Massive totally symmetric fields in AdS(d)

TL;DR

The paper develops a light-cone gauge framework to study free massive totally symmetric bosonic and fermionic fields in $AdS_d$, unifying their treatment via unitary lowest-weight representations $D(E_0,\mathbf{h})$ of $SO(d-1,2)$. It constructs light-cone actions with an AdS mass operator $A$ and an angular-vector operator $B^I$, and provides explicit oscillator-based realizations for the spin degrees of freedom, including the $so(d-2)$ decomposition and the action of $B^I$ for both bosons and fermions. The work derives the connection between the lowest energy $E_0$ and the physical mass parameter $m$ for massive fields (separately for bosonic and fermionic cases) via relations $E_0 = \frac{d-1}{2} + \sqrt{ m^2 + (h_k - k + \tfrac{d-3}{2})^2 }$ (bosons) and $E_0 = m + h_k - k - 2 + d$ (fermions), along with a mass-shell shift formula $m^2 = E_0(E_0+1-d) - E_0^{m=0}(E_0^{m=0}+1-d)$. This framework preserves $so(d-1,2)$ symmetry in the light-cone form and provides concrete operator realizations (including $A$, $B^I$, $M^{IJ}$) essential for AdS/CFT and higher-spin/string theory contexts. The results offer a path to extending to mixed-symmetry fields and dimensional reductions, thereby enriching the toolkit for AdS higher-spin dynamics.

Abstract

Free totally symmetric arbitrary spin massive bosonic and fermionic fields propagating in AdS(d) are investigated. Using the light cone formulation of relativistic dynamics we study bosonic and fermionic fields on an equal footing. Light-cone gauge actions for such fields are constructed. Interrelation between the lowest eigenvalue of the energy operator and standard mass parameter for arbitrary type of symmetry massive field is derived.