Null reductions of the M5-brane

Abstract

We perform a general reduction of an M5-brane on a spacetime that admits a null Killing vector, including couplings to background 4-form fluxes and possible twisting of the normal bundle. We give the non-abelian extension of this action and present its supersymmetry transformations. The result is a class of supersymmetric non-Lorentzian gauge theories in 4+1 dimensions, which depend on the geometry of the six-dimensional spacetime. These can be used for DLCQ constructions of M5-branes reduced on various manifolds.

Non-Lorentzian avatars of (1,0) theories

“…where i, j = 1, 2, 3, 4 and we use ∼ as the exact relation depends upon the details of the null reduction [28]. Furthermore F ∼ − 4 F and G = 4 G where 4 is the Hodge star in x 1 , .…”

“…, x 4 . One finds that the remaining components of H can be determined using six-dimensional self-duality from F and G. It was observed in [13,28] that non-Lorentzian five-dimensional Lagrangians can be constructed and generalized to non-abelian interacting fields by taking F = dA, where A = (A − , A i ) is a five-dimensional gauge field and G = 4 G off-shell. In the action G acts as a Lagrangian multiplier that imposes the anti-self-duality of F on-shell.…”

A nonabelian M5 brane Lagrangian in a supergravity background

“…Our Lagrangian is more general than the 5d SYM Lagrangian that was discovered in [5] because our Lagrangian captures three different types of dimensional reductions associated to a Killing vector that is either spacelike, timelike or lightlike. By choosing our Killing vector field to be lightlike we should be able to make contact with the Lagrangian that was recently found in [22]. We can perform explicit dimensional reduction of our Lagrangian and get a Lagrangian in 5d.…”

“…We may start with abelian gauge group and perform the reduction where dualization is easy to perform following [6]. In 5d we may subsequently find its nonabelian generalization [5,22] which is a nonabelian 5d SYM Lagrangian. But the nonabelian generalization should be unique.…”

Null Dimensional Reduction of M2-Brane

“…In this paper we proceed in similar way when we analyse M2-brane in the M-theory background with null isometry. This is very important problem which, as far as we know, has not been studied yet, with exception of recent paper [33] 2 . We firstly consider M2-brane extended along null isometry direction and perform its double dimensional reduction.…”