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.
Blau, M;
[1]
Thompson, G
[2]
- Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H
- Mainz Univ. (Germany). Inst. fuer Physik
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}
}
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}
}