Higher Symmetries in Quantum Field Theory from String Theory

Explore the emergence of higher symmetries in quantum field theory through the lens of string theory on singular non-compact special holonomy spaces. Delve into the process of cutting and gluing singularities that extend to the boundary of these spaces, revealing how these techniques lead to the appearance of higher symmetries in supersymmetric quantum field theories. Examine the implications of compactifying these spaces and the resulting effects on symmetries using related gluing methods. Investigate specific examples involving elliptically fibered Calabi-Yau manifolds, comparing the findings to dual F-theory interpretations where these symmetries are linked to the arithmetic structure of elliptic curves. This comprehensive lecture provides insights into the intricate relationship between string theory, geometry, and quantum field theory, offering a deeper understanding of higher symmetries and their origins.