Abstract
The O(d, d) invariant worldsheet theory for bosonic string theory with d abelian isometries is employed to compute the beta functions and Weyl anomaly at one-loop. We show that vanishing of the Weyl anomaly coefficients implies the equations of motion of the Maharana-Schwarz action. We give a self-contained introduction into the required techniques, including beta functions, the Weyl anomaly for two-dimensional sigma models and the background field method. This sets the stage for a sequel to this paper on generalizations to higher loops and α′ corrections.
Highlights
Background field method we revisit the techniques for computing the β−functionals of the string nonlinear sigma model defined by d2x√ γ γαβgμν (X) ∂αXμ∂βXν + α R(2) Φ(X), λ = 2πα, (3.1)on a curved Euclidean worldsheet of spherical topology
Given the sigma model action (2.34), our goal is to determine the general form of the total derivative terms λij · φj and Qi1j · φj appearing in the Weyl anomaly coefficients (2.33)
In this paper we have introduced the background material needed to compute beta functions for the duality invariant sigma model of [7,8,9] and shown that at one loop vanishing of the Weyl anomaly implies the O(d, d) invariant target space equations of Maharana-Schwarz
Summary
Our goal is to extract target space field equations from a string sigma model by requiring quantum consistency [16,17,18,19,20]. One ensures that the non-linear sigma model is conformally invariant quantum mechanically by imposing the vanishing of the Weyl anomaly. This condition is often stated to be equivalent to the vanishing of the renormalization-group (RG) beta functions βi, but this is not quite correct for the string sigma model: βi = 0 ensures only rigid scale invariance or, equivalently, the vanishing of the integrated trace d2σ√γ. T α α of the energy-momentum tensor This leads to target space equations for the true “Weyl anomaly coefficients” βi of the schematic form βi = βi + ∆W φi = 0 ,. We shall follow closely the general discussion given by Tseytlin in [22]
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