On exact correlation functions of chiral ring operators in 2d mathcal{N}=left(2, 2right) SCFTs via localization

Abstract

We study the extremal correlation functions of (twisted) chiral ring operators via superlocalization in mathcal{N}=left(2, 2right) superconformal field theories (SCFTs) with central charge c ≥ 3, especially for SCFTs with Calabi-Yau geometric phases. We extend the method in arXiv: 1602.05971 with mild modifications, so that it is applicable to disentangle operators mixing on S2 in nilpotent (twisted) chiral rings of 2d SCFTs. With the extended algorithm and technique of localization, we compute exactly the extremal correlators in 2d mathcal{N}=left(2, 2right) (twisted) chiral rings as non-holomorphic functions of marginal parameters of the theories. Especially in the context of Calabi-Yau geometries, we give an explicit geometric interpretation to our algorithm as the Griffiths transversality with projection on the Hodge bundle over Calabi-Yau complex moduli. We also apply the method to compute extremal correlators in Kähler moduli, or say twisted chiral rings, of several interesting Calabi-Yau manifolds. In the case of complete intersections in toric varieties, we provide an alternative formalism for extremal correlators via localization onto Higgs branch. In addition, as a spinoff we find that, from the extremal correlators of the top element in twisted chiral rings, one can extract chiral correlators in A-twisted topological theories.