Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-11-27
JHEP 0209 (2002) 023
Physics
High Energy Physics
High Energy Physics - Theory
28 pages, no figures; v2: added a footnote and one reference, corrected a typo
Scientific paper
10.1088/1126-6708/2002/09/023
I consider the semiclassical approximation of the graded Chern-Simons field theories describing certain systems of topological A type branes in the large radius limit of Calabi-Yau compactifications. I show that the semiclassical partition function can be expressed in terms of a certain (differential) numerical invariant which is a version of the analytic torsion of Ray and Singer, but associated with flat graded superbundles. I also discuss a `twisted' version of the Ray-Singer norm, and show its independence of metric data. As illustration, I consider graded D-brane pairs of unit relative grade with a scalar condensate in the boundary condition changing sector. For the particularly simple case when the reference flat connections are trivial, I show that the generalized torsion reduces to a power of the classical Ray-Singer invariant of the base 3-manifold.
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