Speaker
Prof.
Michael Freedman
(Microsoft Station Q, USA)
Description
Abstract: For the usual U(1) - principle bundle of
electromagnetism with a U(1) - connection, A, magnetic
charge can be calculated by integrating a local quantity
(magnetic flux). This is no longer true if we allow the
connection to boost the fibers (i.e. where SL(2,R) acts by
linear fractional transformations on the fibers.) This strange
phenomena of magnetic charge without magnet flux allows
the construction of monopoles with exotic topologies. In
condensed matter one can similarly imagine a circle valued
order parameter (say of a superfluid) but with an sl(2,R)-
connection created artificially in the cold-atom settings. In
this case it is possible to produce a 2npi rotational flux from
a connection that is a pure boost. The quantization
condition on the boost is now expressed via hyperbolic
geometry. Finally, a superconductor with sl(2,R)-connection
on a circular order parameter is considered within Ginzburg-
Landau theory. Each of these three examples calls for a
different explanation of how the sl(2,R) behavior could arise.
This is joint work with Roman Lutchyn.
