Lecturer: Prof. Tom Banks
Affiliation: University of California, Santa Cruz
and Rutgers University
Abstract:
The Wheeler DeWitt equation is the
statement that theories of gravity are
topological in the bulk and only have
boundary DOF. This fits with the Covariant
entropy conjecture, which associates an
areas worth of DOF to the boundary of a
causal diamond. For nested diamonds it
implies that the algebra of operators on the
smaller one be a proper subalgebra of that
on the larger one. Jacobson showed,
conversely, that the area law implies
Einstein's equations (except for the c.c.,
which Banks and Fischler argued was an
asymptotic boundary condition). In
Minkowski space, the maximal causal
diamond is Penrose's conformal boundary.
Traditionally we deal with this by introducing
an S matrix, but this only works in
perturbation theory because of the
inevitable existence of states with arbitrary
numbers of arbitrarily soft gravitons (even
when there are no IR divergences). Instead
we introduce an algebra of densities
describing the flow of quantum numbers out
to null infinity. The simplest of these are the
commuting BMS local translations, which
one can diagonalize. The joint spectrum of
the past and future BMS generators defines
a null cone, and all other currents may be
thought of as generalized functions on this
cone. The algebra must include helicity
raising operators and the simplest way to
introduce them (perhaps the only consistent
way) is to write a generalization of the
Awada Gibbons Shaw supersymmetric BMS
algebra. One must define Sterman
Weinberg jet representations of this algebra,
which reveal that particle energy is related
to constraints on the density degrees of
freedom. Retreating from infinity to a finite
causal diamond, the current algebra is
cutoff by cutting off the spectrum of the
Dirac operator on the holographic screen - a
UV/IR correspondence reminiscent of that in
AdS/CFT.
Additional details of the upcoming Joint Seminars
in Theoretical High Energy Physics can be found
on the following link.