Higher-derivative field redefinitions in the presence of boundary

TL;DR

This paper investigates how boundary conditions influence field redefinitions and T-duality corrections in string theory, deriving consistent bulk and boundary actions at order α' that align with known symmetries and previous models.

Contribution

It proposes boundary condition constraints on field redefinitions and T-duality corrections, and derives a minimal gauge-invariant action consistent with symmetries at order α' in string theory.

Findings

Bulk action fixed up to an overall factor

Boundary action determined up to two parameters

Results match the Meissner action and boundary terms

Abstract

Recently it has been proposed that the consistency with T-duality requires the effective action of string theory at order $\alpha'^n$ satisfies the least action principle provided that the values of the massless fields and their derivatives up to order $n$ are known on the boundary. In this paper we speculate that this boundary condition constrains the field redefinitions and the corrections to the T-duality transformations in the presence of boundary, \eg at order $\alpha'$, the metric does not change, and all other massless fields should change to include only the first derivative of the massless fields. Using the above field redefinitions, we write all gauge invariant bulk and boundary couplings in the bosonic string theory at order $\alpha'$ in a minimal scheme. Then using the assumption that the classical effective action of the string theory at the critical dimension is background independent, we fix the coefficients of the independent gauge invariant couplings by imposing $O(1,1)$ symmetry when the background has a circle and by imposing $O(d,d)$ symmetry when the background has $T^d$. These constraints fix the bulk action up to an overall factor, and the boundary action up to two parameters. By requiring the gravity couplings in the boundary action to be consistent with those in the Chern-Simons gravity, the two boundary parameters are also fixed. Up to the above restricted field redefinitions, the bulk and boundary couplings are exactly those in the K.A. Meissner action and its corresponding boundary action.