OM Theory and V-duality

TL;DR

This paper demonstrates that V-duality in OM theory, related to Lorentz boosts of bound states in supergravity, results in equivalent theories connected by Galilean boosts, extending the duality to various noncommutative theories.

Contribution

It shows that V-duality in OM theory is valid and leads to equivalent theories under infinitesimal Lorentz boosts, connecting supergravity bound states and noncommutative theories.

Findings

V-duality holds for OM theory with Galilean boost equivalence.

Lorentz boosts must be infinitesimal for decoupled OM theories.

V-duality extends to noncommutative string and Yang-Mills theories.

Abstract

We show that the (M5, M2, M2$'$, MW) bound state solution of eleven dimensional supergravity recently constructed in hep-th/0009147 is related to the (M5, M2) bound state one by a finite Lorentz boost along a M5-brane direction perpendicular to the M2-brane. Given the (M5, M2) bound state as a defining system for OM theory and the above relation between this system and the (M5, M2, M2', MW) bound state, we test the recently proposed V-duality conjecture in OM theory. Insisting to have a decoupled OM theory, we find that the allowed Lorentz boost has to be infinitesimally small, therefore resulting in a family of OM theories related by Galilean boosts. We argue that such related OM theories are equivalent to each other. In other words, V-duality holds for OM theory as well. Upon compactification on either an electric or a `magnetic' circle (plus T-dualities as well), the V-duality for OM theory gives the known one for either noncommutative open string theories or noncommutative Yang-Mills theories. This further implies that V-duality holds in general for the little m-theory without gravity.