Chern-Simons Theory on Supermanifolds

Abstract

We consider quantum field theories on supermanifolds using integral forms. The latter are used to define a geometric theory of integration and they are essential for a consistent action principle. The construction relies on Picture Changing Operators, analogous to the one introduced in String Theory. As an application, we construct a geometric action principle for N=1 D=3 super-Chern-Simons theory.

21 pages, 1 table

References in corpus (10)

• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• Resolving Witten's Superstring Field Theory
• Supergravity Actions with Integral Forms
• Osp(N|4) supermultiplets as conformal superfields on \partial AdS_4 and the generic form of N=2, D=3 gauge theories
• The Geometry of Supermanifolds and New Supersymmetric Actions
• New Geometrical Approach to Superstrings
• Picture changing operators in supergeometry and superstring theory
• Super-Chern-Simons Theory as Superstring Theory
• Hodge Dualities on Supermanifolds
• Cech and de Rham Cohomology of Integral Forms

Cited by in corpus (12)

• The Integral Form of Supergravity
• The Chern-Simons current in systems of DNA-RNA transcriptions
• M5-brane in the superspace approach
• Anomaly on Superspace of Time Series Data
• Pictures from Super Chern-Simons Theory
• Super Chern-Simons Theory: BV-formalism and $A_{\infty }$-algebras
• Self-Dual Forms in Supergeometry I: The Chiral Boson
• Supersymmetric Wilson Loops via Integral Forms
• Chern-Simons Supergravity on Supergroup Manifolds
• The Integral Form of D=3 Chern-Simons Theories Probing ${\mathbb{C}}^n/\Gamma$ Singularities
• Super AKSZ construction, integral forms, and the 2-dimensional $\mathcal{N}=(1,1)$ sigma model
• Power to Integral Forms