Supergravity dual of c-extremization

TL;DR

This paper establishes a supergravity dual for c-extremization in 2D N=(0,2) SCFTs, showing that the extremization principle corresponds to extremizing the T-tensor in three-dimensional N=2 gauged supergravity, and confirms this with examples from twisted compactifications.

Contribution

It demonstrates that c-extremization in 2D SCFTs is dual to extremizing the T-tensor in 3D gauged supergravity, providing a geometric understanding of the principle.

Findings

Central charge matches between SCFT and supergravity calculations.

The supergravity extremization reproduces known results for twisted compactifications.

Supports the duality between c-extremization and supergravity T-tensor extremization.

Abstract

Recently a general principle, called c-extremization, which determines the exact R-symmetry of two-dimensional SCFTs with N = (0,2) supersymmetry was identified. In this note we show that the supergravity dual corresponds to the extremization of the T-tensor of N = 2 gauged supergravity in three-dimensions. To support this claim, we demonstrate that the expected central charge of SCFTs arising from twisted compactifications of four-dimensional N = 4 SYM on Riemann surfaces, whose gravity dual is a reduction of five-dimensional U(1)^3 gauged supergravity, is recovered in the three-dimensional framework.