An SL(2, Z) Multiplet of Black Holes in $D = 4$ Type II Superstring Theory

TL;DR

This paper constructs an infinite family of magnetically charged black hole solutions in four-dimensional type II superstring theory, forming an SL(2, Z) multiplet, and demonstrates their stability in the extremal limit due to a mass gap.

Contribution

It introduces a new class of black hole solutions in 4D type II superstring theory that form an SL(2, Z) multiplet, leveraging compactification and duality invariance.

Findings

Solutions characterized by two coprime integers for magnetic charges.

Solutions form an SL(2, Z) multiplet under duality.

Extremal solutions are stable due to a mass gap.

Abstract

It is well-known that the conjectured SL(2, Z) invariance of type IIB string theory in ten dimensions also persists in lower dimensions when the theory is compactified on tori. By making use of this recent observation, we construct an infinite family of magnetically charged black hole solutions of type II superstring theory in four space-time dimensions. These solutions are characterized by two relatively prime integers corresponding to the magnetic charges associated with the two gauge fields (from NS-NS and R-R sectors) of the theory and form an SL(2, Z) multiplet. In the extremal limit these solutions are stable as they are prevented from decaying into black holes of lower masses by a `mass gap' equation.