S-Duality and Cosmological Constant in String Theory

TL;DR

This paper investigates how S-duality symmetry in four-dimensional string effective actions is affected by a nonzero cosmological constant, suggesting that S-duality favors a small or vanishing cosmological constant.

Contribution

It demonstrates that nonzero cosmological constant breaks S-duality symmetry and argues that S-duality naturally constrains the cosmological constant to be small or zero.

Findings

S-duality symmetry is broken by nonzero $5$

Exact S-duality would force $5$ to vanish

Small $5$ is favored by the naturalness hypothesis

Abstract

The S-duality invariance of the equations of motion of four dimensional string effective action with cosmological constant, $\Lambda $, is studied. It is demonstrated that the S-duality symmetry of the field equations are broken for nonzero $\Lambda$. The ``naturalness'' hypothesis is invoked to argue that $\Lambda $ should remain small since exact S-duality symmetry will force the cosmological constant to vanish in the string effective action.