One-loop masses of open-string scalar fields in String Theory

TL;DR

This paper develops a method using boundary state formalism to calculate one-loop masses of open-string scalar fields in D-brane models, revealing how these masses can lead to gauge symmetry breaking or stabilization.

Contribution

It introduces a simple boundary state approach for computing one-loop scalar masses in open-string models, including models with broken supersymmetry.

Findings

Mass squared sign correlates with open-string one-loop vacuum amplitude.

Explicit calculations in various D-brane models demonstrate the method.

Scalar masses can be positive or negative, affecting gauge symmetry.

Abstract

In phenomenological models with D-branes, there are in general open-string massless scalar fields, in addition to closed-string massless moduli fields corresponding to the compactification. It is interesting to focus on the fate of such scalar fields in models with broken supersymmetry, because no symmetry forbids their masses. The one-loop effect may give non-zero masses to them, and in some cases mass squared may become negative, which means the radiative gauge symmetry breaking. In this article we investigate and propose a simple method for calculating the one-loop corrections using the boundary state formalism. There are two categories of massless open-string scalar fields. One consists the gauge potential fields corresponding to compactified directions, which can be understood as scalar fields in uncompactified space-time (related with Wilson line degrees of freedom). The other consists "gauge potential fields" corresponding to transverse directions of D-brane, which emerge as scalar fields in D-brane world-volume (related with brane moduli fields). The D-brane boundary states with constant backgrounds of these scalar fields are constructed, and one-loop scalar masses are calculated in the closed string picture. Explicit calculations are given in the following four concrete models: one D25-brane with a circle compactification in bosonic string theory, one D9-brane with a circle compactification in superstring theory, D3-branes at a supersymmetric C^3/Z_3 orbifold singularity, and a model of brane supersymmetry breaking with D3-branes and anti-D7-branes at a supersymmetric C^3/Z_3 orbifold singularity. We show that the sign of the mass squared has a strong correlation with the sign of the related open-string one-loop vacuum amplitude.