Supersymmetry, T-duality and heterotic α′-corrections

Abstract

Higher-derivative interactions and transformation rules of the fields in the effective field theories of the massless string states are strongly constrained by space-time symmetries and dualities. Here we use an exact formulation of ten dimensional $$ \mathcal{N} $$ N = 1 supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order α′-corrections of the heterotic string effective action. The theory contains a supersymmetric and T-duality covariant generalization of the Green-Schwarz mechanism that determines the modifications to the leading order supersymmetry transformation rules of the fields. We compute the resulting field-dependent deformations of the coefficients in the supersymmetry algebra and construct the invariant action, with up to and including four-derivative terms of all the massless bosonic and fermionic fields of the heterotic string spectrum.

$α'$-corrections and their double formulation

“…Using the parametrization of the generalized frame and dilaton, it is straightforward to compute the parametrization of the different projections of the generalized fluxes [19],…”

“…The way to match with the fields presented in the original publication[9] is very well discussed in the appendix of[19].…”

The α′2 correction from double field theory

“…It would be very interesting to try to use it beyond order α 2 , for example to see that one recovers the quartic Riemann terms found in [21] at order α 3 . Another interesting question is including the gauge vectors, and fermions and supersymmetry, [15] in the DFT description of the heterotic string [38], see [39] for a detailed account at order α .…”

Exploring the geometry of supersymmetric double field theory

“…First, can we extend superspace DFT to encode higher derivative α corrections? This certainly seems plausible, and relatively recently, the first-order corrections to N = 1 supersymmetric DFT were constructed at the component level [39]. It would be quite interesting to understand how this construction can be geometrized in superspace, and if that can aid in its extension to higher orders.…”