Higher order corrections to supersymmetry and compactifications of the heterotic string

T-duality of the Riemann curvature corrections to supergravity

“…So it confirms that there is no coupling of one dilaton and three gravitons in the string frame [26,8] or in the Einstein frame. This is not the case, however, for the couplings of two dilatons and two gravitons as we shall see below.…”

Modulus stabilization in higher curvature dilaton gravity

“…Usually such corrections originate naturally in string theory where power expansion in terms of inverse of Regge slope (or string tension) yields the higher curvature corrections to pure Einstein's gravity. Supergravity, as the low energy limit [7][8][9][10][11][12][13][14][15][16][17][18] of heterotic string theory [19][20][21][22][23][24][25][26][27], yields the Gauss-Bonnet (GB) term along with dilaton coupling at the leading order correction. Consequently it became an active area of interest as a modified theory of gravity.…”

Generalized holonomy in String-corrected Spacetimes

“…How this can work is illustrated by the Kähler cases [10,11]. Any Kähler manifold admits a gauge covariantly constant spinor η satisfying…”

“…This review, based on Refs [6,7,8,9], summarizes the geometrical impact that the quartic corrections have on Calabi-Yau, G 2 and Spin 7 holonomy manifolds and on the preservation of supersymmetry in the face of the α corrections, extending the earlier analysis given in Refs [10,11]. It then proceeds to show how this supersymmetry preservation is expressed in the language of generalized structure groups and generalized holonomy for the α -corrected Killing spinor operator.…”

“…For initially Ricci-flat Kähler spaces with a constant dilaton, the O(α ) 3 Y variation X ij boils down to a simple form [10,11] X ij = ∇î∇ĵS 3 (11)…”