Klinker, Frank
Published in
Communications in Mathematical Physics

In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo-) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the one hand and spinor fields on the other hand as equivalent geometric objects. This is the starting point of our...

Rembado, Gabriele
Published in
Communications in Mathematical Physics

We construct a new family of flat connections generalising the KZ connection, the Casimir connection and the dynamical connection. These new connections are attached to simply-laced graphs, and are obtained via quantisation of time-dependent Hamiltonian systems controlling the isomonodromic deformations of meromorphic connections on the sphere.

Zheng, Fan
Published in
Communications in Mathematical Physics

We study a basic plasma physics model—the one-fluid Euler–Poisson system on the square torus, in which a compressible electron fluid flows under its own electrostatic field. In this paper we prove long-term regularity of periodic solutions of this system in 2 spatial dimensions with small data. Our main conclusion is that on a square torus of side ...

Breunhölder, Veronika Lucietti, James
Published in
Communications in Mathematical Physics

We determine all asymptotically flat, supersymmetric and biaxisymmetric soliton and black hole solutions to five-dimensional minimal supergravity. In particular, we show that the solution must be a multi-centred solution with a Gibbons–Hawking base. The proof involves combining local constraints from supersymmetry with global constraints for statio...

Oh, Se-jin Scrimshaw, Travis
Published in
Communications in Mathematical Physics

We first compute the denominator formulas for quantum affine algebras of all exceptional types. Then we prove the isomorphisms among Grothendieck rings of categories CQ(t)(t=1,2,3),CQ(1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepac...

Correggi, Michele Giuliani, Alessandro Seiringer, Robert
Published in
Communications in Mathematical Physics

We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins S ≥ 1/2. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution to the free energy at low temperatures. Our proof comes with explicit, constructive upper and lower bounds ...

Correa, Eder M.
Published in
Communications in Mathematical Physics

In the present work we provide a constructive method to describe contact structures on compact homogeneous contact manifolds. The main feature of our approach is to describe the Cartan–Ehresmann connection (gauge field) for principal U(1)-bundles over complex flag manifolds by using elements of representation theory of simple Lie algebras. This des...

Strauss, Walter A. Wu, Yilun
Published in
Communications in Mathematical Physics

A rotating star may be modeled as a continuous system of particles attracted to each other by gravity and with a given total mass and prescribed angular velocity. Mathematically this leads to the Euler–Poisson system. We prove an existence theorem for such stars that are rapidly rotating, depending continuously on the speed of rotation. This solves...

Monnier, Samuel
Published in
Communications in Mathematical Physics

We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such a...

Gheissari, Reza Hongler, Clément Park, S. C.
Published in
Communications in Mathematical Physics

We study the 2-dimensional Ising model at critical temperature on a simply connected subset Ωδ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Omega_{\delta}}$$\end{do...