On quantum T-duality in σ models

Abstract

The problem of quantum equivalence between non-linear sigma models related by Abelian or non-Abelian T-duality is studied in perturbation theory. Using the anomalous Ward identity for Weyl symmetry we derive a relation between the Weyl anomaly coefficients of the original and dual theories. The analysis is not restricted to conformally invariant backgrounds. The formalism is applied to the study of two examples. The first is a model based on SU (2) non-Abelian T duality. The second represents a simple realization of Poisson-Lie T duality involving the Drinfeld double based on SU (2). In both cases quantum T duality is established at the 1-loop level.

Heterotic α’-corrections in Double Field Theory

“…An elegant way to recover these rules is by performing a canonical transformation [42,43], which shows that the dual models are classically equivalent. The explicit form of the quantum corrections has been pursued using different methods and some partial results are available [44][45][46][47][48][49]. Here, we obtain the O(α ) corrections to the transformation rules of the massless heterotic fields in a manifestly duality covariant way.…”

“…In the absence of α corrections, the Buscher rules were derived by Buscher [39,40] from the sigma model formulation of string theory, and they determine how the metric and two-form degrees of freedom mix g (g, B) and B (g, B) under factorized T-dualities. Other derivations can be found in [41][42][43] and α corrections were explored in [44][45][46][47][48][49], and references therein.…”

Poisson–Lie duality in the string effective action

“…This is all the more a natural question since in [14] two sigma models related by Poisson-Lie duality have been shown to possess the same one loop beta functions. The equivalence holds in spite of a non-vanishing trace for one of the structure constants corresponding to one of the two Lie algebras forming the Drinfeld double.…”

“…The dilaton shift is precisely related to the diffeomorphism transformation that allowed them to conclude the equivalence of the two beta functions. The results of [14] can be interpreted in two different ways: Either it is a coincidence, due to the particularity of their model, that led to the possibility of absorbing the anomalous terms into their dilaton shift (which is the same as a diffeomorphism transformation), or this is symptomatic of a more general phenomenon. The problem of Poisson-Lie duality when some of the structure constants have non-vanishing traces, obviously, requires further investigation.…”

Poisson-Lie T-duality and Bianchi type algebras

“…To do this, we must use the algebraic relations (1), (10) and (12). To make the calculation simple, we need to work with basis of D, where we have 5 :…”