2D BPS Rings from Sphere Partition Functions

Abstract

We consider extremal correlation functions, involving arbitrary number of BPS (chiral or twisted chiral) operators and exactly one anti-BPS operator in 2D N=(2,2) theories. These correlators define the structure constants in the rings generated by the BPS operators with their operator product expansions. We present a way of computing these correlators from the sphere partition function of a deformed theory using localization. Relating flat space and sphere correlators is nontrivial due to operator mixing on the sphere induced by conformal anomaly. We discuss the supergravitational source of this complication and a resolution thereof. Finally, we demonstrate the process for the Quintic GLSM and the Landau-Ginzburg minimal models.

39 pages, 3 figures. Corrected typos and added references

References in corpus (5)

• Sphere Partition Functions and the Zamolodchikov Metric
• $t{t}^{\ast }$ equations, localization and exact chiral rings in 4d N=2 SCFTs
• Comments on N=(2,2) Supersymmetry on Two-Manifolds
• The chiral ring of AdS3/CFT2 and the attractor mechanism
• On exact correlation functions of chiral ring operators in $2d$ $\mathcal{N}=(2,2)$ SCFTs via localization

Cited by in corpus (4)

• Extremal Correlators and Random Matrix Theory
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Twisted Massive Non-Compact Models
• Disordered $\mathcal{N}=(2,2)$ Supersymmetric Field Theories