On Gauged Maximal Supergravity In Six Dimensions

TL;DR

This work constructs a gauged maximal supergravity in six dimensions with SO($5$) gauging by reducing the D=$7$ SO($5$) gauged theory on S$^1$, then demonstrates a smooth $g \to 0$ limit that yields maximal D=$6$ supergravity in the spirit of Tanii. It also shows a complementary D=$5$ limit by turning off the U(1) coupling, and provides full Lagrangians and SUSY rules in Appendices A–D. A domain-wall vacuum descends from the AdS$_7$ ground state, and the reduction preserves supersymmetry, indicating a coherent web of relations among maximal gauged supergravities across D=$7$, D=$6$, and D=$5$ with potential sphere compactifications to higher dimensions. These results illuminate consistent pathways between higher‑ and lower‑dimensional maximal theories and support unified portraits of their AdS/domain‑wall vacua.

Abstract

The maximal SO(5) gauged D=7 supergravity is dimensionally reduced to six dimensions yielding a new SO(5) gauged D=6 model. It is shown that, unlike in D=7, the SO(5) gauge coupling constant can be taken to zero to yield the maximally extended supergravity in six dimensions. It is also shown that the limit of D=5 N=4 SU(2)xU(1) gauged supergravity in which the U(1) coupling constant is turned off can be obtained.