Topological Chern-Simons/Matter Theories

Abstract

We propose a new partially topological theory in three dimensions which couples Chern-Simons theory to matter. The 3-manifolds needed for this construction admit transverse holomorphic foliation (THF). The theory depends only on the choice of such a structure, but not on a choice of metric and in this sense, it is topological. We argue that this theory arises in topological A-model string theory on Lagrangian 3-branes in the presence of additional parallel coisotropic 5-branes. The theory obtained in this way is equivalent to an N=2 supersymmetric Chern-Simons matter theory on the same 3-manifold, which also only depends on the THF structure. The theory is a realization of a topological theory of class H, which allows splitting of a temporal direction from spatial directions. We briefly discuss potential condensed matter applications.

50 pages, 1 figure. v2: references added

References in corpus (11)

• Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
• The Geometry of Supersymmetric Partition Functions
• Supersymmetry on Curved Spaces and Holography
• Remarks on A-branes, Mirror Symmetry, and the Fukaya category
• Topological strings on noncommutative manifolds
• Generalized Superconformal Index for Three Dimensional Field Theories
• Supersymmetric gauge theory and the Yangian
• Braided fusion categories, gravitational anomalies, and the mathematical framework for topological orders in any dimensions
• A-branes and Noncommutative Geometry
• M-theory in the Omega-background and 5-dimensional non-commutative gauge theory
• Lectures on Mirror Symmetry, Derived Categories, and D-branes

Cited by in corpus (14)

• Field Theories With a Vector Global Symmetry
• Dual Boundary Conditions in 3d SCFT's
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Quantum K theory of symplectic Grassmannians
• Holomorphic field theories and Calabi--Yau algebras
• ABJ Quadrality
• Monopole Operators and Bulk-Boundary Relation in Holomorphic Topological Theories
• On Phases of 3d $\mathcal{N}=2$ Chern-Simons-Matter Theories
• Remarks on Berry Connection in QFT, Anomalies, and Applications
• Factorization Algebras for Bulk-Boundary Systems
• A String Dual for Partially Topological Chern-Simons-Matter Theories
• Local Operators from the Space of Vacua of Four Dimensional SUSY Gauge Theories
• Holomorphic boundary conditions for topological field theories via branes in twisted supergravity
• Integrable models from 4d holomorphic BF theory