Matching higher symmetries across Intriligator-Seiberg duality

We study higher symmetries and anomalies of 4d $$ \mathfrak{so} $$ so (2nc) gauge theory with 2nf flavors. We find that they depend on the parity of nc and nf, the global form of the gauge group, and the discrete theta angle. The contribution from the fermions plays a central role in our analysis. Furthermore, our conclusion applies to $$ \mathcal{N} $$ N = 1 supersymmetric cases as well, and we see that higher symmetries and anomalies match across the Intriligator-Seiberg duality between $$ \mathfrak{so} $$ so (2nc) ↔$$ \mathfrak{so} $$ so (2nf − 2nc + 4).

Symmetries of $$ \mathcal{N} $$ = (1, 0) supergravity backgrounds in six dimensions

General $$ \mathcal{N} $$ N = (1, 0) supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) SU(2) superspace; and (ii) conformal superspace. With motivation to develop rigid supersymmetric field theories in curved space, this paper is devoted to the study of the geometric symmetries of supergravity backgrounds. In particular, we introduce the notion of a conformal Killing spinor superfield ϵα, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector ξa and tensor ζa(n) superfields. The former parametrise conformal isometries of supergravity backgrounds, which in turn yield symmetries of every superconformal field theory. Meanwhile, the conformal Killing tensors of a given background are associated with higher symmetries of the hypermultiplet. By studying the higher symmetries of a non-conformal vector multiplet we introduce the concept of a Killing tensor superfield. We also analyse the problem of computing higher symmetries for the conformal d’Alembertian in curved space and demonstrate that, beyond the first-order case, these operators are defined only on a limited class of backgrounds, including all conformally flat ones.

Integrability structures of the generalized Hunter–Saxton equation

We consider integrability structures of the generalized Hunter–Saxton equation. We obtain the Lax representation with non-removable spectral parameter, find local recursion operators for symmetries and cosymmetries, generate an infinite-dimensional Lie algebra of higher symmetries, and prove existence of infinite number of cosymmetries of higher order. Further, we give examples of employing the higher order symmetries to constructing exact globally defined solutions for the generalized Hunter–Saxton equation.