Moduli and K\"ahler potential in fermionic strings

TL;DR

This paper investigates the moduli fields and Kähler potential in fermionic string models, using marginal operators and symmetry arguments to analyze simple and complex orbifold constructions for phenomenological insights.

Contribution

It introduces a method to identify moduli fields via marginal operators and extends the analysis to realistic fermionic models with asymmetric orbifolds.

Findings

Derived the moduli space and Kähler potential for $Z_2\times Z_2$ orbifolds.

Extended the analysis to asymmetric orbifolds and realistic models.

Provided expressions for the full Kähler potential and duality transformations.

Abstract

We study the problem of identifying the moduli fields in fermionic four-dimensional string models. We deform a free-fermionic model by introducing exactly marginal operators in the form of Abelian Thirring interactions on the world-sheet, and show that their couplings correspond to the untwisted moduli fields. We study the consequences of this method for simple free-fermionic models which correspond to $Z_2\times Z_2$ orbifolds and obtain their moduli space and K\"ahler potential by symmetry arguments and by direct calculation of string scattering amplitudes. We then generalize our analysis to more complicated fermionic structures which arise in constructions of realistic models corresponding to asymmetric orbifolds, and obtain the moduli space and K\"ahler potential for this case. Finally we extend our analysis to the untwisted matter sector and derive expressions for the full K\"ahler potential to be used in phenomenological applications, and the target space duality transformations of the corresponding untwisted matter fields.