Deformed Heisenberg charges in three-dimensional gravity

Understand

In this paper, we consider the bulk plus boundary phase space for three-dimensional gravity with negative cosmological constant for a particular choice of conformal boundary conditions: the conformal class of the induced metric at the boundary is kept fixed and the mean extrinsic curvature is constrained to be one.

• Such specific conformal boundary conditions define so-called Bryant surfaces, which can be classified completely in terms of holomorphic maps from Riemann surfaces into the spinor bundle.
• To study the observables and gauge symmetries of the resulting bulk plus boundary system, we introduce an extended phase space, where these holomorphic maps are now part of the gravitational bulk plus boundary phase space.
• The physical phase space is obtained by introducing two sets of Kac-Moody currents, which are constrained to vanish.