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

Abstract

We compare order R 4 terms in the 10-dimensional effective actions of SO(32) heterotic and type I superstrings from the point of view of duality between the two theories. Some of these terms do not receive higher-loop corrections being related by supersymmetry to 'anomaly-cancelling' terms which depend on the antisymmetric 2-tensor. At the same time, the consistency of duality relation implies that the 'tree-level' R 4 super-invariant (the one which has ζ(3)-coefficient in the sphere part of the action) should appear also at higher orders of loop expansion, i.e. should be multiplied by a non-trivial function of the dilaton.December 1995 ⋆ e-mail address: tseytlin@ic.ac.uk † On leave from Lebedev Physics Institute, Moscow.

R4 couplings in M- and type II theories on Calabi-Yau spaces

“…Before we perform the reduction, we notice that besides the low derivative R 2 and R terms, the eleven-dimensional R 4 coupling is going to give rise also to a similar higher-derivative term in D = 5, which we do not discuss here. 1 We follow the conventions of [13,1,2]. In particular, we take the normalization of the elevendimensional term with two t 8 to be π 2…”

Inflation from superstring and M-theory compactification with higher order corrections

“…With phenomena at such high energy, it is expected that we cannot ignore higher order corrections such as higher derivative terms in the theories at least in the early universe. It is known that there are terms of higher orders in the curvature to the lowest effective supergravity action coming from superstrings or M-theory [13,14,15]. With such corrections, they will significantly affect the inflation at the early stage of the evolution of our universe.…”

“…3, we examine solutions to the vacuum Einstein equations with GB corrections, corresponding to the heterotic strings [13,14]. We exhaust possible generalized de Sitter and power-law solutions, and find inflationary models for several types of internal spaces with positive, zero and negative curvatures.…”

One loop superstring effective actions andN=8supergravity

“…For the heterotic string another two independent terms Y 1 and Y 2 appear at order α ′3 [5,18,6]. Their parts which involve only the Weyl tensor are given respectively by…”

“…The results of [15] therefore also include the toroidal compactification of M-theory to d = 4. The superstring α ′3 effective actions contain two independent bosonic terms I X , I Z , from which two separate superinvariants are built [5,18]. These terms are given, at linear order in the NS-NS gauge field B mn , by:…”