A note on higher spin symmetry in the IIB matrix model with the operator interpretation

We study the IIB matrix model in an interpretation where the matrices are differential operators defined on curved spacetimes. In this interpretation, coefficients of higher derivative operators formally appear to be massless higher spin fields. In this paper, we examine whether the unitary symmetry of the matrices includes appropriate higher spin gauge symmetries. We focus on fields that are bosonic and relatively simple in the viewpoint of the representation of Lorentz group. We find that the additional auxiliary fields need to be introduced in order to see the higher spin gauge symmetries explicitly. At the same time, we point out that a part of these extra fields are gauged-away, and the rest of part can be written in terms of a totally symmetric tensor field. The transformation to remove its longitudinal components exists as well. As a result, we observe that the independent physical DoF are the transverse components of that symmetric field, and that the theory describes the corresponding higher spin field. We also find that the field is not the Fronsdal field, rather the generalization of curvature.Comment: 1+14 pages, 1 figure; discussion on EOM added, Version to appear in NPB (v2

Hillclimbing saddle point inflation

Recently a new inflationary scenario was proposed in arXiv:1703.09020 which can be applicable to an inflaton having multiple vacua. In this letter, we consider a more general situation where the inflaton potential has a (UV) saddle point around the Planck scale. This class of models can be regarded as a natural generalization of the hillclimbing Higgs inflation (arXiv:1705.03696).Comment: 5 pages, 3 figures; Report number added (v2

A new picture of quantum tunneling in the real-time path integral from Lefschetz thimble calculations

It is well known that quantum tunneling can be described by instantons in the imaginary-time path integral formalism. However, its description in the real-time path integral formalism has been elusive. Here we establish a statement that quantum tunneling can be characterized in general by the contribution of complex saddle points, which can be identified by using the Picard-Lefschetz theory. We demonstrate this explicitly by performing Monte Carlo simulations of simple quantum mechanical systems, overcoming the sign problem by the generalized Lefschetz thimble method. We confirm numerically that the contribution of complex saddle points manifests itself in a complex ``weak value'' of the Hermitian coordinate operator $\hat{x}$ evaluated at time $t$, which is a physical quantity that can be measured by experiments in principle. We also discuss the transition to classical dynamics based on our picture.Comment: 39 pages, 7 figure

Wilsonian Effective Action and Entanglement Entropy

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In arXiv:2103.05303, we have proposed the notion of $\mathbb{Z}_M$ gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. As shown in the next paper arXiv:2105.02598, the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.Comment: 29 pages, 10 figures; typos corrected, published version in Symmetry (v2

Backpropagating Hybrid Monte Carlo algorithm for fast Lefschetz thimble calculations

The Picard-Lefschetz theory has been attracting much attention as a tool to evaluate a multi-variable integral with a complex weight, which appears in various important problems in theoretical physics. The idea is to deform the integration contour based on Cauchy's theorem using the so-called gradient flow equation. In this paper, we propose a fast Hybrid Monte Carlo algorithm for evaluating the integral, where we "backpropagate" the force of the fictitious Hamilton dynamics on the deformed contour to that on the original contour, thereby reducing the required computational cost by a factor of the system size. Our algorithm can be readily extended to the case in which one integrates over the flow time in order to solve not only the sign problem but also the ergodicity problem that occurs when there are more than one thimbles contributing to the integral. This enables, in particular, efficient identification of all the dominant saddle points and the associated thimbles. We test our algorithm by calculating the real-time evolution of the wave function using the path integral formalism.Comment: 29 pages, 2 figures (v2) references added, figures updated (v3) analogy to backpropagation clarified; final version to appear in JHE

Large N Analysis of TTˉT\bar{T}-deformation and Unavoidable Negative-norm States

We study non-perturbative quantum aspects of $T\bar{T}$-deformation of a free $O(N)$ vector model by employing the large $N$ limit. It is shown that bound states of the original field appear and inevitably become negative-norm states. In particular, the bound states can be regarded as the states of the conformal mode in a gravitational theory, where the Liouville action is induced with the coefficient proportional to the minus of central charge. To make the theory positive-definite, some modification is required so as to preserve diffeomorphism invariance due to the Faddeev-Popov ghosts with a negative central charge.Comment: 1+20 pages, 1 figur