Dynamics of Multiple Kaluza-Klein Monopoles in M- and String Theory

TL;DR

The paper analyzes the world-volume dynamics of multiple Kaluza-Klein monopoles in M-theory and string theories to test dualities. By constructing the low-energy theories from zero modes on multicenter Taub-NUT backgrounds, it shows that M-theory/IIA yield a $U(N)$-type gauge structure in $(6+1)$D, IIB yields a $(2,0)$ theory with $N$ tensor multiplets, and heterotic theory maps to a flat or deformed moduli space related to $N$-particle BPS monopoles in $SU(2)$. Singular points reveal enhanced gauge symmetry (M/IIA) or tensionless strings (IIB), while heterotic coincidences preserve a non-singular monopole moduli space. The results consistently align with duality conjectures and suggest a string-theoretic realization of the $(2,0)$ theory on KK monopoles with potential ties to Matrix theory on tori. Overall, the work provides a concrete world-volume framework for testing dualities and understanding the rich structure of KK monopole dynamics.

Abstract

We analyse the world-volume theory of multiple Kaluza-Klein monopoles in string and M-theory by identifying the appropriate zero modes of various fields. The results are consistent with supersymmetry, and all conjectured duality symmetries. In particular for M-theory and type IIA string theory, the low energy dynamics of N Kaluza-Klein monopoles is described by supersymmetric U(N) gauge theory, and for type IIB string theory, the low energy dynamics is described by a (2,0) supersymmetric field theory in (5+1) dimensions with N tensor multiplets and tensionless self-dual strings. It is also argued that for the Kaluza-Klein monopoles in heterotic string theory, the apparently flat moduli space gets converted to the moduli space of BPS monopoles in SU(2) gauge theory when higher derivative corrections to the supergravity equations of motion are taken into account.