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arXiv · 2205.12320

Quantum field theoretic representation of Wilson surfaces: I higher coadjoint orbit theory

Roberto Zucchini
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Abstract

This is the first of a series of two papers devoted to the partition function realization of Wilson surfaces in strict higher gauge theory. A higher version of the Kirillov-Kostant-Souriau theory of coadjoint orbits is presented based on the derived geometric framework, which has shown its usefulness in 4--dimensional higher Chern--Simons theory. An original notion of derived coadjoint orbit is put forward. A theory of derived unitary line bundles and Poisson structures on regular derived orbits is constructed. The proper derived counterpart of the Bohr--Sommerfeld quantization condition is then identified. A version of derived prequantization is proposed. The difficulties hindering a full quantization, shared with other approaches to higher quantization, are pinpointed and a possible way--out is suggested. The theory we elaborate provide the geometric underpinning for the field theoretic constructions of the companion paper.

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Roberto Zucchini. 2022-05-24. Quantum field theoretic representation of Wilson surfaces: I higher coadjoint orbit theory. https://doi.org/10.1007/jhep10(2022)132

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