T-duality and two-loop renormalization flows*

Abstract

Manifest T-duality covariance of the one-loop renormalization group flows is shown for a generic bosonic sigma model with an abelian isometry, by referring a set of previously derived consistency conditions to the tangent space of the target. For a restricted background, T-duality transformations are then studied at the next order, and the ensuing consistency conditions are found to be satisfied by the two-loop Weyl anomaly coefficients of the model. This represents an extremely non-trivial test of the covariance of renormalization group flows under T-duality, and a stronger condition than T-duality invariance of the string background effective action.

The world-sheet corrections to dyons in the Heterotic theory

“…At the supergravity approximation the SO(6, 22) × SL(2, Z) duality transformations can be applied on the dyonic black hole to obtain a general dyonic black hole [38]. Reminiscent to T-duality and α ′ corrections [39,40,41], we expect that the duality transformations themselves get modified by the α ′ corrections. In this note we do not use the duality transformations.…”

Two-Loop Beta Functions without Feynman Diagrams

“…However, while the latter satisfy them exactly, the former satisfy them up to a target reparametrization [2,5].…”

“…After briefly reviewing the first nontrivial order, we will consider, as in [5], a restricted class of backgrounds in order to probe the consistency conditions at O ͑a 0 2 ͒. In order to be self-contained we begin by deriving, from basic principles, the corrected duality transformations at O ͑a 0 2 ͒ first presented in [6].…”

“…As it turns out, the consistency conditions (8) on g mn and b mn alone also allows for an independent determination of the dilaton transformation (or "shift") f f 2 1 2 ln g 00 . Applying (7) to this then yields the dilaton beta function [5].…”

Duality and the Renormalization Group

“…In what follows, we will explore in detail the analogous constraints in the context of 2d bosonic sigma models, in order of increasing complexity: Sections 2 and 3 contain a review of previously published work [3], [4], [5] on, respectively, the fully generic one-loop case and the purely metric two-loop case, while Section 4 comprises results obtained in the course of more recent investigations [6], and presents the setup for the fully generic two-loop case, in the presence of torsion. In this case, where all possible backgrounds are included, the issue of scheme dependence will also be discussed in some detail, as it arises for the first time to complicate matters in a considerable way.…”