Can a Lattice String Have a Vanishing Cosmological Constant?

TL;DR

This paper proves that certain one-loop partition functions with a vanishing cosmological constant cannot be realized by consistent lattice strings, highlighting the ongoing challenge of constructing non-supersymmetric string models with zero cosmological constant.

Contribution

It demonstrates the impossibility of realizing specific one-loop partition functions with zero cosmological constant using consistent lattice strings.

Findings

Certain one-loop partition functions cannot be realized by lattice strings.

A new test for one-loop partition functions of lattice strings is proposed.

Constructing non-supersymmetric strings with zero cosmological constant remains unresolved.

Abstract

We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must satisfy.