Weyl Group Invariance and p-brane Multiplets

TL;DR

The paper addresses how Weyl groups of U-duality, realized as discrete subgroups of $E_{n(+n)}$, act as permutation symmetries on field strengths in type IIA string theory compactifications to $D\ge3$, organizing all supersymmetric $p$-brane solitons into finite multiplets. By mapping dilaton vectors to weight vectors of appropriate Lie groups (ranging from $SL$, $SO$, to $E_6$, $E_7$, $E_8$) and examining Chern-Simons modifications, the authors show that the leading-order Lagrangians are invariant under these Weyl actions, and that the Bogomol’nyi matrices governing supersymmetry are preserved. They further decompose the U-Weyl group into S, T, and X duality subgroups, clarifying how NS-NS and RR sectors transform and how T- and X-duality-induced multiplets arise, including a table of Weyl multiplets for various $p$-brane sectors. The work demonstrates that Weyl groups act as stability duality groups of the vacuum, preserving the number of participating field strengths and the supersymmetry fraction, thereby providing a unifying algebraic framework to classify and relate $p$-brane solutions across dimensions via dimensional reduction and dualities.

Abstract

In this paper, we study the actions of the Weyl groups of the U duality groups for type IIA string theory toroidally compactified to all dimensions $D\ge 3$. We show how these Weyl groups implement permutations of the field strengths, and we discuss the Weyl group multiplets of all supersymmetric $p$-brane solitons.