Mass Gaps and Braneworlds -- In Memory of Peter Freund

TL;DR

This paper explores a novel dimensional reduction in supergravity where a mass gap prevents a continuum of Kaluza-Klein states, enabling a consistent lower-dimensional effective theory despite the non-compact transverse space.

Contribution

It introduces a reduction method with a mass gap in non-compact transverse spaces, addressing the continuum of Kaluza-Klein states problem in supergravity compactifications.

Findings

Mass gap separates zero mode from continuum edge.

Reduction avoids continuum of Kaluza-Klein states.

Lower-dimensional theory requires integrating out massive states.

Abstract

Remembering the foundational contributions of Peter Freund to supergravity, and especially to the problems of dimensional compactification, reduction is considered with a non-compact space transverse to the lower dimensional theory. The known problem of a continuum of Kaluza-Klein states is avoided here by the occurrence of a mass gap between a single normalizable zero-eigenvalue transverse wavefunction and the edge of the transverse state continuum. This style of reduction does not yield a formally consistent truncation to the lower dimensional theory, so developing the lower-dimensional effective theory requires integrating out the Kaluza-Klein states lying above the mass gap.