Abstract
Recent work has shown that local supersymmetry on a spacetime boundary in N-extended AdS supergravity in chiral variables implies coupling to a boundary OSp(N|2)C super Chern–Simons theory. Consequently there has been a proposal to define and calculate the entropy S for the boundary, in the supersymmetric version of loop quantum gravity, for the minimal case N=1, via this super Chern–Simons theory. We give an overview of how supergravity can be treated in loop quantum gravity. We review the calculation of the dimensions of the quantum state spaces of UOSp(1|2) super Chern–Simons theory with punctures, and its analytical continuation, for the fixed quantum super area of the surface, to OSp(1|2)C. The result is S=aH/4 for large (super) areas. Lower order corrections can also be determined. We begin also a discussion of the statistical mechanics of the surface degrees of freedom by calculating the grand canonical partition function at zero chemical potential. This is a new result.
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