Kelly Jay Davis | Searcharxiv

arXiv1994

A-Genus and the Sigma Model

This set of lecture notes presents a pedantic derivation of the connection between the $ {\hat A} $-genus of spacetime's loop space and the genus one partition function of the $ N=1/2 $ sigma model. It concludes with some remarks on possible generalizations of the $ {\hat A} $-genus which follow naturally from the `stringy' point-of-view but have yet to be explored mathematically. This set of lecture notes is geared towards a mathematical audience unfamiliar with the $ N=1/2 $ sigma model.

hep-th↗

arXiv1993

The Zamolodchikov C-Function, Classical Closed String Field Theory, The Duistermaat-Heckman Theorem, The Renormalization Group, and all that

In this article we formulate a `topological' field theory by employing a generalization of the Duistermaat-Heckman Theorem to localize the path-integral of the `topological action' C^2 , where C is a slight modification of the Zamolodchikov C-Function, over the space of all two-dimensional field theories to the fixed points of the renormalization group's identity component. Also, we propose an interpretation of the background independent classical closed string field theory action S in terms of the Zamolodchikov C-Function's modification.

hep-th↗