Hilbert space of curved βγsystems on quadric cones

Abstract

We clarify the structure of the Hilbert space of curved βγsystems defined by a quadratic constraint. The constraint is studied using intrinsic and BRST methods, and their partition functions are shown to agree. The quantum BRST cohomology is non-empty only at ghost numbers 0 and 1, and there is a one-to-one mapping between these two sectors. In the intrinsic description, the ghost number 1 operators correspond to the ones that are not globally defined on the constrained surface. Extension of the results to the pure spinor superstring is discussed in a separate work.

45 pages

References in corpus (6)

• Chiral de Rham complex and the half-twisted sigma-model
• Two-Dimensional Models With (0,2) Supersymmetry: Perturbative Aspects
• On the cohomology and inner products of the Berkovits superparticle and superstring
• Partition Functions, Localization, and the Chiral de Rham complex
• Curved Beta-Gamma Systems and Quantum Koszul Resolution
• A simple BRST system with quadratically constrained ghosts

Cited by in corpus (10)

• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• One-loop Superstring Amplitude From Integrals on Pure Spinors Space
• The geometry of pure spinor space
• Hidden exceptional symmetry in the pure spinor superstring
• On quasimaps to quadrics
• Local algebra and string theory
• Partition function of beta-gamma system on orbifolds
• A formula for the partition function of the beta-gamma system on the cone pure spinors
• Straightened law for quantum isotropic Grassmannian OGr^+(5,10)
• Beta-gamma system, pure spinors and Hilbert series of arc spaces