Construction and Application of Adjusted Higher Gauge Theories

This PhD thesis investigates several aspects of nonabelian higher gauge theories, which appear in many areas of physics, notably string theory and gauged supergravity. We show that nonabelian higher gauge theory admits a consistent classical nonperturbative formulation insofar as a higher nonabelian parallel transport exists consistently, without requiring certain curvature components (fake curvature) to vanish. Next, we explore examples of nonabelian higher gauge theories that naturally appear in high-energy physics. Using a generalisation of $L_\infty$-algebras called $E_2L_\infty$-algebras, we show that tensor hierarchies of gauged supergravity naturally admit a formulation in terms of higher nonabelian gauge theories. Furthermore, toroidal compactifications of string theory exhibiting T-duality also naturally contain higher gauge symmetry, which explain several features of nongeometric compactifications (Q- and R-fluxes). Based on the papers arXiv:1911.06390, arXiv:2106.00108, and arXiv:2204.01783 coauthored with Christian Saemann and Leron Borsten.