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I have studied Chern-Simons (CS) theory somewhat and I am puzzled by the question of how diff. and gauge invariance in CS theory are related, e.g. in $SU(2)$ CS theory. In particular, I would like to know about the relation between large gauge transformations and large diffeos. If you know any good sources, I would be really grateful. Thank you!

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Maybe you're talking about this?… – Siva Apr 1 '13 at 7:29
The context here is U(1) CS, but it may be useful background if you haven't seen it already – twistor59 Apr 2 '13 at 18:29
up vote 5 down vote accepted

A useful textbook for your purposes is "Gravitation and gauge symmetries" by M. Blagojevic (IOP, 2002). It has a chapter on Chern-Simons theory and its relation to 3-dimensional gravity.

If that textbook is not accessible to you I suggest that you look at Max Banados' talk or Steve Carlip's review

The first two section of Ed Witten's paper and references therein should also be useful.

BTW, the SL(2)xSL(2) Chern-Simons theory is basically the "Palatini" formulation of 3D gravity in terms of Cartan variables (dreibein and dualized spin connection). It is a unique feature of 3 dimensions that you can linearly combine the Vielbein with the dualized connection, since only in 3 dimensions the dual of an antisymmetric tensor is a vector. The gauge symmetries of this Chern-Simons theory correspond to diffeos and local Lorentz trafos (at least on-shell).

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Take a look at the book "Lecture notes on Chern-Simons-Witten theory" by Sen Hu, it consists of notes of Witten's lectures on the subject. You can easily download it with google search "lecture notes on chern-simons-witten theory djvu". I am not a specialist, but it seems that in classical theory the action is invariant with respect to diffeomorphisms and not gauge invariant. Though the theory is well-defined if the action takes integer values. So the constant k is quantized. There are some subtleties with boundary data, I hope the book can clarify these.

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