1994/07/18 by Andrei Johansen · 21 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #BRST quantization #Black Holes and Theoretical Physics #Central charge #Cohomology #Current algebra #Geometry and complex manifolds #Invariant (physics) #Primary field #Superconformal algebra #Supermultiplet #Virasoro algebra #hep-th
paper · pdf · doi:10.1016/0550-3213(94)00408-7
published in Nuclear Physics B 436(1-2), 291-341 (Elsevier BV) · NBI-HE-94-34, Latex, 57 pages
arxiv created 1994/07/18 · openalex publication_date 1995/02/01 · arxiv updated 2011/07/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study a supersymmetric theory twisted on a Kähler four manifold M=Σ1 × Σ2 , where Σ1,2 are 2D Riemann surfaces. We demonstrate that it possesses a "left-moving" conformal stress tensor on Σ1 (Σ2) in a BRST cohomology, which generates the Virasoro algebra with the conventional commutation relations. The central charge of the Virasoro algebra has a purely geometric origin and is proportional to the Euler characteristic \c of the Σ2 (Σ1) surface. It is shown that this construction can be extended to include a realization of a Kac-Moody algebra in BRST cohomology with a level proportional to the Euler characteristic \c . This structure is shown to be invariant under renormalization group. A representation of the algebra W1+∞ in terms of a free chiral supermultiplet is also given. We discuss the role of instantons and a possible relation between the dynamics of 4D Yang-Mills theories and those of 2D sigma models.