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The generalized Lefschetz thimble method is a promising approach that attempts to solve the sign problem in Monte Carlo methods by deforming the integration contour using the flow equation. Here we point out a general problem that occurs due to the property of the flow equation, which extends a region on the original contour exponentially to a region on the deformed contour. Since the growth rate for each eigenmode is governed by the singular values of the Hessian of the action, a huge hierarchy in the singular value spectrum, which typically appears for large systems, leads to various technical problems in numerical simulations. We solve this hierarchical growth problem by preconditioning the flow so that the growth rate becomes identical for every eigenmode. As an example, we show that the preconditioned flow enables us to investigate the real-time quantum evolution of an anharmonic oscillator with the system size that can hardly be achieved by using the original flow., Comment: 35 pages, 5 figures

We propose an experiment for constructing a spatial cat state of a suspended mirror with an order of $\mathcal{O}$(mg). The mirror is set at the center of two mirrors, creating two optical cavities and optical springs. The induced potential exhibits a double-well shape, and its deformation resembles a second-order phase transition as a function of laser power. We estimate an adiabatic condition for the ground state wave function to metamorphose from a localized state at the origin to a spatial cat state within the double-well potential, within a coherence time determined by mechanical and environmental noises. Our estimation suggests that such a construction is possible if we can provide an ultra-high finesse optical cavity with $F = 2.5 \times 10^5$ and a length of $0.3$ cm, along with a shot-noise-limited laser at $7.9$ nW. The necessary mechanical coherence time is approximately one second., Comment: 5 pages, 4 figures

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 figures; v2: reference added

Quantum transduction between microwave and optical photons plays a key role in quantum communication among remote qubits. Although the quantum transduction schemes generating communication photons have been successfully demonstrated by using optomechanical interfaces, the low conversion efficiency remains an obstacle to the implementation of a quantum network consisting of multiple qubits. Here, we present an efficient quantum transduction scheme using a one-dimensional diamond optomechanical crystal cavity tuned at a color-center emission without optomechanical coupling. The optomechanical crystal cavity incorporates a thin aluminum nitride (AlN) pad piezoelectric coupler near the concentrator cavity region, while retaining ultrasmall mechanical and optical mode volumes of about 1.5 \times 10^{-4} and ~0.2({\lambda}/n)^3, respectively. The energy level of a coherent color-center electron is manipulated by a strong mechanical-mode-color-center electron-coupling rate up to 16.4MHz. In our system, we theoretically predict that the population-conversion efficiency from a single microwave photon into an optical photon can reach 15% combined with current technologies. The coherent conversion efficiency is over 10% with a reasonably pure decay time of T^2_{*} > 10 ns. Our results imply that an atomic color center strongly coupled to the optomechanical crystal cavity will offer a highly efficient quantum transduction platform., Comment: 24 pages, 7 figures

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 JHEP

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)

This is an extended version of the previous paper arXiv:2103.05303 to study entanglement entropy (EE) of a half space in interacting field theories. In the previous paper, we have proposed a novel method to calculate EE based on the notion of $\mathbb{Z}_M$ gauge theory on Feynman diagrams, and shown that EE consists of two particular contributions, one from a renormalized two-point correlation function in the two-particle irreducible (2PI) formalism and another from interaction vertices. In this paper, we further investigate them in more general field theories and show that the non-Gaussian contributions from vertices can be interpreted as renormalized correlation functions of composite operators., Comment: 42 pages, 15 figures; typos corrected, discussion on general configurations of twists extended in Sec.VII, version to appear in PRD (v2)

We study a $T\bar{T}$-deformed $O(N)$ vector model, which is classically equivalent to the Nambu-Goto action with static gauge. The thermal free energy density can be computed exactly by using the Burgers equation as a special property of $T\bar{T}$-deformation. The resulting expression is valid for an arbitrary value of $N$. One may consider a large $N$ limit while preserving this expression. We try to derive this result in the field-theoretical approach directly by employing the large $N$ limit. As a result, the leading contribution coincides with the exact one. That is, the $1/N$ corrections are cancelled out through a non-trivial mechanism., Comment: 16 pages, no figures

