Publication 24-CNA-016

Variational Dual Solutions of Chern-Simons Theory

Amit Acharya
Dept. of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
acharyaamit@cmu.edu

Janusz Ginster
Weierstrass Institute
Berlin, Germany
ginster@wias-berlin.de

Ambar N. Sengupta
Department of Mathematics
University of Connecticut
Storrs, CT 06269
ambarnsg@gmail.com

Abstract: A scheme for generating weakly lower semi-continuous action functionals corresponding to the Euler-Lagrange equations of Chern-Simons theory is described. Coercivity is deduced for such a functional in appropriate function spaces to prove the existence of a minimizer, which constitutes a solution to the Euler-Lagrange equations of Chern-Simons theory in a relaxed sense. A geometric analysis is also made, especially for the gauge group SU(2), relating connection forms on the bundle to corresponding forms in the dual scheme.

Get the paper in its entirety as  24-CNA-016.pdf

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