Aspects of Higher Spin Symmetry and Its Breaking

Abstract

This thesis explores different aspects of higher spin symmetry and its breaking in the context of Quantum Field Theory, AdS/CFT and String Theory. In chapter 2, we study the constraints imposed by the existence of a single higher spin conserved current on a three-dimensional conformal field theory (CFT). A single higher spin conserved current implies the existence of an infinite number of higher spin conserved currents. The correlation functions of the stress tensor and the conserved currents are then shown to be equal to those of a free field theory. Namely a theory of N free bosons or free fermions. This is an extension of the Coleman-Mandula theorem to CFT's, which do not have a

conventional S-matrix. In chapter 3, we consider three-dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large N limit, in the sense that

the operators separate into single-trace and multi-trace and obey the usual large N

factorization properties. We assume that the only single trace operators are the higher spin currents plus an additional scalar. Using the slightly broken higher spin symmetry we constrain the three-point functions of the theories to leading order in N. We show that there are two families of solutions. One family can be realized as a theory of N fermions with an O(N) Chern-Simons gauge field, the other as a N bosons plus the Chern-Simons gauge field.

In chapter 4, we consider several aspects of unitary higher-dimensional conformal field theories. We investigate the dimensions of spinning operators via the crossing equations in the light-cone limit. We find that, in a sense, CFTs become free at large spin and 1/s is a weak coupling parameter. The spectrum of CFTs enjoys additivity: if two twists τ1, τ2 appear in the spectrum, there are operators whose twists are arbitrarily close to τ1+τ2. We characterize how τ1+τ2 is approached at large spin by solving the crossing equations analytically. Applications include the 3d Ising model, theories with a gravity dual, SCFTs, and patterns of higher spin symmetry breaking.

In chapter 5, we consider higher derivative corrections to the graviton three-point coupling within a weakly coupled theory of gravity. We devise a thought experiment involving a high energy scattering process which leads to causality violation if the graviton three-point vertex contains the additional structures. This violation cannot be fixed by adding conventional particles with spins J ≤ 2. But, it can be fixed by adding an infinite tower of extra massive particles with higher spins, J > 2. In AdS theories this implies a constraint on the conformal anomaly coefficients (a-c)/c lesssim {1 over Delta_{gap}^2}$ in terms of $Delta_{gap}$, the dimension of the lightest single particle operator with spin J > 2. For inflation, or de Sitter-like solutions, it indicates the existence of massive higher spin particles if the gravity wave non-gaussianity deviates significantly from the one computed in the Einstein theory.