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N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant

Abstract

Gauge theory with a topological N=2 symmetry is discussed. This theory captures the de Rahm complex and Riemannian geometry of some underlying moduli space M and the partition function equals the Euler number {sub {chi}}(M) of M. Moduli spaces of instantons and of flat connections in 2 and 3 dimensions are explicitly dealt with. To motivate the constructions the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics are explained and a new kind of supersymmetric quantum mechanics is introduced, based on the Gauss-Codazzi equations. The gauge theory actions are interpreted from the Atiyah-Jeffrey point of view and related to super-symmetric quantum mechanics on spaces of connections. As a consequence of these considerations the Euler number {sub {chi}}(M) of the moduli space of flat connections as a generalization to arbitrary three-manifolds of the Casson invariant. The possibility of constructing a topological version of the Penner matrix model is also commented. (author). 63 refs.
Authors:
Blau, M; [1]  Thompson, G [2] 
  1. Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H
  2. Mainz Univ. (Germany). Inst. fuer Physik
Publication Date:
Nov 01, 1991
Product Type:
Technical Report
Report Number:
NIKHEF-H-91-28; MZ-TH-91-40.
Reference Number:
SCA: 662210; PA: AIX-24:039761; SN: 93000980286
Resource Relation:
Other Information: DN: This work was supported by the Netherlands Foundation for Fundamental Research of Matter (Stichting FOM) and the German Ministry for Research and Technology (Bundesministerium fuer Forschung und Technologie).; PBD: Nov 1991
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; UNIFIED GAUGE MODELS; TOPOLOGICAL MAPPING; GAUGE INVARIANCE; INSTANTONS; MODULAR STRUCTURES; PARTITION FUNCTIONS; QUANTUM FIELD THEORY; QUANTUM MECHANICS; RIEMANN SPACE; SPACE GROUPS; SUPERSYMMETRY; TOPOLOGY; 662210; UNIFIED THEORIES AND MODELS
OSTI ID:
10145395
Research Organizations:
Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H
Country of Origin:
Netherlands
Language:
English
Other Identifying Numbers:
Other: ON: DE93624029; CNN: Contract no. 06MZ760; TRN: NL92C0607039761
Availability:
OSTI; NTIS; INIS
Submitting Site:
NLN
Size:
[39] p.
Announcement Date:
Jul 05, 2005

Citation Formats

Blau, M, and Thompson, G. N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant. Netherlands: N. p., 1991. Web.
Blau, M, & Thompson, G. N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant. Netherlands.
Blau, M, and Thompson, G. 1991. "N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant." Netherlands.
@misc{etde_10145395,
title = {N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant}
author = {Blau, M, and Thompson, G}
abstractNote = {Gauge theory with a topological N=2 symmetry is discussed. This theory captures the de Rahm complex and Riemannian geometry of some underlying moduli space M and the partition function equals the Euler number {sub {chi}}(M) of M. Moduli spaces of instantons and of flat connections in 2 and 3 dimensions are explicitly dealt with. To motivate the constructions the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics are explained and a new kind of supersymmetric quantum mechanics is introduced, based on the Gauss-Codazzi equations. The gauge theory actions are interpreted from the Atiyah-Jeffrey point of view and related to super-symmetric quantum mechanics on spaces of connections. As a consequence of these considerations the Euler number {sub {chi}}(M) of the moduli space of flat connections as a generalization to arbitrary three-manifolds of the Casson invariant. The possibility of constructing a topological version of the Penner matrix model is also commented. (author). 63 refs.}
place = {Netherlands}
year = {1991}
month = {Nov}
}