Axionic Band Structure of the Cosmological Constant

TL;DR

This paper explores how multiple axions in theories of quantum gravity can naturally produce a vast landscape of vacua, potentially explaining the smallness of the cosmological constant through their complex band structure.

Contribution

It introduces a framework where the axionic landscape's structure is determined by instanton charges, leading to an exponential number of vacua that could address the cosmological constant problem.

Findings

Number of vacua scales as |det(Q)|~exp(N)

Dominant instantons set the primary vacuum structure

Subleading instantons lift degeneracies and create a rich landscape

Abstract

We argue that theories with multiple axions generically contain a large number of vacua that can account for the smallness of the cosmological constant. In a theory with N axions, the dominant instantons with charges Q determine the discrete symmetry of vacua. Subleading instantons break the leading periodicity and lift the vacuum degeneracy. For generic integer charges the number of distinct vacua is given by |det(Q)|~exp(N). Our construction motivates the existence of a landscape with a vast number of vacua in a large class of four-dimensional effective theories.