Schwinger-Keldysh formalism. Part II: thermal equivariant cohomology [PDF]
Journal of High Energy Physics, 2017 Causally ordered correlation functions of local operators in near-thermal quantum systems computed using the Schwinger-Keldysh formalism obey a set of Ward identities.
Felix M. Haehl +2 more
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Topological correlators and surface defects from equivariant cohomology
Journal of High Energy Physics, 2020 We find a one-dimensional protected subsector of N $$ \mathcal{N} $$ = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the ...
Rodolfo Panerai +2 more
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BRST quantization and equivariant cohomology: localization with asymptotic boundaries [PDF]
Journal of High Energy Physics, 2018 We develop BRST quantization of gauge theories with a soft gauge algebra on spaces with asymptotic boundaries. The asymptotic boundary conditions are imposed on background fields, while quantum fluctuations about these fields are described in terms of ...
Bernard de Wit +2 more
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Twisting and localization in supergravity: equivariant cohomology of BPS black holes [PDF]
Journal of High Energy Physics, 2019 We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in [1].
Imtak Jeon, Sameer Murthy
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Equivariant smooth Deligne cohomology [PDF]
arXiv, 2003 On the basis of Brylinski's work, we introduce a notion of equivariant smooth Deligne cohomology group, which is a generalization of both the ordinary smooth Deligne cohomology and the ordinary equivariant cohomology. Using the cohomology group, we classify equivariant circle bundles with connection, and equivariant gerbes with connection.
Kiyonori Gomi
arxiv +3 more sources
Hopf Algebra Equivariant Cyclic Cohomology, K-theory and Index Formulas [PDF]
arXiv, 2003 For an algebra B with an action of a Hopf algebra H we establish the pairing between even equivariant cyclic cohomology and equivariant K-theory for B. We then extend this formalism to compact quantum group actions and show that equivariant cyclic cohomology is a target space for the equivariant Chern character of equivariant summable Fredholm modules.
Sergey Neshveyev, Lars Tuset
arxiv +3 more sources
A new description of equivariant cohomology for totally disconnected groups [PDF]
arXiv, 2004 We consider smooth actions of totally disconnected groups on simplicial complexes and compare different equivariant cohomology groups associated to such actions. Our main result is that the bivariant equivariant cohomology theory introduced by Baum and Schneider can be described using equivariant periodic cyclic homology.
Christian Voigt
arxiv +3 more sources
Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation [PDF]
Entropy, 2020 In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space of evolution” associated to
Frédéric Barbaresco
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An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson [PDF]
arXiv, 2005 This paper provides an introduction to equivariant cohomology and homology using the approach of Goresky, Kottwitz, and MacPherson. When a group G acts suitably on a variety X, the equivariant cohomology of X can be computed using the combinatorial data of a skeleton of G-orbits on X.
Julianna Tymoczko
arxiv +3 more sources
Schubert Classes in the Equivariant K-Theory and Equivariant Cohomology of the Lagrangian Grassmannian [PDF]
arXiv, 2006 We give positive formulas for the restriction of a Schubert Class to a T-fixed point in the equivariant K-theory and equivariant cohomology of the Lagrangian Grassmannian. Our formulas rely on a result of Ghorpade-Raghavan, which gives an equivariant Grobner degeneration of a Schubert variety in the neighborhood of a T-fixed point of the Lagrangian ...
Victor Kreiman
arxiv +3 more sources