High Energy Physics - Theory
[Submitted on 3 Oct 2025
]
Title: Inverse Monoid Topological Quantum Field Theories and Open-Closed Grand Canonical Symmetric Orbifolds
Title: 逆独异元拓扑量子场论和开-闭大 canonical 对称轨道模型
Abstract: We present an open-closed topological quantum field theory for inverse monoids which generalizes the theory of principle fiber bundles with finite gauge group over Riemann surfaces with boundary. The theory is constructed using the isomorphism between the semisimple inverse monoid algebra and a matrix algebra which lies at the heart of monoid structure and representation theory. An example that we study in detail is the Ivanov-Kerov monoid of partial permutations. We review motivations from string theory for the resulting grand canonical theory of covers with boundaries.
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