Manifest Duality for Partially Massless Higher Spins
(45 pages)

By writing the theory of a partially massless spins field in a first order formalism, and defining the associated generalised curvature, one can construct dualities which are analogous to the electricmagnetic duality in massless spin1 D=4. A symmetric sindex gauge field is dual to another partially massless sindex gauge field, for all spins s and depths t.

On curved backgrounds, the underlying (A)dS group has spins representations for which gauge invariances remove 2t+1 of the 2s+1 helicity components. These are called partially massless fields of depth t. For massless spin1 fields, we have a gauge invariant Maxwell field strength and an electromagnetic duality. For massless spin2, we analogously have the Riemann curvature tensor and dual (Weyl tensor). Here, the authors have generalised to partially massless fields of arbitrary spin and depth, defining generalised curvatures and dualities.

Stability in higherderivative matter field theories
(7 pages)

Previously, 1306.1835 has proposed higherderivative matter fields, and can be written via nondynamical auxiliary fields. In such a theory, there are two free parameters. Demanding stability of a Minkowski vacuum, as well as the absence of tachyons, places bounds on these parameters.

One can interpret such nonconventional higherderivative matter fields as a modification to gravity. These considerations restrict this possible modification to GR. The two bounds derived here are necessary, but by no mean sufficient  the parameter space of these higherderivative theories is potentially very restricted.
