On the application of the field-redefinition theorem to the heterotic superstring theory

M. D. Pollock

doi:10.1140/epjp/i2015-15087-3

2024 Impact factor 2.9

EPJ PLUS - Condensed Matter and Complex Systems

This article has an erratum: [https://doi.org/10.1140/epjp/s13360-024-05378-7]

Eur. Phys. J. Plus (2015) 130: 87
https://doi.org/10.1140/epjp/i2015-15087-3

Regular Article

On the application of the field-redefinition theorem to the heterotic superstring theory

M. D. Pollock^a

V. A. Steklov Mathematical Institute, Russian Academy of Sciences, Ulitsa Gubkina 8, 119991, Moscow, Russia

^a mdp30@cam.ac.uk

Received: 23 February 2015
Accepted: 30 March 2015
Published online: 5 May 2015

Abstract

The ten-dimensional effective action $\hat S$ which defines the heterotic superstring theory at low energy is constructed by hypothesis in such a way that the resulting classical equation of motion for the space-time metric $\hat g_{AB}$ simultaneously implies the vanishing of the beta-function for the N = 1 supersymmetric non-linear sigma-model on the world sheet. At four-loop order it was found by Grisaru and Zanon (see also Freeman et al.) that the effective Lagrangian $\hat L$ so constructed differs in the numerical coefficient of the term $\hat L_3 = \hat R\hat R_{ABCD} \left( {\hat R_{EF}^{A D} \hat R^{CEFB} + \tfrac{1} {4}\hat R_{ EF}^{AB} \hat R^{CDEF} } \right)$ from that obtained directly from the four-point gravitational scattering amplitude. The two expressions can be related via a metric field redefinition $\hat g_{AB} \to \hat g'_{AB} = \left( {1 + \delta '\hat L_3 /\hat R} \right)\hat g_{AB}$ , activation of which, however, results in the appearance of ghosts at higher gravitational order $\mathcal{R}^n$ , n > 4, as shown by Lawrence. Here, we prove, after reduction of $\hat S$ to the physical dimensionality D = 4, that the corresponding field redefinition yields the identity g′_ij = g_ij, signified by L₃/R = 0, in a Friedmann space-time generated by a perfect-fluid source characterized by adiabatic index γ ≡ 1 + p/ρ, where p is the pressure and ρ is the energy density, if, and only if, κ⁶ρ³γ²(γ − 1) = 0. That is, the theory remains free of ghosts in Minkowski space ρ = 0, in a maximally symmetric space-time γ = 0, or in a dust Universe γ = 1. Further aspects of ghost freedom and dimensional reduction, especially to D = 4, are discussed.