Fractional formulation of Podolsky Lagrangian density

Lagrangians which depend on higher-order derivatives appear frequently in many areas of physics. In this paper, we reformulate Podolsky's Lagrangian in fractional form using left-right Riemann-Liouville fractional derivatives. The equations of motion are obtained using the fractional Euler Lagrange equation. In addition, the energy stress tensor and the Hamiltonian are obtained in fractional form from the Lagrangian density. The resulting equations are very similar to those found in classical field theory.

Hadamard’s variational formula in terms of stress and strain tensors

Starting from a Lagrangian action functional for two scalar fields we construct, by variational methods, the Laplacian Green function for a bounded domain and an appropriate stress tensor. By a further variation, imposed by a given vector field, we arrive at an interior version of the Hadamard variational formula, previously considered by P. Garabedian. It gives the variation of the Green function in terms of a pairing between the stress tensor and a strain tensor in the interior of the domain, this contrasting the classical Hadamard formula which is expressed as a pure boundary variation.

Brown-York charges at null boundaries

The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface. We consider the generalization of this stress tensor to null hypersurfaces. Such a stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle, which fixes an induced Carroll structure on the null boundary. The formula for the mixed-index tensor Tij takes a remarkably simple form that is manifestly independent of the choice of auxiliary null vector at the null surface, and we compare this expression to previous proposals for null Brown-York stress tensors. The stress tensor we obtain satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the hypersurface, as a result of the null constraint equations. For transformations that act covariantly on the boundary structures, the Brown-York charges coincide with canonical charges constructed from a version of the Wald-Zoupas procedure. For anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry, which we explicity verify for a set of symmetries associated with finite null hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.

Regge trajectories for the (2, 0) theories

We investigate the structure of conformal Regge trajectories for the maximally supersymmetric (2, 0) theories in six dimensions. The different conformal multiplets in a single superconformal multiplet must all have similarly-shaped Regge trajectories. We show that these super-descendant trajectories interact in interesting ways, leading to new constraints on their shape. For the four-point function of the stress tensor multiplet supersymmetry also softens the Regge behavior in some channels, and consequently we observe that ‘analyticity in spin’ holds for all spins greater than −3. All the physical operators in this correlator therefore lie on Regge trajectories and we describe an iterative scheme where the Lorentzian inversion formula can be used to bootstrap the four-point function. Some numerical experiments yield promising results, with OPE data approaching the numerical bootstrap results for all theories with rank greater than one.