The low energy effective action describing the Kaluza-Klein reduction of string theory on a $\textit{d}$-torus possesses a continuous O($\textit{d}$, $\textit{d}$) global symmetry. The non-geometric piece of this symmetry, parameterized by a bi-vector $\textit{β}$, was recently shown to effectively act as a hidden symmetry on the massless RR and universal NSNS fields of the ten dimensional parent theory, fixing their couplings. Here we extend the analysis of this symmetry to the massless gauge and fermion fields of heterotic supergravity. While the interactions of the boson fields are univocally fixed by $\textit{β}$ symmetry, we find four bilinear and two quartic $\textit{β}$ invariant combinations of fermions whose relative coefficients in the action must be determined by supersymmetry. Although not fully fixed, bilinear and quartic fermion couplings are strongly restricted by $\textit{β}$ symmetry at leading order in $\textit{α}$ .

Argentina

Walter Baron

Carmen Núñez

Jesús Rodríguez

$\textit{β}$ symmetry of heterotic supergravity

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   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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.

Eric Lescano

Supersymmetry, T-duality and heterotic α′-corrections

The generalized Kerr-Schild ansatz (GKSA) is a powerful tool for constructing exact solutions in Double Field Theory (DFT). In this paper we focus in the heterotic formulation of DFT, considering up to four-derivative terms in the action principle, while the field content is perturbed by the GKSA. We study the inclusion of the generalized version of the Green-Schwarz mechanism to this setup, in order to reproduce the low energy effective heterotic supergravity upon parametrization. This formalism reproduces higher-derivative heterotic background solutions where the metric tensor and Kalb-Ramond field are perturbed by a pair of null vectors. Next we study higher-derivative contributions to the classical double copy structure. After a suitable identification of the null vectors with a pair of U(1) gauge fields, the dynamics is given by a pair of Maxwell equations plus higher derivative corrections in agreement with the KLT relation.

Higher-derivative heterotic Double Field Theory and classical double copy

We construct the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetric extension of the generalized Kerr-Schild ansatz in the flux formulation of Double Field Theory. We show that this ansatz is compatible with   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetry as long as it is not written in terms of generalized null vectors. Supersymmetric consistency is obtained through a set of conditions that imply linearity of the generalized gravitino perturbation and unrestricted perturbations of the generalized background dilaton and dilatino. As a final step we parametrize the previous theory in terms of the field content of the low energy effective 10-dimensional heterotic supergravity and we find that the perturbation of the 10-dimensional vielbein, Kalb-Ramond field, gauge field, gravitino and gaugino can be written in terms of vectors, as expected.