Exact Results on Higher Dimensional Quantum Field Theories

Abstract

This thesis aims at studying the higher dimensional quantum field theories, engi- neered from the string theory. These theories are genuinely strongly interactive, thus being difficult to be understood within the conventional QFT framework. In particular, I focus on those 5d / 6d QFTs which can be deformed to the weakly coupled 5d Yang-Mills theories, in which the deformation is caused either by a rel- evant operator or by a circle compactification. Instantons are crucial for observing the physics of 5d / 6d QFTs which correspond to the UV fixed points of certain 5d SYMs. In the first half of the thesis, I obtain the general expression for the instanton partition function of 5d SYMs and apply it to study the spectrum of various UV QFTs. The second half focuses on the 6d non-critical strings, which are key objects of 6d QFTs. Two types of 6d strings, M-strings and E-strings, are considered, for which the worldsheet gauge theories are explicitly developed.