https://doi.org/10.1140/epjp/i2018-12022-2
Regular Article
On the dynamics of superstring compactification
V. A. Steklov Mathematical Institute, Russian Academy of Sciences, Ulitsa Gubkina 8, 119991, Moscow, Russia
* e-mail: mdp30@cam.ac.uk
Received:
21
January
2018
Accepted:
16
April
2018
Published online:
23
May
2018
Compactification of the ten-dimensional heterotic superstring theory to four dimensions gives rise to two moduli potentials 
, 
, the positive semi-definiteness of which places constraints on the Euler characteristic 
of the internal space 
and the adiabatic index 
of the effective matter source of energy-density 
and pressure 
that generates the physical four-space 
, namely 
, 
, or 
, 
. Here, we show how fermion-bilinear condensation in the internal space, first put forward by Helayël-Neto and Smith, determines the field 
, thus reducing the moduli space to a single canonical field 
with a potential ˜ , which is positive semi-definite under the same conditions that ensure positive semi-definiteness of , , and has a minimum at a value of 
that is approximately constant far from the Planck era at 
. The fields 
, 
, which are canonically normalized in the zero-slope limit, are modified by contributions originating from the higher-derivative gravitational terms 
and 
, but the associated kinetic energy remains positive for times 
, guaranteeing classical stability of the solution, since the generalized indeterminacy principle implies a minimum physically measurable time 
for the superstring theory.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018
