Fermions, quantum gravity and holography in two dimensions
Physical Review D(2024)
摘要
We study a model comprising N flavors of Kähler Dirac fermion propagating
on a triangulated two dimensional disk which is constrained to have a negative
average bulk curvature. Dirichlet boundary conditions are chosen for the
fermions. Quantum fluctuations of the geometry are included by summing over all
possible triangulations consistent with these constraints. We show in the limit
N→∞ that the partition function is dominated by a regular
triangulation of two dimensional hyperbolic space. We use strong coupling
expansions and Monte Carlo simulation to show that in this limit boundary
correlators of the fermions have a power law dependence on boundary separation
as one expects from holography. However we argue that this behavior breaks down
for any finite number of massive fields in the thermodynamic limit and quantum
fluctuations of the bulk geometry drive the theory into a non-holographic
phase. In contrast, for massless fermions we find evidence that the boundary is
conformal even for finite N. This is consistent with theoretical results in
quantum Liouville theory.
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