Entanglement entropy (EE) in interacting field theories has two important issues: renormalization of UV divergences and non-Gaussianity of the vacuum. In this letter, we investigate them in the framework of the two-particle irreducible formalism. In particular, we consider EE of a half space in an interacting scalar field theory. It is formulated as $\mathbb{Z}_M$ gauge theory on Feynman diagrams: $\mathbb{Z}_M$ fluxes are assigned on plaquettes and summed to obtain EE. Some configurations of fluxes are interpreted as twists of propagators and vertices. The former gives a Gaussian part of EE written in terms of a renormalized 2-point function while the latter reflects non-Gaussianity of the vacuum., Comment: 7 pages, 8 figures; detailed derivations of equations and 4 figures added (v2); minor corrections, published version in PRD (v3)

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 figure

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)

We propose a novel gauge-invariant regularization for the perturbative chiral gauge theory.Our method consists of the two ingredients: use of the domain-wall fermion to describe a chiral fermion with Pauli-Villars regulators and application of the di- mensional regularization only to the gauge field. This regularization is implemented in the Lagrangian level, unlike other gauge-invariant regularizations (eg. the covariant regularizations). We show that the Abelian (fermion number) anomaly is reproduced correctly in this formulation. We also show that once we add the counter terms to the full theory, then the renormalization in the chiral gauge theory is automatically achieved., Comment: 26 pages, 16 figures

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)

The IIB matrix model is one of the candidates for nonperturbative formulation of string theory, and it is believed that the model contains gravitational degrees of freedom in some manner. In some preceding works, it was proposed that the matrix model describes the curved space where the matrices represent differential operators that are defined on a principal bundle. In this paper, we study the dynamics of the model in this interpretation, and point out the necessity of the principal bundle from the viewpoint of the stability and diffeomorphism invariance. We also compute the one-loop correction which possibly yields a mass term for each field due to the principal bundle. We find that the correction does generate some mass terms with the supersymmetry broken, while fields in the original IIB matrix model remain massless. The positivity is not violated as long as the number of bosonic degrees of freedom is larger than the fermionic counterpart. The generation of mass terms means that the new mass scale emerges through the loop correction., Comment: 20 pages, 6 figures

It is well-known that there exists a close relation between a large $N$ matrix model and noncommutative (NC) field theory: The latter can be naturally obtained from the former by expanding it around a specific background. Because the matrix model can be a constructive formulation of string theory, this relation suggests that NC field theory can also include quantum gravity. In particular, the NC $U(1)$ gauge theory attracts much attention because its low-energy effective action partially contains gravity where the metric is determined by the $U(1)$ gauge field. Thus, the NC $U(1)$ gauge theory could be a quantum theory of gravity. In this paper, we investigate the scenario by calculating the scattering amplitude of massless test particles, and find that the NC $U(1)$ gauge theory correctly reproduces the amplitude of the usual graviton exchange if the noncommutativity that corresponds to the background of the matrix model is appropriately averaged. Although this result partially supports the relation between the NC $U(1)$ gauge theory and gravity, it is desirable to find a mechanism by which such an average is naturally realized., Comment: 13 pages, 3 figures; a statement related to Appendix clarified(v2)

Free massive higher spin fields in weak background gravitational fields are discussed. Contrary to the spin one case, higher spin fields should have nontrivial non-minimal couplings to the curvature. A precise analysis is given for the spin 2 case, and it is shown that two conditions should be satisfied among five non-minimal coupling constants, which we derive both in the Hamiltonian and Lagrangian formalisms. It is checked that the linearized limit of the massive gravity theory indeed has the non-minimal couplings that satisfy the conditions. We also discuss the form of the non-minimal couplings for the spin 3 case., Comment: 19 pages; discussion on spin 3 added, references added (v2); footnote 9 corrected (v3)