A categorical construction of 4D TQFTs
Louis Crane, David N. Yetter
TL;DR
This paper presents a new categorical method for constructing four-dimensional topological quantum field theories from modular tensor categories, with a detailed proof for the SU(2)q case at roots of unity, relevant to quantum physics interpretations.
Contribution
It introduces a novel categorical construction of 4D TQFTs from modular tensor categories, including a complete proof for the SU(2)q case at roots of unity.
Findings
Constructed 4D TQFT from modular tensor categories
Completed proof for SU(2)q at roots of unity
Potential implications for Chern-Simons state in quantum gravity
Abstract
We construct a four dimensional topological Quantum Field Theory from a modular tensor category. We complete the proof in the case of SU(2)q at a root of unity. Our construction may be important in the physical interpretation of the Chern Simons state in the Ashtekar variables.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic structures and combinatorial models · Noncommutative and Quantum Gravity Theories