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

Abstract

We study the extremal correlation functions of (twisted) chiral ring operators via superlocalization in $\mathcal{N}=(2,2)$ superconformal field theories (SCFTs) with central charge $c\ge 3$, 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 $2d$ $\mathcal{N}=(2,2)$ (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.

50 pages + 3 appendices, typos corrected, the journal version

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• Sphere Partition Functions and the Zamolodchikov Metric
• $t{t}^{\ast }$ equations, localization and exact chiral rings in 4d N=2 SCFTs
• Exact correlation functions in SU(2) N=2 superconformal QCD
• The chiral ring of AdS3/CFT2 and the attractor mechanism
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Cited by in corpus (7)

• Extremal Correlators and Random Matrix Theory
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• 2D BPS Rings from Sphere Partition Functions
• Twisted Massive Non-Compact Models
• Disordered $\mathcal{N}=(2,2)$ Supersymmetric Field Theories