STU Black Holes and String Triality

TL;DR

This paper explores the duality and symmetry properties of STU black holes in string theory, revealing a triality among different black hole solutions and their charge configurations, with implications for understanding non-perturbative symmetries.

Contribution

It introduces a duality framework connecting STU black holes with stringy black holes via Sp(8, Z) transformations, highlighting a triality symmetry among solutions.

Findings

Area formula is moduli independent and exhibits ${[SL(2,Z)]}^3$ symmetry.

Dual black hole solutions are related through specific Sp(8, Z) transformations.

All three duality symmetries (S, T, U) are non-perturbative and mix electric and magnetic charges.

Abstract

We find double-extreme black holes associated with the special geometry of the Calabi-Yau moduli space with the prepotential F=STU. The area formula is STU-moduli independent and has ${[SL(2,Z)]}^3$ symmetry in space of charges. The dual version of this theory without prepotential treats the dilaton S asymmetric versus T,U-moduli. We display the dual relation between new (STU) black holes and stringy (S|TU) black holes using particular Sp(8, Z) transformation. The area formula of one theory equals that of the dual theory when expressed in terms of dual charges. We analyse the relation between (STU) black holes to string triality of black holes: (S|TU), (T|US), (U|ST) solutions. In the democratic STU-symmetric version we find that all three S and T and U duality symmetries are non-perturbative and mix electric and magnetic charges.