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arXiv · 1912.12331

Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of $BF$ theory

Fridrich Valach·Donald Ray Youmans
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Abstract

We give an interpretation of the holographic correspondence between two-dimensional $BF$ theory on the punctured disk with gauge group ${\rm PSL}(2,\mathbb R)$ and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian $S^1$-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

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Fridrich Valach, Donald Ray Youmans. 2019-12-27. Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of $BF$ theory. https://doi.org/10.1007/jhep12(2020)189

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