Small treatise on spin-3/2 fields and their dual spectral functions

In this work we systematically study various aspects of spin-3/2 fields in a curved background. We mostly focus on a minimally coupled massive spin-3/2 field in arbitrary dimensions, and solve the equation of motion either explicitly or numerically in AdS, Schwarzschild-AdS and Reissner-Nordström-AdS backgrounds. Although not the main focus of this work, we also make a connection with the gravitino equation of motion in gauged supergravity. Motivated by the AdS/CFT correspondence, we emphasize calculational improvements and technical details of the dual spectral functions. We attempt to provide a coherent and comprehensive picture of the existing literature

On marginal deformations and non-integrability

We study the interplay between a particular marginal deformation of $\mathcal{N}$ = 4 super Yang-Mills theory, the β deformation, and integrability in the holographic setting. Using modern methods of analytic non-integrability of Hamiltonian systems, we find that, when the β parameter takes imaginary values, classical string trajectories on the dual background become non-integrable. We expect the same to be true for generic complex β parameter. By exhibiting the Poincaré sections and phase space trajectories for the generic complex β case, we provide numerical evidence of strong sensitivity to initial conditions. Our findings agree with expectations from weak coupling that the complex β deformation is non-integrable and provide a rigorous argument beyond the trial and error approach to non-integrability