Torsion on Hyperbolic Manifolds and the Semiclassical Limit for Chern–simons Theory

Abstract

The invariant integration method for Chern-Simons theory for gauge group SU (2) and manifold Γ\H 3 is verified in the semiclassical approximation. The semiclassical limit for the partition function associated with a connected sum of hyperbolic 3-manifolds is presented. We discuss briefly L 2 − analytical and topological torsions of a manifold with boundary.

Exact Holography and Black Hole Entropy in N = 8 $$ \mathcal{N}=8 $$ and N = 4 $$ \mathcal{N}=4 $$ String Theory

“…The component Z 1-loop arises from the determinant over the non-zero modes. This determinant consists of two different contributions: one is a local contribution coming from a zeta function regularized determinant which is topological [60,61], and so it does not depend on either r or |Γ|. The other contribution comes from the zero modes, which we now describe.…”

Semiclassical approximation for Chern-Simons theory and 3-hyperbolic invariants

“…In addition the cohomology H(M; Ad ξ) of M with respect to the local system related to Ad ξ vanishes. Date: May, 1999. This note is an extension of the two previous papers [13,14]. Here our aim is to use again the invariant integration method [15,16] in its simplest form in order to evaluate the semiclassical approximation in the Chern-Simons theory.…”

Heat-kernel asymptotics of locally symmetric spaces of rank one and Chern-Simons invariants

“…For real hyperbolic manifolds of the form Γ\H 3 the dependence of the L 2 − analytic torsion (1.8) on zeta functions can be expressed in terms of Selberg functions Z Γ (s; χ). In the presence of non-vanishing Betti numbers b i ≡ b i (X) = rank Z H i (X Γ ; Z)) we have [ 11,14] [T (2) an…”

“…(1.8) This note is an extension of previous papers [ 11,12,13,14,15,16,17,18]. Our aim is to evaluate the semiclasssical partition function, weighted by exp[ √ −1kCS(A)].…”