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.
