Dilaton, Antisymmetric Tensor and Gauge Fields in String Effective Theories at the One--loop Level

TL;DR

This paper examines how the dilaton field influences gauge couplings in string effective theories at one-loop, resolving previous discrepancies and deriving the exact effective Lagrangian, with implications for the coupling of antisymmetric tensor fields.

Contribution

It provides the first explicit calculation of one-loop gauge couplings in string theories, clarifies the dilaton dependence, and compares different superfield representations for coupling to gauge fields.

Findings

No one-loop dilaton-dependent correction to the holomorphic f-function from massive string modes.

The linear multiplet formulation correctly reproduces string S-matrix elements for the antisymmetric tensor coupling.

Explicit one-loop scattering amplitude calculations clarify the dilaton's role in gauge couplings.

Abstract

We investigate the dependence of the gauge couplings on the dilaton field in string effective theories at the one--loop level. First we resolve the discrepancies between statements based on symmetry considerations and explicit calculations in string effective theories on this subject. A calculation of the relevant one--loop scattering amplitudes in string theory gives us further information and allows us to derive the exact form of the corresponding effective Lagrangian. In particular there is no dilaton dependent one--loop correction to the holomorphic $f$--function arising from massive string modes in the loop. In addition we address the coupling of the antisymmetric tensor field to the gauge bosons at one--loop. While the string S--matrix elements are not reproduced using the usual supersymmetric Lagrangian with the chiral superfield representation for the dilaton field, the analogue Lagrangian with the dilaton in a linear multiplet naturally gives the correct answer.