Dyonic Membranes

TL;DR

This paper constructs supersymmetric dyonic membrane solutions in eight-dimensional supergravity, revealing their duality properties and connections to string theory and heterotic dualities.

Contribution

It introduces new dyonic membrane solutions in D=8 supergravity that exhibit specific duality symmetries and are related to string theory compactifications.

Findings

Solutions are supersymmetric and satisfy a Bogomolnyi bound.

Membranes fill out orbits of an SL(2,Z) duality group.

Solutions are non-singular when uplifted to D=11 supergravity.

Abstract

We present dyonic multi-membrane solutions of the N=2 D=8 supergravity theory that serves as the effective field theory of the $T^2$-compactified type II superstring theory. The `electric' charge is fractional for generic asymptotic values of an axion field, as for D=4 dyons. These membrane solutions are supersymmetric, saturate a Bogomolnyi bound, fill out orbits of an $Sl(2;\Z)$ subgroup of the type II D=8 T-duality group, and are non-singular when considered as solutions of $T^3$-compactified D=11 supergravity. On $K_3$ compactification to D=4, the conjectured type II/heterotic equivalence allows the $Sl(2;\Z)$ group to be reinterpreted as the S-duality group of the toroidally compactified heterotic string and the dyonic membranes wrapped around homology two-cycles of $K_3$ as S-duals of perturbative heterotic string states.