Inconsistency of Breathing Mode Extensions of Maximal Five-Dimensional Supergravity Embedding

TL;DR

This paper investigates the possibility of including a breathing-mode scalar in the consistent reduction of type IIB supergravity to five dimensions and finds that such an inclusion leads to inconsistency, challenging previous conjectures.

Contribution

The study demonstrates that augmenting the standard ${ m N}=8$ supergravity reduction with a breathing-mode scalar is inconsistent, clarifying limitations of Kaluza-Klein reductions on $S^5$.

Findings

Breathing-mode scalar inclusion breaks the reduction's consistency.

Standard ${ m N}=8$ supergravity reduction relies on specific properties of type IIB theory.

Adding the breathing-mode scalar destroys the delicate balance required for a consistent reduction.

Abstract

Recent work on consistent Kaluza-Klein reductions on Einstein-Sasaki spaces prompted an intriguing conjecture that there might exist a consistent $S^5$ reduction of type IIB supergravity to give five-dimensional ${\cal N}=8$ gauged supergravity coupled to a massive supermultiplet that includes the breathing-mode scalar. Motivated by this, we investigate the possibility of augmenting the usual ${\cal N}=8$ supergravity reduction to include a breathing-mode scalar, and we show that this is in fact inconsistent. The standard reduction to the massless ${\cal N}=8$ supermultiplet depends for its consistency on a delicate interplay between properties of the ten-dimensional type IIB theory and properties of the Killing vectors on $S^5$. Our calculations show that turning on the breathing-mode is sufficient to destroy the balance, and hence render the reduction inconsistent.