Torsion-Free Generalized Connections and Heterotic Supergravity

Abstract

Abstract. This work revisits the notions of connection and curvature in generalized geometry, with emphasis on torsion-free generalized connections on a transitive Courant algebroid. As an application, we provide a mathematical derivation of the equations of motion of heterotic supergravity in terms of the Ricci tensor of a generalized metric, inspired by the work of Coimbra, Strickland-Constable and Waldram.

Generalised geometry for string corrections

“…A key new point here is that we naturally obtain the correct gravitational connection in the Bianchi identity. The α ′ -corrected generalised geometry in the heterotic string context has previously been considered in [30,31]. A similar construction describing heterotic α ′ -corrections in the DFT formalism was presented in recent work [32].…”

“…5 We refer to section 3 for explanations and definitions. These structures were used in [30,31] to construct heterotic actions. On the physics side, constructing heterotic theories by reduction has been discussed in [43][44][45], the form of the generalised Lie derivative and the local generalised geometry in the DFT context is given in [46], and in [47] it is shown how such generalised structures via dimensional reduction.…”

“…in [30,31]. The problem however is that the new extended generalised tangent bundle is too large and there will be unphysical degrees of freedom.…”

“…The problem however is that the new extended generalised tangent bundle is too large and there will be unphysical degrees of freedom. In particular, the GL(n, R) connection in [30,31] has to be put in by hand. This is reflecting the fact that the GL(n, R) symmetry is not independent but is the group that rotates bases for the tangent and cotangent spaces.…”

Generalised geometry and flux vacua

“…In heterotic compactifications, the anomaly cancellation condition implies that H is, in the general case, no longer closed. A generalised geometry for the heterotic string must therefor be formulated in a way that does not require closure H. Some steps in this direction have been taken, see [49][50][51].…”