Higher Spin Symmetries in Quantum Field Theories

Abstract

Non-perturbative techniques are important for studying Quantum field theory and Conformal field theory. Symmetries provide us with a powerful tool to study the conformal field theories non-perturbatively. Higher spin symmetries are an important class of symmetries which are found in a large number of theories. Higher spin symmetry allows us to study CFTs without a lagrangian and in a model independent way. Correlation functions are the most important quantities in CFTs and knowing the symmetry algebra, we can relate different correlation functions of the theory using higher spin equations. Usual technique of calculating them using conformal invariance becomes inefficient for correlators with higher spin currents. We show that higher spin symmetry provides us with an easy way by simplifying our problem of solving second order differential equations into that of solving algebraic equations. Going away from the conformal fixed point makes it difficult to calculate correlation functions in the absence of any general analysis technique. Exploring the nature of symmetry in the non-conformal cases can provide us with an efficient method to calculate complicated non-conformal correlators. We provide some evidence for the existence of the symmetry in non-conformal cases. We also extend the analysis to finite temperature and higher dimensions.