Nagy, Ákos Oliveira, Gonçalo
Published in
Letters in Mathematical Physics

We study solutions to the Kapustin–Witten equations on ALE and ALF gravitational instantons. On any such space and for any compact structure group, we prove asymptotic estimates for the Higgs field. We then use it to prove a vanishing theorem in the case when the underlying manifold is R4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackag...

Fajman, David Urban, Liam

We study the asymptotic behaviour of solutions to the linear wave equation on cosmological spacetimes with Big Bang singularities and show that appropriately rescaled waves converge against a blow-up profile. Our class of spacetimes includes Friedman-Lema\^itre-Robertson-Walker (FLRW) spacetimes with negative sectional curvature that solve the Eins...

Gisonni, Massimo Grava, Tamara Ruzza, Giulio
Published in
Letters in Mathematical Physics

We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles. We also provide effective formulæ for generating functions of multipoint correlators of the Jacobi Unitary ...

Pérez-Sánchez, Carlos I
Published in
Letters in mathematical physics

We focus on functional renormalization for ensembles of several (say n ≥ 1 ) random matrices, whose potentials include multi-traces, to wit, the probability measure contains factors of the form exp [ - Tr ( V 1 ) × ⋯ × Tr ( V k ) ] for certain noncommutative polynomials V 1 , … , V k ∈ C ⟨ n ⟩ in the n matrices. This article shows how the "algebra ...

Marcelli, Giovanna

We consider time-dependent perturbations which are relatively bounded with respect to the square root of an unperturbed Hamiltonian operator, and whose commutator with the latter is controlled by the full perturbed Hamiltonian. The perturbation is modulated by two auxiliary parameters, one regulates its intensity as a prefactor and the other one co...

Kunduri, Hari K. Lucietti, James
Published in
Letters in Mathematical Physics

We prove uniqueness and existence theorems for four-dimensional asymptotically flat, Ricci-flat, gravitational instantons with a torus symmetry. In particular, we prove that such instantons are uniquely characterised by their rod structure, which is data that encode the fixed point sets of the torus action. Furthermore, we establish that for every ...

Buchholz, Detlev Ciolli, Fabio Ruzzi, Giuseppe Vasselli, Ezio

A universal C*-algebra of gauge invariant operators is presented, describing the electromagnetic field as well as operations creating pairs of static electric charges having opposite signs. Making use of Gauss' law, it is shown that the string-localized operators, which necessarily connect the charges, induce outer automorphisms of the algebra of t...

Henheik, Joscha Teufel, Stefan Wessel, Tom
Published in
Letters in Mathematical Physics

Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations pertu...

Merkulov, Sergei Živković, Marko
Published in
Letters in Mathematical Physics

We prove that the action of the Grothendieck–Teichmüller group on the genus completed properad of (homotopy) Lie bialgebras commutes with the reversing directions involution of the latter. We also prove that every universal quantization of Lie bialgebras is homotopy equivalent to the one which commutes with the duality involution exchanging Lie bra...

Baseilhac, Pascal
Published in
Letters in Mathematical Physics

The equitable presentation of the quantum algebra Uq(sl2^)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_q(\widehat{sl_2})$$\end{document} is considered. This presen...