Heterotic string covariant amplitudes and low-energy effective action

Heterotic α’-corrections in Double Field Theory

“…The action includes gauge and gravitational Chern-Simons terms in the two-form field strength, in addition to quadratic terms of the Yang-Mills field strength and of the Riemann curvature tensor with torsion. These contributions were originally obtained from tree level scattering amplitudes of the massless heterotic string states [20,21]. An alternative method to construct the gravitational part of this action was developed in [22], making use of a symmetry that exists between the Yang-Mills and supergravity fields in ten dimensions.…”

“…, n g are indices in the adjoint representation of the heterotic gauge group. The action can be written as [20,21]- [26] S = d 10 x √ −g e −2φ R + 4g µν ∂ µ φ∂ ν φ − 1 12 g µσ g ντ g ρξ H µνρ H στ ξ (1.1)…”

Heterotic — type I superstring duality and low-energy effective actions

“…Let us start with the R, R 2 , R 3 terms. Since the 3-graviton amplitude in the heterotic string theory does not receive string loop corrections [31,19,20,13,21] …”

“…The relevant tree-level terms in the heterotic string action can be written in the following symbolic form [11,19,20,34] (α ′ is absorbed into G µν ;the trace in the fundamental representation of SO(32) and trR 2 ≡ R ab µν R baµν )…”

“…2 There are, indeed, examples of terms in the string effective actions which are either not renormalised by string higher-loop corrections (like second-derivative terms and 'anomalycancelling' terms, see, e.g., [12,13,14,15]) or receive contributions only from specific orders of string perturbative expansion (see [16,17]). In [18] we considered a term quartic in the gauge field strength trF 4 which, in heterotic string theory, is absent at the tree level [19,20] but appears at the one-loop level [21,22,23]. We have argued that it does not receive corrections from higher loops since D = 10 supersymmetry relates [24,25] it to the 'anomaly-cancelling' term BtrF 4 [26] which is not renormalised at higher orders [27,15] (see also below).…”