Topological Chern-Simons Sigma Model

Abstract

We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N=4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N=4, one for N=5,6, and four for N=8. We construct the two types of N=4 topological theories, which we call A/B-models, in full detail. The A-model has been recently studied by Kapustin and Saulina. The B-model is new and it consists solely of a Chern-Simons term of a complex gauge field up to BRST-exact terms. We also compare the new theories with topological Yang-Mills theories and find some interesting connections. In particular, the A-model seems to offer a new perspective on Casson invariant and its relation to Rozansky-Witten theory.

31 pages, no figure; v2. references added

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Cited by in corpus (12)

• 1/2-BPS Wilson Loops and Vortices in ABJM Model
• Effective action of three-dimensional extended supersymmetric matter on gauge superfield background
• A profusion of $1/2$ BPS Wilson loops in $\mathcal{N}=4$ Chern-Simons-matter theories
• Low-energy effective actions in three-dimensional extended SYM theories
• Localization and Duality for ABJM Latitude Wilson Loops
• The Quantum Theory of Chern-Simons Supergravity
• Background field formalism and construction of effective action for N=2, d=3 supersymmetric gauge theories
• Three-dimensional N=4 supersymmetry in harmonic N=3 superspace
• Gravitational free energy in topological AdS/CFT
• A superspace description of Chern-Simons theory in Batalin-Vilkovisky formulation
• Boundary Conditions in Topological AdS${}_4$/CFT${}_3$
• A Topological Chern-Simons Sigma Model and New Invariants of Three-Manifolds