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  Ground State Degeneracy of 2+1D U(1) Chern Simons Theory?

+ 4 like - 0 dislike

I am a physics graduate student trying to understand more mathematical aspects of gauge theories.

How can I understand ground state degeneracy of a simple Chern Simons Theory: 2+1D U(1) $S= \int_M kAdA$ for different k- values (integers, rationals, irrationals?) on torus or other manifolds in a more mathematics/differential geometry oriented way? I have seen the calculation in physics literature, but I cant figure out how to translate it in differential geometry language.

I know it must be there somewhere in literature, but I am not able to find it. Thank you for your help.

This post imported from StackExchange MathOverflow at 2014-11-02 16:32 (UTC), posted by SE-user ShuklaS
asked Oct 29, 2014 in Theoretical Physics by ShuklaS (20 points) [ no revision ]
retagged Nov 2, 2014
If you want to ask questions to mathematicians, it is important that you learn which words they can understand. For example: "ground state" is better understood by mathematicians as "lowest energy eigenspace" (in which case you should also specify which Hamiltonian you are talking the eigenvalues of, otherwise mathematicians will again complain that they don't know what you're talking about). Also "degeneracy" in math is called "of dimension greater than one"...

This post imported from StackExchange MathOverflow at 2014-11-02 16:32 (UTC), posted by SE-user André Henriques
Have you read the paper by Axelrod-DellaPietra-Witten on the subject?

This post imported from StackExchange MathOverflow at 2014-11-02 16:32 (UTC), posted by SE-user André Henriques

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