1994/07/07 by Matthias Blau, G.E. Thompson, George Thompson · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Commutator #Equivariant map #Gauge group #Gauge theory #Group (periodic table) #Infinitesimal #Lie algebra #Lie conformal algebra #Lie group #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Supersymmetry #Symplectic geometry #hep-th
paper · pdf · doi:10.1016/0550-3213(95)00058-z
published as Nucl.Phys. B439 (1995) 367-394 · LaTex file, 40 A4 pages, IC/94/108 and ENSLAPP-L-469/94
arxiv created 1994/07/07 · openalex publication_date 1995/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We analyze in detail the equivariant supersymmetry of the G/G model. In spite of the fact that this supersymmetry does not model the infinitesimal action of the group of gauge transformations, localization can be established by standard arguments. The theory localizes onto reducible connections and a careful evaluation of the fixed point contributions leads to an alternative derivation of the Verlinde formula for the Gk WZW model. We show that the supersymmetry of the G/G model can be regarded as an infinite dimensional realization of Bismut's theory of equivariant Bott-Chern currents on Kähler manifolds, thus providing a convenient cohomological setting for understanding the Verlinde formula. We also show that the supersymmetry is related to a non-linear generalization (q-deformation) of the ordinary moment map of symplectic geometry in which a representation of the Lie algebra of a group G is replaced by a representation of its group algebra with commutator [g,h] = gh-hg. In the large k limit it reduces to the ordinary moment map of two-dimensional gauge theories.