An analytic torsion for graded D-branes

Abstract

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.

28 pages, no figures; v2: added a footnote and one reference, corrected a typo

References in corpus (10)

• Derived Categories and Zero-Brane Stability
• D-Brane Stability and Monodromy
• Enhanced D-Brane Categories from String Field Theory
• Generalized complexes and string field theory
• String field theory and brane superpotentials
• Holomorphic potentials for graded D-branes
• Unitarity, D-brane dynamics and D-brane categories
• Graded Lagrangians, exotic topological D-branes and enhanced triangulated categories
• Graded Chern-Simons field theory and graded topological D-branes
• Gauge-fixing, semiclassical approximation and potentials for graded Chern-Simons theories

Cited by in corpus (3)

• On the boundary coupling of topological Landau-Ginzburg models
• Localization and traces in open-closed topological Landau-Ginzburg models
• D-brane effective action and tachyon condensation in topological minimal models