Speaker
Description
In this talk, construction of the superfield action of the $N = (1, 0)$, $d = 6$ non-Abelian tensor multiplet based on the non-Abelian tensor hierarchies is discussed. The supersymmetric systems of tensors with non-Abelian gauge symmetries are considered to be necessary tools for low-energy effective description of multiple M5-branes, as well as superconformal theories in six dimensions. The proper actions of such systems are not known, with no-go theorem implying that non-Abelian deformation of the tensor gauge symmetry is impossible in local theory with no other fields. Situation is even more complicated in six dimensions, as tensor field here is self-dual and arguments were given by Witten that superconformal action should not exist. Nevertheless, construction of a theory that captures at least some properties of the non-Abelian tensors is of interest, and many approaches have been proposed, with tensor hierarchies being the most conventional, local and Lorentz-covariant. The supersymmetric actions, constructed within the tensor hierarchy approach, however, suffer from instabilities as the kinetic term of the scalar fields is not positive-definite. In this talk, the manifestly supersymmetric action of the non-Abelian tensor is proposed that involves the positive-definite metric in the scalar sector. In the modified action, the self-dual equation of motion of the tensor field is induced by a composite Lagrange multiplier, which is not a component of a standard dynamical tensor multiplet. As a result, the constraint that enforces the gauge group to be non-compact, as in the usual tensor hierarchies, can be avoided. It is shown that for tensor field belonging to particular representations of $SU(3)$ and $SO(4)$ gauge groups, the Lagrangian multiplier is not dynamical. The talk is based on [N. Kozyrev, Supersymmetrizing the Pasti-Sorokin-Tonin action, JHEP 03 (2023) 223].
