Football Shaped Extra Dimensions and the Absence of Self-Tuning

TL;DR

This paper demonstrates that certain 6D brane-world models with extra dimensions do not achieve self-tuning of the cosmological constant when the brane tension changes, aligning with Weinberg's no-go theorem.

Contribution

The paper refutes claims of self-tuning in co-dimension two brane-world models by showing they cannot maintain flatness after phase transitions, clarifying their limitations.

Findings

Brane tension changes lead to non-flat branes.

Self-tuning mechanisms fail in these models.

Results align with Weinberg's no-go theorem.

Abstract

There have been some recent claims that brane-worlds of co-dimension two in a 6D bulk with compact extra dimensions may lead to self-tuning of the effective 4D cosmological constant. Here we show that if a phase transition occurs on a flat brane, so as to change its tension, then the brane will not remain flat. In other words, there is really no self-tuning in such models, which can in fact be understood in four-dimensional terms and are therefore subject to Weinberg's no-go theorem.