Effective action of bosonic string theory at order alpha '^2

Mohammad R Garousi

doi:10.1140/epjc/s10052-019-7357-4

Mohammad R Garousi

Open Access

https://doi.org/10.1140/epjc/s10052-019-7357-4

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Abstract

Recently, it has been shown that the gauge invariance requires the minimum number of independent couplings for B-field, metric and dilaton at order alpha '^2 to be 60. In this paper we fix the corresponding 60 parameters in string theory by requiring the couplings to be invariant under the global T-duality transformations. The Riemann cubed terms are exactly the same as the couplings that have been found by the S-matrix calculations.

Highlights

String theory is a quantum theory of gravity with a finite number of massless fields and a tower of infinite number of massive fields reflecting the stringy nature of the gravity
There are various gauge symmetries in the effective actions which are corresponding to the various massless fields, e.g., the diffeomorphism symmetry corresponds to the metric and the gauge symmetry corresponds to the Kalb-Ramond field or B-field
The important part of the calculations is that there are 60 relations between the 60 parameters in (6) and the parameter b1, i.e., the T-duality constraint fixes all 60 parameters at order α 2 in terms of the overall factor of the couplings at order α ! This ends our illustration of the fact that the T-duality constraint on the effective action can fix uniquely the effective action of bosonic string theory at order α 2

Summary

Introduction

String theory is a quantum theory of gravity with a finite number of massless fields and a tower of infinite number of massive fields reflecting the stringy nature of the gravity. Another approach is to reduce the D-dimensional gauge invariant theory on a circle and impose the T-duality symmetry by constraining the couplings in the (D − 1)-dimensional spacetime to be Z2 scalars [19] where Z2-group is the Buscher rules [20,21] plus their α -deformations [22,23,24] Using this approach for the case that B-field is zero, the known gravity and dilaton couplings in the effective actions at orders α , α 2, α 3 have been found in [25,26], up to some overall factors.

Gauge invariance constraint

T-duality invariance constraint

T-duality constraint at order α 2

Discussion