M5 from M2

Abstract

Recently an action based on Lie 3-algebras was proposed to describe M2-branes. We study the case of infinite dimensional Lie 3-algebras based on the Nambu-Poisson structure of three dimensional manifolds. We show that the model contains self-dual 2-form gauge fields in 6 dimensions, and the result may be interpreted as the M5-brane world-volume action.

Higher Spins from Nambu–Chern–Simons Theory

“…It is natural to expect that the SDiff(S 3 ) BLG action can be rewritten as the M5 brane action, and indeed this latter point of view has been taken in a number of works. To our knowledge the full SDiff(S 3 ) BLG model has not yet been rewritten in six-dimensional language; [43] did so for the quadratic theory while [44] achieved this for the interacting theory in a "Carrollian" limit. If this connection is true, our results could be relevant to the physics of M5 branes; one wonders about the interpretation of the quantization of the NCS level in this context.…”

Effective action for Dp-brane in large RR (p − 1)-form background

“…Starting with the D4-brane case [8] which is derived from the M5-brane theory in Cfield background [5,6,7], we can straightforwardly go down to D3-brane and D2-brane theories via the T-duality transformation rules listed above. To go up to D5-brane, we need to look for Lagrangians that would reduce to the D4-brane theory through the replacements (39)-(47).…”

“…When there is a large longitudinal NS-NS B-field background, the effective theory of a D-brane is deformed to a non-commutative gauge theory [3,4], as a result of the fact that the B-field background changes the zero modes of open strings, so that higher derivative terms are turned on. Similarly, when there is a large longitudinal C-field background in M theory, the effective theory of M5-brane is a Nambu-Poisson gauge theory [5,6,7]. The interaction mediated by open membranes under the effect of the C-field is characterized by the gauge symmetry of volume-preserving diffeomorphism, where the volume-form is defined by the C-field.…”

Quiver Chern–Simons theories and 3-algebra orbifolds

“…We start with the infinite dimensional 3-algebra, which is the Nambu bracket of functions on T 3 . The physical meaning of such theory with an infinite number of fields is rather unclear, although one might conceive it is suggestive of higher-dimensional M-theory branes [15,16,17,18]. In this paper we use the Nambu bracket theory as a technical tool and impose a 3-algebra version of orbifold truncation which effectively reduces T 3 → T 2 .…”