Curved Beta-Gamma Systems and Quantum Koszul Resolution

Abstract

We consider the partition function of beta-gamma systems in curved space of the type discussed by Nekrasov and Witten. We show how the Koszul resolution theorem can be applied to the computation of the partition functions and to characters of these systems and find a prescription to enforce the hypotheses of the theorem at the path integral level. We illustrate the technique in a few examples: a simple 2-dimensional target space, the N-dimensional conifold, and a superconifold. Our method can also be applied to the Pure Spinor constraints of superstrings.

harvmac, 17 pages

References in corpus (7)

• Current Algebras and Differential Geometry
• Covariant Quantization of Superstrings Without Pure Spinor Constraints
• Lectures on curved beta-gamma systems, pure spinors, and anomalies
• Chiral de Rham complex and the half-twisted sigma-model
• Two-Dimensional Models With (0,2) Supersymmetry: Perturbative Aspects
• Lower-dimensional pure-spinor superstrings
• Partition Functions of Pure Spinors

Cited by in corpus (5)

• Partition Functions, Localization, and the Chiral de Rham complex
• Hilbert space of curved βγsystems on quadric cones
• Grassmannian Sigma Models
• A simple BRST system with quadratically constrained ghosts
• Beta-gamma system, pure spinors and Hilbert series of arc spaces