T-duality and α′-corrections

Abstract

Abstract:We construct an O(d, d) invariant universal formulation of the first-order α ′ -corrections of the string effective actions involving the dilaton, metric and two-form fields. Two free parameters interpolate between four-derivative terms that are even and odd with respect to a Z 2 -parity transformation that changes the sign of the two-form field. The Z 2 -symmetric model reproduces the closed bosonic string, and the heterotic string effective action is obtained through a Z 2 -parity-breaking choice of parameters. The theory is an extension of the generalized frame formulation of Double Field Theory, in which the gauge transformations are deformed by a first-order generalized Green-Schwarz transformation. This deformation defines a duality covariant gauge principle that requires and fixes the fourderivative terms. We discuss the O(d, d) structure of the theory and the (non-)covariance of the required field redefinitions.

Second order higher-derivative corrections in Double Field Theory

“…These were anticipated in [26] and we find that there are no extra terms such as total derivatives nor interactions that could have been allowed by gauge symmetries and required by duality. This is also consistent with the results in [15].…”

“…This is consistent with the findings in [15]. The second order contribution is rather lengthy, and it helps to separate it in powers of the two-form and dilaton as follows…”

“…Given reservations like these, one would be tempted to dismiss the theory altogether. However, recent works [14,15] show specific connections between HSZ theory and the heterotic and bosonic strings, so understanding aspects of the former may be of wider relevance for the latter.…”

“…Some [13] are based on an enlargement of the generalized tangent space, and others [14,15] on deformations of the generalized gauge symmetries. The full set of consistent duality covariant first-order deformations of the generalized gauge transformations was shown in [15] to be governed by two free parameters. While specific choices of these parameters account for the deformations relevant to the heterotic and the bosonic string, a combination of these corresponds to HSZ theory.…”

“…Recent works discussing the duality structure of the first order corrections to the heterotic string are [10][11][12][13]. In [14,15], a two parameter family of first order consistent deformations of DFT was introduced, containing in a unified framework the corrections to bosonic [16] and heterotic strings [16][17][18].…”