Chern-Simons theory on S1-bundles: Abelianisation and q-deformed Yang-Mills theory - INSPIRE

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Chern-Simons theory on S1-bundles: Abelianisation and q-deformed Yang-Mills theory

Matthias Blau
(
- Neuchatel U.
)
,
George Thompson
(
- ICTP, Trieste
)

Jan, 2006

38 pages

Published in:

JHEP 05 (2006) 003

e-Print:

hep-th/0601068 [hep-th]

DOI:

10.1088/1126-6708/2006/05/003

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Abstract:

We study Chern-Simons theory on 3-manifolds

M

that are circle-bundles over 2-dimensional surfaces

\Sigma

and show that the method of Abelianisation, previously employed for trivial bundles

\Sigma \times S^1

, can be adapted to this case. This reduces the non-Abelian theory on

M

to a 2-dimensional Abelian theory on

\Sigma

which we identify with q-deformed Yang-Mills theory, as anticipated by Vafa et al. We compare and contrast our results with those obtained by Beasley and Witten using the method of non-Abelian localisation, and determine the surgery and framing presecription implicit in this path integral evaluation. We also comment on the extension of these methods to BF theory and other generalisations.

gauge field theory: Yang-Mills
Chern-Simons term
field theory: deformation
fibre bundle: S(1)
BF model
operator: determinant
differential forms: symplectic
differential geometry
cohomology
group: Weyl

References(22)

Figures(0)

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