On Derivation of Goldman Bracket

Abstract

In this paper, we obtain an infinite dimensional Lie algebra of exotic gauge invariant observables that is closed under Goldman-type bracket associated with monodromy matrices of flat connections on a compact Riemann surface for $G_2$ gauge group. As a by-product, we give an alternative derivation of known Goldman bracket for classical gauge groups $GL(n,\mathbb{R})$, $SL(n,\mathbb{R})$, $U(n)$, $SU(n)$, $Sp(2n,\mathbb{R})$ and $SO(n)$.

35 pages, possible applications added to the introduction, references added ,accepted version to appear in JHEP

References in corpus (1)

• M-Theory Dynamics On A Manifold Of G_2 Holonomy