How to calculate the correlation function in twisted SYM \(N=2\), \(N_f=4\) QFT on a projective plane
type: Item
instance of: scholarly article
title: How to calculate the correlation function in twisted SYM \(N=2\), \(N_f=4\) QFT on a projective plane
zbMATH Open document ID: 0944.57023
DOI: 10.1007/BF02362465
author: M. Leenson
author: A. L. Gorodentsev
published in: Journal of Mathematical Sciences (New York)
publication date: 1997-11-06T00:00:00Z
review text: Let \({\mathfrak M}\) be the moduli space of \(\mu\)-stable torsion-free coherent sheaves \(F\) with \(\text{rk} (F)=2\), \(c_1(F)=-1\), \(c_2(F)=k\) on \(P_2(C)\) and \({\mathcal G}\) the universal bundle on \({\mathfrak M}\). The sequence of the topological constants \(a_k=c_{4k-4} ({\mathcal G}^{\otimes 4})\) appears as coefficients of the correlation function in the \(N=2\), \(N_f=4\) supersymmetric Yang-Mills theory with \(SO(3)\) gauge group [\textit{Ch. Okonek}, \textit{M. Schneider}, and \textit{H. Spindler}, Vector bundles on complex projective spaces, Prog. Math. 3 (1980; Zbl 0438.32016)]. One explains how to calculate the coefficients \(a_k\) for SYM \(N=2\) \(SO(3)\)-gauge QFT with four flavors (spinor fields) in terms of top Chern classes of \({\mathcal G}\), and one calculates several initial coefficients \((k=1,2, \dots,7)\) via the Bott residue formula. A geometrical description of the moduli spaces with 2-dimensional torus action on them is given. See also [\textit{A. L. Gorodentsev}, in ``Algebraic geometry and its applications'', Aspects Math. E 25, 47-59 (1994; Zbl 0845.14011)].
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 58D29
Mathematics Subject Classification ID: 81R25
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 57R22
Mathematics Subject Classification ID: 57R56
zbMATH DE Number: 1017619
zbMATH Keywords: gauge group
zbMATH Keywords: Yang-Mills theory
zbMATH Keywords: supersymmetry
reviewed by: Maido Rahula
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1017619