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Kahler Potential and Ambiguities in 4d N=2 SCFTs

Jaume Gomis, Nafiz Ishtiaque

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.

Kahler Potential and Ambiguities in 4d N=2 SCFTs

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.

Paper Structure

This paper contains 4 sections, 69 equations.

Table of Contents

  1. Introduction
  2. Kähler Potential from Lg Partition Function
  3. Off-shell ${\cal N}=2$ Poincaré Supergravity for $S^4$
  4. The Kähler ambiguity Supergravity Counterterm