D=5 M-theory radion supermultiplet dynamics

TL;DR

The paper analyzes radion dynamics in heterotic M-theory braneworlds by performing a consistent 5D→4D truncation that yields gravity coupled to a two-scalar $SL(2,R)/U(1)$ sigma model for the radion and its pseudoscalar. It constructs a solitonic string solution and shows that finite-energy configurations require an $SL(2,Z)$ identification of the target space, which imposes a minimum brane separation and avoids brane collisions. It then analyzes the conditions under which the pseudoscalar can be truncated, derives SUSY-based potentials from a holomorphic superpotential, and discusses the cyclic-universe potential's incompatibility with the underlying theory, as well as the impact of Kaluza-Klein corrections on the potentials. The work highlights the role of modular symmetries in radion cosmology and outlines avenues for constructing $SL(2,Z)$-invariant radion potentials and exploring their 5D brane-interaction origins.

Abstract

We show how the bosonic sector of the radion supermultiplet plus d=4, N=1 supergravity emerge from a consistent braneworld Kaluza-Klein reduction of D=5 M--theory. The radion and its associated pseudoscalar form an SL(2,R)/U(1) nonlinear sigma model. This braneworld system admits its own brane solution in the form of a 2-supercharge supersymmetric string. Requiring this to be free of singularities leads to an SL(2,Z) identification of the sigma model target space. The resulting radion mode has a minimum length; we suggest that this could be used to avoid the occurrence of singularities in brane-brane collisions. We discuss possible supersymmetric potentials for the radion supermultiplet and their relation to cosmological models such as the cyclic universe or hybrid inflation.

Figures (4)

• Figure 1: The five-dimensional interpretation of the solitonic string as the intersection of a membrane with the two boundary 3-branes, with the intersecting string delocalized along the membrane.
• Figure 2: The approximation to the cyclic universe potential necessarily exhibits a positive bump near the origin.
• Figure 3: The part of the two-field potential that is relevant for a calculation of the spectrum of density perturbations. The $\chi=0$ section represents the original one-field potential. Note the instability in the form of a saddle point at the minimum of the $\chi=0$ section.
• Figure 4: Graph of an originally constant cosmological potential after inclusion of massive Kaluza-Klein supermultiplet corrections. The height $V_0$ of the original uncorrected potential determines the range of $\phi=e^{\frac{b}{2}}$ values where the corrections eventually become important.