Candidates for anti-de Sitter Horizons

TL;DR

This paper identifies specific four-dimensional bases of non-compact singularities and proves they admit Kähler-Einstein metrics, enabling their use as horizons in string theory models related to the AdS/CFT correspondence.

Contribution

It demonstrates the existence of Kähler-Einstein metrics on bases of certain non-compact singularities, facilitating their application in string theory compactifications.

Findings

Existence of Kähler-Einstein metrics on these bases.

Identification of four-dimensional bases from toric descriptions.

Potential use as horizons in AdS/CFT models.

Abstract

We find, from the toric description of the moduli space of D3-branes on non-compact six-dimensional singularities $\C^3/\Z_3$ and $\C^3/\Z_5$ in the blown-down limit, the four-dimensional bases on which these singular spaces are complex cones, and prove the existence of K\"ahler-Einstein metrics on these four-dimensional bases. This shows, in particular, that one can use the horizons obtained from these base spaces by a U(1)-foliation as compact parts of the target space for Type-IIB string theory with $\ads{5}$ in the context of the AdS-CFT correspondence.