Non-abelian action for multiple five-branes with self-dual tensors

Abstract

Abstract:We construct an action for non-abelian 2-form in 6-dimensions. Our action consists of a non-abelian generalization of the abelian action of Perry and Schwarz for a single five-brane. It admits a self-duality equation on the field strength as the equation of motion. It has a modified 6d Lorentz symmetry. On dimensional reduction on a circle, our action gives the standard 5d Yang-Mills action plus higher order corrections. Based on these properties, we propose that our theory describes the gauge sector of multiple M5-branes in flat space.

The (2, 0) superconformal bootstrap

“…23 The latter value is quite close to the generalized free-field solution at Δ 0 ¼ 8, to which it presumably would converge at higher Λ. The leading 1=c behavior obtained from supergravity, while consistent with the bound, does not appear to follow it very closely.…”

“…We emphasize that these are the first estimates of On the right we display the bound for very large c, with the green dashed line corresponding to the supergravity result (2.7). 23 As discussed in [102] this monotonicity is a generic property of the kind of bounds studied here. 24 A similar pattern was observed for 4d N ¼ 4 SCFTs in [62]: the bounds are saturated with much better accuracy for spin greater than zero.…”

“…It is unclear whether an unconventional (nonlocal?) Lagrangian for the interacting (2, 0) theories could be written down (see, e.g., [21][22][23][24][25][26] for a partial list of attempts), but in any event it would be unlikely to lend itself to a semiclassical approximation.…”

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.…”

Higher gauge theories from Lie n-algebras and off-shell covariantization

“…This direction was further investigated in [6], where a 5-dimensional superconformal action was proposed, as a candidate to study the dynamics of N = (2, 0) self-dual nonabelian tensors in 6 dimensions. In [7] an action for a nonabelian 2-form in 6 dimensions, whose equation of motion gives a self-duality constraint on the field strength, was proposed. It contains manifest Lorentz symmetry in 5 dimensions and upon dimensional reduction it leads to 5-dimensional Yang-Mills theory accompanied with some higher derivative corrections.…”