Non-Abelian localization for Chern-Simons theory

By C. Beasley, E. Witten. 2005

165 citations recorded by the source corpus.

We reconsider Chern-Simons gauge theory on a Seifert manifold M (the total space of a nontrivial circle bundle over a Riemann surface). When M is a Seifert manifold, Lawrence and Rozansky have shown from the exact solution of Chern-Simons theory that the partition function has a remarkably simple structure and can be rewritten entirely as a sum of local contributions from the flat connections on M. We explain how this empirical fact follows from the technique of non-abelian localization as applied to the Chern-Simons path integral. In the process, we show that the partition function of Chern-Simons theory on M admits a topological interpretation in terms of the equivariant cohomology of the moduli space of flat connections on M.

Subfields: Applied Mathematics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4e1edab7f4beb87d3cbb5cf1106d633b8d60568b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Marcos Mariño
2. M. Zabzine
3. J. Källén
4. Mina Aganagic
5. E. Witten
6. C. Vafa
7. H. Kanno
8. A. Klemm

In Mathematical Physics

1. Marcos Mariño
2. Mina Aganagic
3. Sh. Shakirov
4. E. Witten
5. C. Vafa
6. M. Zabzine
7. J. Källén
8. Sergei Gukov

In Nuclear and High Energy Physics

1. Marcos Mariño
2. Mina Aganagic
3. Sh. Shakirov
4. C. Vafa
5. Sergei Gukov
6. E. Witten
7. M. Zabzine
8. J. Källén

Citations in the corpus

• Analytic Continuation Of Chern-Simons Theory (2010, background): “This has apparently not been established in complete generality, though it can plausibly be done using localization formulas [32].”
• Twisted supersymmetric 5D Yang-Mills theory and contact geometry (2012, methodology): “The computation we will do is very similar to the ones performed in [1, 6, 15, 16], with a matrix model as the end result.”
• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere (2012, background): “The typical calculation of an additional phase in 3D Chern-Simons theory in the localization framework can be found in [38] (see also [17] for a discussion in a similar context), where it gives rise to the famous shift of the Chern-Simons level.”
• Knot Homology from Refined Chern-Simons Theory (2011, background): “A theory such as ours is in essence two dimensional, as all of its topological data can be phrased in terms of Σ [65,61].”
• Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, methodology): “It was later rederived using geometric localization techniques in [13], and Abelianization techniques in [17].”
• The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral (2020, unknown): “avity is closely related to a noncompact Chern-Simons theory [66], so we may be able to draw inspiration from previous studies of compact Chern-Simons theories on Seifert manifolds (some examples are [67,68]). Due to the emergence of the near-horizon AdS 2 region where quantum uctuations are importa”