Enhanced Gauge Symmetries in Superstring Theories

TL;DR

This paper explores how certain four-dimensional N=4 superstring theories exhibit enhanced gauge symmetries at special vacua, revealing deep connections between different string compactifications and non-perturbative states.

Contribution

It demonstrates the equivalence of enhanced symmetry groups in different N=4 theories and links non-perturbative states to geometric features of compactification manifolds.

Findings

K3×T2 compactification shares symmetry groups with T6-compactified heterotic string

Massless states include magnetically charged and dyonic states approaching zero mass

Membrane wrapping modes induce symmetry enhancement in D=11 supergravity

Abstract

Certain four-dimensional $N=4$ supersymmetric theories have special vacua in which massive charged vector supermultiplets become massless, resulting in an enhanced non-abelian gauge symmetry. We show here that any two $N=4$ theories having the same Bogomolnyi spectrum at corresponding points of their moduli spaces have the same enhanced symmetry groups. In particular, the $K_3\times T^2$ compactified type II string is argued to have the same enhanced symmetry groups as the $T^6$-compactified heterotic string, giving further evidence for our conjecture that these two string theories are equivalent. A feature of the enhanced symmetry phase is that for every electrically charged state whose mass tends to zero as an enhanced symmetry point is approached, there are magnetically charged and dyonic states whose masses also tend to zero, a result that applies equally to N=4 super Yang-Mills theory. These extra non-perturbative massless states in the $K_3$ compactification result from $p$-branes wrapping around collapsed homology two-cycles of $K_3$. Finally, we show how membrane `wrapping modes' lead to symmetry enhancement in D=11 supergravity, providing further evidence that the $K_3$-compactified D=11 supergravity is the effective field theory of the strong coupling limit of the $T^3$-compactified heterotic string.