Towards an M5-brane model I: A 6d superconformal field theory

Abstract

We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang-Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the ABJM model. While this action is certainly not the desired M5-brane model, we regard it as a key stepping stone towards a potential construction of the (2,0)-theory.

Higher Structures, Self‐Dual Strings and 6d Superconformal Field Theories

“…Interestingly, our Lie 4-algebra string ω sk (g) satisfies these axioms. [45,50] This is very encouraging, as it gives us a link between supergravity and our action and a similar link was also present in the case of the Chern-Simons matter actions of M2-brane models.…”

“…There are, in fact, many more reasons for choosing the string Lie 2-algebra as a higher gauge algebra, and we refer to the papers [45,50] for further details.…”

“…. stands for additional terms irrelevant for our discussion, and A q i denotes the representation of su(N) on R 2N 2 obtained by an embedding u(n) → sp(n), see [50] for details. The covariant derivatives on the spinors in the vector, tensor, and hypermultiplets follow trivially.…”

“…The first two terms are specializations of general actions found in [54] and [55], respectively. The last term was constructed in [50]. While a PST action for the bosonic part of L gauge was given before in [56], the supersymmetric extension was announced but not completed.…”

Towards a tensionless string field theory for the $$ \mathcal{N}=\left(2,0\right) $$ CFT in d = 6

“…Several Lagrangian constructions have been proposed, including the matrix model approach involving a low-energy limit [7,8], the dimensional deconstruction approach [9], and the decompactification limit of d = 5 maximally supersymmetric Yang-Mills theory [10,11]. For other proposals, see [12][13][14][15][16][17] and references therein. Another interesting approach is based on the idea of the conformal bootstrap [18], which does not rely on the existence of a Lagrangian.…”