Kahler Potential and Ambiguities in 4d N=2 SCFTs

TL;DR

This paper proves that the S^4 partition function of 4d N=2 SCFTs computes the Kahler potential on the conformal manifold, clarifying the nature of Kahler ambiguities via supergravity counterterms.

Contribution

It provides a new elementary proof using supersymmetry Ward identities and explicitly constructs the Kahler ambiguity counterterm in 4d N=2 supergravity.

Findings

Partition function computes the Kahler potential on the conformal manifold.

Kahler ambiguities are realized by local supergravity counterterms.

Explicit construction of the Kahler ambiguity counterterm in off-shell supergravity.

Abstract

The partition function of four-dimensional N=2 superconformal field theories on S^4 computes the exact Kahler potential on the space of exactly marginal couplings [1]. We present a new elementary proof of this result using supersymmetry Ward identities. The partition function is a section rather than a function, and is subject to ambiguities coming from Kahler transformations acting on the Kahler potential. This ambiguity is realized by a local supergravity counterterm in the underlying SCFT. We provide an explicit construction of the Kahler ambiguity counterterm in the four dimensional N=2 off-shell supergravity theory that admits S^4 as a supersymmetric background.