Symmetry Breaking at enhanced Symmetry Points

TL;DR

This paper explores how boundary condensates affect string compactifications at special symmetry points, leading to a sigma model description, symmetry breaking, and mixing between open and closed strings.

Contribution

It introduces a boundary condensate framework at enhanced symmetry points, linking open-string scattering to the principal chiral model and analyzing symmetry breaking and string mixing effects.

Findings

Tree-level amplitudes match the principal chiral model in low energy limit.

One-loop beta function vanishing yields equations of motion for the sigma model.

Quantum corrections induce open-closed string mixing and symmetry breaking.

Abstract

The influence of world-sheet boundary condensates on the toroidal compactification of bosonic string theories is considered. At the special points in the moduli space at which the closed-string theory possesses an enhanced unbroken $G\times G$ symmetry (where $G$ is a semi-simple product of simply laced groups) a scalar boundary condensate parameterizes the coset $G\times G/G$. Fluctuations around this background define an open-string generalization of the corresponding chiral nonlinear sigma model. Tree-level scattering amplitudes of on-shell massless states (\lq pions') reduce to the amplitudes of the principal chiral model for the group $G$ in the low energy limit. Furthermore, the condition for the vanishing of the renormalization group beta function at one loop results in the familiar equation of motion for that model. The quantum corrections to the open-string theory generate a mixing of open and closed strings so that the coset-space pions mix with the closed-string $G\times G$ gauge fields, resulting in a Higgs-like breakdown of the symmetry to the diagonal $G$ group. The case of non-oriented strings is also discussed.