Exploring Non-Perturbative Aspects of Higher Dimensional Theories

Abstract

This thesis aims to provide systematic approaches to studying higher dimensional supersymmetric theories. We first study spectra of BPS states in supersymmetric quantum field theories in five and six dimensions. We propose that generalization of the blowup equation facilitates the computation of BPS spectra for arbitrary 5d/6d field theories having UV completions. We demonstrate this idea by explicitly computing supersymmetric partition functions of various theories including all rank-1 and rank-2 theories, as well some exotic cases. The results provide non-trivial checks for dualities between field theories and evidences for the existence of exotic theories. This idea is generalized into 6d little string theories and 5d/6d field theories in presence of the half-BPS Wilson loop operators. We find that blowup approach along with the modular properties of elliptic genera of 2d worldvolume theories on strings in the 6d little string theories determines their the BPS spectra. We also consider Wilson loops using both gauge theoretic and geometric languages, and compute the partition function counting 1d BPS bound states to the loop operators. Furthermore, we study the superconformal index of 5d non-Lagrangian supercon- formal field theories using two novel methods. One is using Higgs branch flows from UV Lagrangian theories, and the other involves the relation between O7−-plane and O7+-plane. We employ these methods to compute the superconformal index of rank-1 non-Lagrangian theories and identify their global symmetries. Lastly, we consider BPS spectra of 6d supergravity theories. We propose a general modular ansatz for the elliptic genera of 6d supergravity theories. Through the application of mirror symmetry to the modular ansatz of F-theory model, we compute the elliptic genera and validating the ansatz. We extend this method to non-geometric theories and confirm that they satisfy the swampland conjectures including weak gravity conjecture, distance conjecture and emergent string conjecture.