Modular invariance and nonrenormalizable interactions

TL;DR

This paper investigates how modular invariance constrains nonrenormalizable superpotential terms in string theory, showing that such terms are generally nonvanishing and can be reformulated to exhibit invariance, with implications for phenomenology.

Contribution

It demonstrates that modular invariance requires certain nonrenormalizable terms to be nonzero and can be reformulated to display invariance, advancing understanding of string theory interactions.

Findings

Modular invariance constrains nonrenormalizable superpotential terms.

Explicit verification in free fermionic models confirms the structure.

Reformulation shows nonrenormalizable terms can be invariant under modular transformations.

Abstract

We examine the modular properties of nonrenormalizable superpotential terms in string theory and show that the requirement of modular invariance necessitates the nonvanishing of certain Nth order nonrenormalizable terms. In a class of models (free fermionic formulation) we explicitly verify that the nontrivial structure imposed by the modular invariance is indeed present. Alternatively, we argue that after proper field redefinition, nonrenormalizable terms can be recast as to display their invariance under the modular group. We also discuss the phenomenological implications of the above observations.