coulomb branch. The compactified theory has a very complicated wall-crossing pattern, but on the other hand, there seems to be no wall-crossing for 5d theory. In this talk, I will keep track of the wall-crossing phenomenon from compactified theory to its 5d limit, and see how the wall-crossing turns off. We find the...
In 1992 Wirthmuller showed that for any root system of type A,B,C,D,G,F and E6,E7, the ring of weak Jacobi forms invariant under Weyl group is a polynomial algebra. However, it has recently been proved that for E8 the ring is not a polynomial algebra. I will present how to describe E8 Weyl invariant Jacobi forms properly, both weak and holomorphic, and also how to used them in the modular...
We study the WKB periods for the $(r+1)$-th order ordinary differential equation (ODE) with polynomial potential which is obtained by the Nekrasov-Shatashvili limit of $(A_r, A_N)$ Argyres-Douglas theory in Omega background. We derive the thermodynamic Bethe ansatz (TBA) equations governing the exact WKB periods, which provides a generalization of the ODE/IM correspondence. Varying the moduli...
We propose a new method to construct the bulk theory in $d+1$ dimensions from $d$ dimensional field theory, using a so-called fundamental flow. We show that the conformal symmetry at the boundary is converted to the AdS isometry in the bulk even at the quantum level. We define the metric operators, whose VEV describes the AdS space. We derive the GKP-Witten formula for the bulk scalar field....
We describe conformal defects of p dimensions in a free theory on a d-dimensional flat space as boundary conditions on the conformally flat space Hp+1×Sd−p−1. We classify two types of boundary conditions, Dirichlet type and Neumann type, on the boundary of the subspace Hp+1 which correspond to the types of conformal defects in the free theory. We find Dirichlet boundary conditions always...
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...
The target space duality of string theory without spacetime supersymmetry, which is constructed by splitting the Narain lattice by a shift-vector with order 2, is investigated. We show that the duality symmetry of such a model is obtained by imposing a congruence condition on $O\left(d_{L},d_{R},\mathbb{Z}\right) $, that is, the non-supersymmetric string model is invariant under a congruence...
One-loop scattering amplitudes in string theories involve configuration-space integrals over genus-one surfaces with coefficients of Kronecker-Eisenstein series in the integrand. A conjectural basis of integrands under Fay identities and integration by parts was recently constructed out of chains of Kronecker-Eisenstein series. In this work, we decompose a variety of more general genus-one...
We introduce worldsheet variables for a certain moduli space associated with a Dynkin diagram of finite type. The construction is based on gluing a pair of A-type quivers. We find new nonlinear factors that characterize such spaces as hypersurface arrangement complement. We study various topological properties using a finite-field method and propose conjectures about quasi-polynomial point...
We perform numerical studies of the type IIB matrix model, which was proposed as a nonperturbative formulation of superstring theory in 1996. The complex Langevin method is used in order to overcome the sign problem, which occurs in applying Monte Carlo methods. In particular, we investigate how the signature of the space-time is determined dynamically in this model, and discuss the...
Recently, it is proposed that the Hawking radiation contains the information of a region inside the horizon called islands. In the calculation of the entanglement entropy of the Hawking radiation, the dominant contribution comes from the configuration with wormholes between replica geometries. Thus, the entanglement entropy of the Hawking radiation effectively includes the contribution from...
Entanglement entropy (EE) in field theory has been discussed as a measure for quantum entanglement between spatially separated regions. While there are a lot of studies on EE in CFT and free theories, EE in general interacting field theories is of interest in an attempt to associate the effect of the entanglement with low-energy physics. In this talk, I introduce our study on EE in interacting...
I will introduce the notion of target space entanglement. Quantum entanglement is closely related to the structure of spacetime in quantum gravity. For quantum field theories or statistical models, we usually consider the base space entanglement. However, target space instead of base space sometimes directly connects to our spacetime, for example, perturbative string theories. We thus need...
We study how information geometry is described by bulk geometry in the gauge/gravity correspondence. We consider a quantum information metric that measures the distance between the ground states of two field theories, where one is obtained by perturbing the other. We find a universal formula that represents the quantum information metric in terms of back reaction to the bulk geometry. This...
Under holographic prescription for Schwinger-Keldysh closed time contour for non-equilibrium system, we consider fluctuation effect of the order parameter in a holographic superconductor model. Near the critical point, we derive the time-dependent Ginzburg-Landau effective action governing dynamics of the fluctuating order parameter. In a semi-analytical approach, the time-dependent...
We investigate infrared logarithms in inflationary Universe from holographic perspective. We derive gravitational Fokker-Planck and Langevin equations to investigate the time evolution of the de Sitter entropy $S=\pi/G_N H^2(t)$. $H(t)$ is the time dependent effective Hubble parameter and $G_N$ is the Newton's constant. Our approach focuses on the conformal modes to respect local Lorentz...
