Quantum Field Theory at Strong Coupling

Abstract

Strongly-coupled Quantum Field Theories (QFT) do not admit a perturbative expansion in the coupling and a Lagrangian formulation is not suitable for such theories. This forces us to rely on non-perturbative techniques like bootstrap, and duality where symmetries (global and broken) play an important role in computing observables like correlation functions. A class of such strongly-coupled QFTs admits conformal invariance, hence, called Conformal Field Theories (CFT), which completely constrains the two-point and three-point correlations. Conformal bootstrap has led to interesting developments in the study of CF T s and is applicable at strong or weak coupling. These studies are restricted mostly to position space and Mellin space. Recently, momentum-space CFT is gaining attention due to its connection to cosmology, flat-space scattering amplitudes, and theories where perturbation theory is amenable. However, momentum-space CFT has not undergone much development compared to position-space CFT . In this work, I will mostly focus on 3D CF T correlation functions in momentum- space and show new results even at the level three-point function that was not discovered in position space. I will discuss the existence of substructures within the three-point correlation functions which will help us demonstrate double-copy and a correspondence to flat-space scattering amplitude. In this thesis, a systematic way to compute three-point functions of arbitrary spins in momentum space is also discussed. In the cosmological correlator context, these momentum space CFT correlation functions play an important role. In particular, in this thesis, it is shown how the α-vacua correlation function in dS space can be understood in terms of the CFT correlation function in momentum space if we relax OPE consistency. A special class of CFTs called the Chern-Simons Matter Theories is also discussed. This class of CFTs, admits a strong-weak duality and a Vasiliev dual in one higher dimension. We use analytical bootstrap tools and duality to compute the four-point functions of the scalar operator in the Supersymmetric Chern-Simons Matter theories and an all-loop conjecture for the anomalous dimension of the scalar operators in Chern-Simons theories which is not possible to compute via the Higher-Spin symmetry. We justify our calculations via various checks.