String triality, black hole entropy and Cayley's hyperdeterminant

TL;DR

This paper explores the invariance of a string theory model under duality symmetries, linking black hole entropy to Cayley's hyperdeterminant and quantum entanglement, revealing deep mathematical structures in string theory.

Contribution

It establishes that the entropy of certain extremal black holes in the N=2 STU model is given by Cayley's hyperdeterminant, connecting string dualities, black hole physics, and quantum information.

Findings

Black hole entropy expressed as hyperdeterminant

Duality symmetries constrain black hole solutions

Connection between string theory and quantum entanglement

Abstract

The four-dimensional N=2 STU model of string compactification is invariant under an SL(2,Z)_S x SL(2,Z)_T x SL(2,Z)_U duality acting on the dilaton/axion S, complex Kahler form T and the complex structure fields U, and also under a string/string/string triality S-T-U. The model admits an extremal black hole solution with four electric and four magnetic charges whose entropy must respect these symmetries. It is given by the square root of the hyperdeterminant introduced by Cayley in 1845. This also features in three-qubit quantum entanglement.