Warped Schwarzian theory

Abstract

We consider the (twisted) warped Virasoro group Diff($S^1$)$⋉$ C${}^{\infty }$($S^1$) in the presence of its three cocycles. We compute the Kirillov-Kostant-Souriau symplectic 2-form on coadjoint orbits. We then construct the Euclidean action of the `warped Schwarzian theory' associated to the orbit with SL(2,$\mathbb{R}$)$\times$U(1) stabilizer as the effective theory of the reparametrization over the base circle and evaluate the corresponding one-loop-exact path integral. We further discuss thermodynamics of the wSch theory in comparison with the complex SYK model.

20 pages, v2 typos corrected refs added, v3 added a new section on thermodynamics in comparison to the complex SYK

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• A Matrix Model for Flat Space Quantum Gravity
• A Solvable Model of Flat Space Holography
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