13,061 research outputs found
Three-Dimensional Extended Bargmann Supergravity
We show that three-dimensional General Relativity, augmented with two vector
fields, allows for a non-relativistic limit, different from the standard limit
leading to Newtonian gravity, that results into a well-defined action which is
of the Chern-Simons type. We show that this three-dimensional `Extended
Bargmann Gravity', after coupling to matter, leads to equations of motion
allowing a wider class of background geometries than the ones that one
encounters in Newtonian gravity. We give the supersymmetric generalization of
these results and point out an important application in the context of
calculating partition functions of non-relativistic field theories using
localization techniques.Comment: 6 pages, v2: typo's corrected, reference updated, accepted for
publication in Phys. Rev. Let
Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
We study dynamical optimal transport metrics between density matrices
associated to symmetric Dirichlet forms on finite-dimensional -algebras.
Our setting covers arbitrary skew-derivations and it provides a unified
framework that simultaneously generalizes recently constructed transport
metrics for Markov chains, Lindblad equations, and the Fermi
Ornstein--Uhlenbeck semigroup. We develop a non-nommutative differential
calculus that allows us to obtain non-commutative Ricci curvature bounds,
logarithmic Sobolev inequalities, transport-entropy inequalities, and spectral
gap estimates
Newton-Cartan supergravity with torsion and Schr\"odinger supergravity
We derive a torsionfull version of three-dimensional N=2 Newton-Cartan
supergravity using a non-relativistic notion of the superconformal tensor
calculus. The "superconformal" theory that we start with is Schr\"odinger
supergravity which we obtain by gauging the Schr\"odinger superalgebra. We
present two non-relativistic N=2 matter multiplets that can be used as
compensators in the superconformal calculus. They lead to two different
off-shell formulations which, in analogy with the relativistic case, we call
"old minimal" and "new minimal" Newton-Cartan supergravity. We find
similarities but also point out some differences with respect to the
relativistic case.Comment: 30 page
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