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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., 42 pages, 15 figures; typos corrected, discussion on general configurations of twists extended in Sec.VII, version to appear in PRD (v2)

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., 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)

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

We study a T 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 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 canceled out through a non-trivial mechanism.

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., 13 pages, 3 figures; a statement related to Appendix clarified(v2)

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)

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)