One-day workshop for QFT and string theory
(organized by K. Yoshida, H. Kanno, H. Itoyama), December 14, 2018
Title and Abstract
Sanefumi Moriyama
Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
M2-brane is one of the central topics in understanding non-perturbative effects of string theory. Recently it was proposed that multiple M2-branes on various backgrounds are described by various superconformal Chern-Simons theories, whose partition function reduces to a matrix model due to the localization technique for supersymmetric gauge theories. These super Chern-Simons matrix models are known to correspond to quantum version of algebraic curves. From the viewpoint of symmetry, the algebraic curve of genus one, called the del Pezzo curve, enjoys symmetry of the exceptional algebra, while the super Chern-Simons matrix model is described by the free energy of topological strings on the del Pezzo background with the symmetry broken. In this talk, I introduce the quantum version of algebraic curves for our purpose of studying M2-branes and explain how the study of the symmetry aspects helps in understanding M2-branes.
Katsushi Ito
TBA equations and resurgent quantum mechanics
We derive the Thermodynamic Bethe Ansatz (TBA) equations for the exact WKB periods in 1-dimensional quantum mechanics with arbitrary polynomial potentials. These equations provide a generalization of the ODE/IM correspondence. We show that these TBA equations provide a powerful method to solve the spectral problems in quantum mechanics. This talk is based on the work in collaboration with Marcos Marino and Hongfei Shu (arXiv:1811.04812[hep-th]).
Eiki Iyoda
Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models
The Sachdev-Ye-Kitaev (SYK) model attracts attention in the context of information scrambling, which represents delocalization of quantum information and is quantified by the out-of-time-ordered correlators (OTOC). The SYK model contains N fermions with disordered and four-body interactions. Using the fact that the two-point and four-point functions can be calculated analytically in the limit of large-N and low-energy limit, it is shown that the SYK model exhibits the fastest scrambling in the sense of "the chaotic bound". The SYK model has been investigated also in condensed matter physics because of its relevance to non-Fermi liquid, quantum criticality, and the effect of disorder in strongly correlated systems.
In this talk, after reviewing the SYK model and the chaotic bound, we consider the role of disorder of the SYK model. We introduce a variant of the SYK model, which we refer to as the Wishart SYK model and includes the clean SYK model without quenched disorder as a special case. We investigate the Wishart SYK model for complex fermions and that for hard-core bosons. We show that the ground state of the Wishart SYK model is massively degenerate and the residual entropy is extensive, and that the Wishart SYK model for complex fermions is integrable. In addition, we numerically investigate the OTOC and level statistics of the SYK models. At late times, the OTOC of the fermionic Wishart SYK model exhibits large temporal fluctuations, in contrast with smooth scrambling in the original SYK model. We argue that the large temporal fluctuations of the OTOC are a consequence of a small effective dimension of the initial state. We also show that the level statistics of the fermionic Wishart SYK model is in agreement with the Poisson distribution, while the bosonic Wishart SYK model obeys the GUE or the GOE distribution.
Jun-ichi Sakamoto
Weyl invariance of string theories in generalized supergravity backgrounds
It has recently been shown that a set of the generalized type IIB supergravity equations follows from the requirement of kappa symmetry of the type IIB Green-Schwarz superstring theory defined on an arbitrary background. The result ensures the classical consistency of the superstring on the generalized supergravity backgrounds. However, the quantum consistency of string theories defined on such backgrounds is not clear.
In this talk, we show the Weyl invariance of the bosonic string sigma model on a generalized gravity background by constructing a possible local-counterterm explicitly. This result seems likely to support that string theories can be consistently defined on arbitrary generalized supergravity backgrounds.
This talk is based on the works: arXiv:1703.09567,1811.10600.
Kotaro Tamaoka
A Generalized Entanglement Entropy and Holography
We generalize the entanglement entropy so that it can extract the minimal surfaces (Ryu-Takayanagi surfaces) anchored on not boundary but bulk. First, we explain properties of the generalized one and its basic ingredients. Then, we explicitly compute the generalized entropy for mixed states in two-dimensional CFT with the bulk dual. We will see agreement with the entanglement wedge cross section, a generalized version of the minimal surfaces. This talk is based on 1809.09109.
Ryota Kojima
Triangulation of 2-loop MHV Amplituhedron from Sign Flips
Recently Nima Arkani-Hamed and Jaroslav Trnka found a new mathematical object, the Amplituhedron that its 'volume' is the amplitude in planar N=4 SYM. To obtain higher point amplitude from the general amplituhedron, we need to triangulate it into a simple one. We consider the triangulation of 2-loop MHV amplituhedron from ”sign flip” definition. And we also found a formula of n-point 2-loop MHV amplitude from this triangulation. In this talk, I will briefly explain the amplituhedron and its property, then I will talk about a new triangulation and the new formula of 2-loop MHV amplitude.
Yuki Yokokura
Entropy inside evaporating black holes
Gravity and thermodynamics are fundamental. Gravity interacts among all matters and thermodynamics governs universal behaviors of macroscopic objects. These two are tightly connected in black hole entropy. We study its origin in the framework of field theory. Suppose that we form a black hole in the heat bath quasi-statically. Then, we consider the back reaction from radiation of the bath and Hawking radiation produced during the formation, and we solve the semi-classical Einstein equation in a self-consistent manner. We obtain a solution indicating that a dense object is formed with radiations stuffed inside. It has neither horizon nor singularity if there are many d.o.f. of fields. Instead, it has a surface but looks like an ordinary black hole from the outside. Such an object should be the black hole. Finally, we show that the entropy area law is reproduced by integrating the entropy density inside the object.
Yutaka Matsuo
Plane Partition Realization of (Web of) W-algebra Minimal Models
Two-dimensional chiral algebras are an essential tool to study string theory and related mathematical physics. Recently a graphical representation of their Hilbert space was found and the basis of the representation is associated with the plane partition. In this talk, we explain a new family of chiral algebras defined geometrically at the vertex of intersecting branes and their plane partition realization. In particular, we show a general rule to realize the minimal models.