Abstract
We clarify the relation between various approaches to the manifestly T-duality symmetric string. We explain in detail how the PST covariant doubled string arises from an unusual gauge fixing. We pay careful attention to the role of "spectator" fields in this process and also show how the T-duality invariant doubled dilaton emerges naturally. We extend these ideas to non-Abelian T-duality and show they give rise to the duality invariant formalism based on the semi-Abelian Drinfeld Double. We then develop the N=(0,1) supersymmetric duality invariant formalism.
Highlights
Group to a manifest symmetry of a spacetime action and in the E11 program of West [11] and collaborators
We pay careful attention to the role of “spectator” fields in this process and show how the T-duality invariant doubled dilaton emerges naturally. We extend these ideas to non-Abelian T-duality and show they give rise to the duality invariant formalism based on the semi-Abelian Drinfeld Double
In this paper we have clarified many missing details in the construct of the manifestly T-duality symmetric worldsheet theory and shown how such a formulation can be obtained through a novel gauge fixing choice
Summary
Our starting point is some compact D-dimensional manifold M endowed with a metric g and a closed 3-form H. Our starting point, the gauged Lagrange density eq (2.8) is already “doubled” as both the original coordinates x and the dual coordinates xappear This was suggested in [37] (see [48] for a detailed development) where it was shown that by making the non-Lorentz covariant gauge choice A=| = A= ≡ A and subsequently integrating out A one recovers Tseytlin’s non-Lorentz covariant doubled formulation [2, 3]. The GL(d, Z) subgroup of the duality group preserves Ω, but for the remaining components of O(d, d; Z), namely B-field shifts and Buscher dualities, one needs to exercise more care Normalised this topological term [5] evaluates to the sum of products of winding numbers around canonically dual cycles and in a fixed winding sector evaluates to πZ contributing a sign in the path integral.
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