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

Abstract

Abstract We study the extremal correlation functions of (twisted) chiral ring operators via superlocalization in $$ \mathcal{N}=\left(2,\ 2\right) $$ N = 2 , 2 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 S 2 in nilpotent (twisted) chiral rings of 2d SCFTs. With the extended algorithm and technique of localization, we compute exactly the extremal correlators in 2d $$ \mathcal{N}=\left(2,\ 2\right) $$ N = 2 , 2 (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.