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We study constraints on the effective field theory (EFT) from the relative entropy between two theories: we refer to these as target and reference theories. The consequence of the non-negativity of the relative entropy is investigated by choosing some reference theories for a given target theory. We consider the target and reference theories described by field theories, quantum mechanical models, etc. It is found that the constraints on EFTs, e.g., the single massless scalar field with the dimension-eight operator, and SMEFT dimension-eight bosonic operators, arise when the higher-derivative operators are generated by the interaction between heavy and light fields. In particular, the constraints on the SMEFT dimension-eight bosonic operators with the SU(N) and SU(n) gauge fields, and the operator quartics in the Higgs are newly studied, and some stronger bounds than the unitarity and causality considerations are derived. The constraints on Einstein-Maxwell theory with higher-derivative operators from the non-negativity of relative entropy are also investigated. The constraints on such EFTs from the relative entropy hold under an assumption that perturbative corrections from the interaction involving higher-derivative operators of light fields are not dominant in the EFTs. The consequence of this study on the weak gravity conjecture and the second law of thermodynamics is also discussed. [ABSTRACT FROM AUTHOR]

We consider the U(1) gauge theory on a four-dimensional torus, where the instanton number is restricted to an integral multiple of p. This theory possesses the nontrivial higher-group structure, which can be regarded as a generalization of the Green–Schwarz mechanism, between Z q 1-form and Z p 3-form symmetries. Here, Z q is a subgroup of the center of U(1). Following the recent study of the lattice construction of the U (1) / Z q principal bundle, we examine how such a structure is realized on the basis of lattice regularization. [ABSTRACT FROM AUTHOR]

We investigate the conjectured bound on the Lyapunov exponent for a charged particle with angular motion in the Kerr-Newman-AdS black hole. The Lyapunov exponent is calculated based on the effective Lagrangian. We show that the negative cosmological constant reduces the chaotic behavior of the particle, namely, it decreases the Lyapunov exponent. Hence, the bound is more effective in the AdS spacetime than in the flat spacetime. Nevertheless, we find that the bound can be violated when the angular momenta of the black hole are turned on. Moreover, we show that in an extremal black hole, the bound is more easily violated compared to that in a nonextremal black hole. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "Higher-group structure in lattice Abelian gauge theory under instanton-sum modification." The corrections made in this erratum are related to equations in the continuum theory discussed in Section 2. The original discussions falsely attributed the periodicity of the compact scalar to the 2π periodicity, and the definition of the 4-form gauge field was incorrect. However, these modifications do not affect any conclusions in the lattice theory. The erratum also introduces new equations and conditions to maintain the periodicity of certain variables and to admit nontrivial configurations. The authors express gratitude to Ryo Yokokura for discussions and apologize for an error in the text. [Extracted from the article]

We consider resolutions of codimension-two enhanced singularities from SO(12) to E7 and from E7 to E8 in six-dimensional F-theory, where a half-hypermultiplet arises for generic complex structures achieving them. The exceptional fibers at the enhanced point exhibit different structures depending on how the colliding 7-brane approaches the stack of gauge 7-branes, as previously observed by Morrison and Taylor in the case of the enhancement from SU(6) to E6. When the colliding brane approaches them as O(s), where s is the coordinate of the base space along the gauge 7-branes, the resolution process ends up with fewer exceptional fibers than naively expected from the Kodaira classification, with a non-Dynkin intersection matrix including half-integral intersection numbers. We confirm that the exceptional fibers at the enhanced point form extremal rays of the cone of the positive weights of the relevant pseudo-real representation, explaining why a half-hypermultiplet arises there. By altering the ordering of the singularities blown up in the process, we obtain, for both SO(12) → E7 and E7 → E8, the intersection diagram on every other row of the corresponding box graphs. We present detailed derivations of the intersection diagrams of the exceptional fibers at the singularity enhanced points by examining how an exceptional curve is lifted up on the chart arising due to the subsequent blowing-up process. When the colliding brane approaches the stack of branes as O(s2), we obtain additional conifold singularity at the enhanced point, which completes the full Dynkin diagram of the enhanced group as was found previously. [ABSTRACT FROM AUTHOR]