Transformation of Black-Hole Hair under Duality and Supersymmetry

TL;DR

This paper investigates how observable charges of four-dimensional objects in string theory transform under duality groups, revealing the duality-invariant nature of the Bogomol'nyi bound and the role of scalar hair in supersymmetric black holes.

Contribution

It analyzes the transformation properties of charges under duality and supersymmetry, introducing a duality-invariant Bogomol'nyi bound that includes scalar hair.

Findings

Charges form two complex representations of the duality group.

The Bogomol'nyi bound is invariant under duality transformations.

Massless black holes are T duals of massive black holes, with scalar hair and naked singularities.

Abstract

We study the transformation under the String Theory duality group of the observable charges (mass, angular momentum, NUT charge, electric, magnetic and different scalar charges) of four dimensional point-like objects whose asymptotic behavior constitutes a subclass closed under duality. The charges fall into two complex four-dimensional representations of the duality group. T duality (including Buscher's) has an O(1,2) action on them and S duality a U(1) action. The generalized Bogomol'nyi bound is an U(2,2)-invariant built out of one representations while the other representation (which includes the angular momentum) never appears in it. The bound is manifestly duality-invariant. Consistency between T duality and supersymmetry requires that primary scalar hair is included in the Bogomol'nyi bound. Four-dimensional supersymmetric massless black holes are the T duals in time of massive supersymmetric black holes. Non-extreme massless ``black holes'' are the T duals of the non-extreme black holes and have primary scalar hair and naked singularities.