Super-Chern-Simons Theory as Superstring Theory

Abstract

Superstrings and topological strings with supermanifolds as target space play a central role in the recent developments in string theory. Nevertheless the rules for higher-genus computations are still unclear or guessed in analogy with bosonic and fermionic strings. Here we present a common geometrical setting to develop systematically the prescription for amplitude computations. The geometrical origin of these difficulties is the theory of integration of superforms. We provide a translation between the theory of supermanifolds and topological strings with supertarget space. We show how in this formulation one can naturally construct picture changing operators to be inserted in the correlation functions to soak up the zero modes of commuting ghost and we derive the amplitude prescriptions from the coupling with an extended topological gravity on the worldsheet. As an application we consider a simple model on R^(3|2) leading to super-Chern-Simons theory.

hravmac, 50pp

References in corpus (12)

• ICTP Lectures on Covariant Quantization of the Superstring
• N=2 strings and the twistorial Calabi-Yau
• Covariant One-Loop Amplitudes in D=11
• Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring
• Mirror Symmetry and Supermanifolds
• Marginal Deformations of N=4 SYM from Open/Closed Twistor Strings
• Multigluon amplitudes, $\mathcal{N}=4$ constraints and the WZW model
• On the b-antighost in the Pure Spinor Quantization of Superstrings
• Topological Open Membranes
• Strings in Twistor Superspace and Mirror Symmetry
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• Algebraic structure of Yang-Mills theory

Cited by in corpus (23)

• Pure Spinor Formalism as an N=2 Topological String
• Conformal Sigma-Models on Supercoset Targets
• Supergravity Actions with Integral Forms
• D=11 massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries
• Lower-dimensional pure-spinor superstrings
• Partition Functions of Pure Spinors
• Kappa-symmetry for coincident D-branes
• Cech and de Rham Cohomology of Integral Forms
• Hodge Dualities on Supermanifolds
• Comments on BRST quantization of strings
• Chern-Simons Theory on Supermanifolds
• Partition Functions, Localization, and the Chiral de Rham complex
• Super Chern-Simons Theory: BV-formalism and $A_{\infty }$-algebras
• String Theories on Flat Supermanifolds
• Gauged Linear Sigma Model on Supermanifold
• Chern-Simons theory in the SO(5)/U(2) harmonic superspace
• Superconformal Symmetry in Linear Sigma Model on Supermanifolds
• Integration of Superforms and Super-Thom Class
• Entropy Current Formalism for Supersymmetric Theories
• On perturbative field theory and twistor string theory
• Balanced Superprojective Varieties
• Twistor Spaces, Mirror Symmetry and Self-dual Kahler Manifolds
• Power to Integral Forms