Partition Functions, Localization, and the Chiral de Rham complex

Abstract

We propose a localization formula for the chiral de Rham complex generalizing the well-known localization procedure in topological theories. Our formula takes into account the contribution due to the massive modes. The key to achieve this is to view the non-linear beta-gamma system as a gauge theory. For abelian gauge groups we are in the realm of toric geometry. Including the b-c system, the formula reproduces the known results for the elliptic genus of toric varieties. We compute the partition function of several models.

52 pages, Latex, no figures

References in corpus (23)

• Phases of $N=2$ Theories In Two Dimensions
• Super-Poincare Covariant Quantization of the Superstring
• Mirror Manifolds And Topological Field Theory
• Integrating Over Higgs Branches
• ICTP Lectures on Covariant Quantization of the Superstring
• Elliptic Genera and Applications to Mirror Symmetry
• 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
• Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals
• Two-Dimensional Models With (0,2) Supersymmetry: Perturbative Aspects
• Mirror symmetry in two steps: A-I-B
• Instantons beyond topological theory II
• Equivariant Localization of Path Integrals
• Super-Chern-Simons Theory as Superstring Theory
• Chiral Poincaré duality
• Partition Functions of Pure Spinors
• Lower-dimensional pure-spinor superstrings
• Quantum Field Theory as Effective BV Theory from Chern-Simons
• Toric Geometry and Calabi-Yau Compactifications
• Curved Beta-Gamma Systems and Quantum Koszul Resolution
• Two-Dimensional Twisted Sigma Models And The Theory of Chiral Differential Operators
• The Half-Twisted Orbifold Sigma Model and the Chiral de Rham Complex

Cited by in corpus (10)

• Elliptic genera of 2d N=2 gauge theories
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Hilbert space of curved βγsystems on quadric cones
• The $\mathsf{C}{\mathsf{P}}^{\mathsf{n}-1}$-model with fermions: a new look
• On Projections to the Pure Spinor Space
• Y-Formalism and Curved Beta-Gamma Systems
• The Half-Twisted Orbifold Sigma Model and the Chiral de Rham Complex
• A simple BRST system with quadratically constrained ghosts
• Beta-gamma system, pure spinors and Hilbert series of arc spaces
• Mixed anomalies of chiral algebras compactified to smooth quasi-projective surfaces