Topological anomalies for Seifert 3-manifolds

Abstract

We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our approach the Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the topological gravity BRST transformations. A cohomological characterization of the geometrical moduli which affect the partition function is obtained. In the Seifert context Chern-Simons topological (framing) anomaly is BRST trivial. We compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of 3d supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant.

31 pages; v2: some comments added, references added; v3: published version, 1+34 pages, one appendix explaining the relation with the supergravity approach added, minor comments and two references added

References in corpus (4)

• Notes on SUSY Gauge Theories on Three-Sphere
• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• Three-Dimensional Superconformal Field Theory on Conic Space as Hologram of Charged Topological Black Hole
• The Coupling of Chern-Simons Theory to Topological Gravity

Cited by in corpus (17)

• Comments on twisted indices in 3d supersymmetric gauge theories
• Localization on three-dimensional manifolds
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• How to resum perturbative series in 3d N=2 Chern-Simons matter theories
• Introduction to localization in quantum field theory
• An introduction to supersymmetric field theories in curved space
• $q$-Virasoro modular double and 3d partition functions
• Supersymmetry anomalies in $\mathcal{N}=1$ conformal supergravity
• $\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries
• Localization on $Ad{S}_2\times S^1$
• New Supersymmetric Localizations from Topological Gravity
• Supersymmetry anomalies in new minimal supergravity
• The topological structure of supergravity: an application to supersymmetric localization
• Deformations of Supergravity and Supersymmetry Anomalies
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Topological phase, spin Chern-Simons theory and level rank duality on lens space
• The coupling of Poisson sigma models to topological backgrounds