by
Vladimir Dobrev(Bulgarian Academy of Science, Sofia)
→
Europe/Berlin
313
313
Description
We give a group-theoretic interpretation of non-relativistic
holography as equivalence between representations of the
Schr\"odinger algebra describing bulk fields and boundary fields.
Our main result is the explicit construction of the boundary-to-bulk
operators for which we first construct the two-point Green function
in the bulk. Further we show that these operators and the bulk-to-boundary
operators are intertwining operators. In analogy to the relativistic
case, we show that each bulk field has two boundary fields with
conjugated conformal weights. These fields are related by another
intertwining integral operator given by a two-point function on the
boundary.
Analogously to the relativistic result of Klebanov-Witten we give
the conditions when both boundary fields are physical. Finally, we
recover in our formalism earlier non-relativistic results
in a less general setting for scalar fields by Son and others.