Notes on Vanishing Cosmological Constant without Bose-Fermi Cancellation

TL;DR

This paper presents a method to construct non-supersymmetric point particle theories with vanishing one-loop cosmological constant using asymmetric orbifolds, without requiring bose-fermi cancellation, highlighting a novel approach to cosmological constant problems.

Contribution

It introduces a systematic construction of non-supersymmetric theories with zero one-loop cosmological constant via asymmetric orbifolds, distinct from string vacua.

Findings

Constructed models with vanishing one-loop cosmological constant.

Demonstrated the approach using toroidal asymmetric orbifolds with Lie algebra lattices.

Showed the theories are non-supersymmetric yet have zero cosmological constant.

Abstract

In this article we discuss how one can systematically construct the point particle theories that realize the vanishing one-loop cosmological constant without the bose-fermi cancellation. Our construction is based on the asymmetric (or non-geometric) orbifolds of supersymmetric string vacua. Using the building blocks of their partition functions and their modular properties, we construct the theories which would be naturally identified with certain point particle theories including infinite mass spectra, but not with string vacua. They are obviously non-supersymmetric due to the mismatch of the bosonic and fermionic degrees of freedom at each mass level. Nevertheless, it is found that the one-loop cosmological constant vanishes, after removing the parameter effectively playing the role of the UV cut-off. As concrete examples we demonstrate the constructions of the models based on the toroidal asymmetric orbifolds with the Lie algebra lattices (Englert-Neveu lattices) by making use of the analysis given in [26].