Superpotential of three dimensional $$ \mathcal{N} $$ = 1 heterotic supergravity

Abstract

We dimensionally reduce the ten dimensional heterotic supergravity action on spacetimes of the form M (2,1) × Y , where M (2,1) is three dimensional maximally symmetric Anti de Sitter or Minkowski space, and Y is a compact seven dimensional manifold with G 2 structure. In doing so, we derive the real superpotential functional of the corresponding three dimensional N = 1 theory. We confirm that extrema of this functional correspond to supersymmetric heterotic compactifications on manifolds of G 2 structure in the large volume, weak coupling limit to first order in α . We make some comments on the role of the superpotential functional with respect to the coupled moduli problem of instanton bundles over G 2 manifolds.

Generalising G2 geometry: involutivity, moment maps and moduli

“…We hope to return to this fascinating topic in the near future. Some interesting results on 3d, N = 1 theories coming from heterotic strings on G 2 manifolds were also discussed in [110][111][112].…”

Three-dimensional flux vacua from IIB on co-calibrated G2 orientifolds

“…Because of the O-plane truncations, the preservation of supersymmetry on our background boils down to the supersymmetry Killing equations that arise from Type I string theory with F Y M = 0, which can in turn be related to Heterotic string theory via S-duality. Earlier work on Heterotic string flux compactifications [23], has shown that backgrounds with…”

“…In other words H (HET) 3 ≡ T ( ) is identified with the full antisymmetric G2 torsion (2.7). In [23] the W 7 is also present and relates to the dilaton via dφ (HET) = 2W 7 , however, the specific orbifolding we use for our twisted torus projects it out, such that we are strictly working with a co-calibrated G2. In addition an external component of the H (HET) 3 flux is also allowed to be switched on, and is also related to the G2 torsion.…”

“…Two comments are in order here. First, note that in [23] there is an overall factor e n that relates the gravitino mass to the superpotential via m 3/2 = e n P. Here we have implicitly set it to unit, that is we have n = 0, because in our case the gravitino mass is given directly by m 3/2 = P on supersymmetric AdS as seen from (3.14). Secondly, in (4.2) we have not performed any additional Weyl rescalings, therefore it is still written in the original Heterotic string frame.…”

“…Here we pursue this direction further by working instead with manifolds with G2structure. There is an extended bibliography on flux compactifications with G2-structure, for example 4D vacua have been studied in [16][17][18][19][20][21] and 3D vacua of Heterotic strings have been studied for example in [22,23]. The simplest deviation from G2 holonomy is co-calibrated G2-structures, which will be our main focus.…”