Connections, Field Redefinitions and Heterotic Supergravity

Abstract

We study heterotic supergravity at $\mathcal{O}({\alpha }^{\prime })$, first described in detail in 1989 by Bergshoeff and de Roo. In particular, we discuss an ambiguity of a connection choice on the tangent bundle. It is well known that at $\mathcal{O}({\alpha }^{\prime })$ the Hull connection gives a consistent supergravity theory with supersymmetry transformations given in the usual way. We consider deformations of this connection corresponding to field redefinitions, and the necessary corrections to the supersymmetry transformations. We are interested in the moduli space of such field redefinitions which allow for supersymmetric solutions to the equations of motion. We show that for solutions on $M_4\times X$, where $M_4$ is Minkowski and $X$ is compact, the moduli space of infinitesimal field redefinitions is given by $H^{(0,1)}(X,\text{End}(TX))$. This space corresponds to infinitesimally close connections for which the equations of motion are satisfied. The setup suggests a symmetry between the gauge connection and the tangent bundle connection, as also employed by Bergshoeff and de Roo. We argue that this symmetry should be kept to higher orders in ${\alpha }^{\prime }$, and propose a natural choice for the corresponding tangent bundle connection used in curvature computations. In particular, the Hull connection should be corrected at second and higher orders in ${\alpha }^{\prime }$ from this point of view.

30 pages, minor corrections and changes, explanations added

References in corpus (10)

• Double Field Theory Formulation of Heterotic Strings
• Double Field Theory at Order ${\alpha }^{\prime }$
• Generalised geometry for string corrections
• Torsional Heterotic Geometries
• Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications
• Heterotic $\alpha$'-corrections in Double Field Theory
• Algebroids, Heterotic Moduli Spaces and the Strominger System
• Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets
• Heterotic fluxes and supersymmetry
• Order ${\alpha }^{\prime }$ heterotic domain walls with warped nearly Kähler geometry

Cited by in corpus (30)

• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• T-duality and ${\alpha }^{\prime }$-corrections
• Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications
• Heterotic Effective Action and Duality Symmetries Revisited
• Gaugino Condensation and the Cosmological Constant
• A Metric for Heterotic Moduli
• Quadratic ${\alpha }^{\prime }$-Corrections to Heterotic Double Field Theory
• Finite deformations from a heterotic superpotential: holomorphic Chern--Simons and an $L_{\infty }$ algebra
• The infinitesimal moduli space of heterotic $G_2$ systems
• The Heterotic Superpotential and Moduli
• The Universal Geometry of Heterotic Vacua
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• On the Effective Field Theory of Heterotic Vacua
• Chiral operators in two-dimensional (0,2) theories and a test of triality
• Heterotic Quantum Cohomology
• The Abelian Heterotic Conifold
• Superpotential of Three Dimensional $\mathcal{N}=1$ Heterotic Supergravity
• T-duality, Non-geometry and Lie Algebroids in Heterotic Double Field Theory
• The heterotic ${\mathrm{G}}_2$ system on contact Calabi--Yau $7$-manifolds
• Expanding Universe and Dynamical Compactification Using Yang-Mills Instantons
• Conformal Invariance of (0,2) Sigma Models on Calabi-Yau Manifolds
• Heterotic Moduli Stabilisation and Non-Supersymmetric Vacua
• Small gauge transformations and universal geometry in heterotic theories
• Balanced and Aeppli Parameters for the Heterotic Moduli
• Generalised Geometry and Flux Vacua
• The Massless Spectrum of Heterotic Compactifications
• Moduli in General $SU(3)$-Structure Heterotic Compactifications
• The quaternionic Heisenberg group and Heterotic String Solutions with non-constant dilaton in dimensions 7 and 5
• Heterotic solitons on four-manifolds