2 research outputs found
Current Algebra and Conformal Field Theory on a Figure Eight
We examine the dynamics of a free massless scalar field on a figure eight
network. Upon requiring the scalar field to have a well defined value at the
junction of the network, it is seen that the conserved currents of the theory
satisfy Kirchhoff's law, that is that the current flowing into the junction
equals the current flowing out. We obtain the corresponding current algebra and
show that, unlike on a circle, the left- and right-moving currents on the
figure eight do not in general commute in quantum theory. Since a free scalar
field theory on a one dimensional spatial manifold exhibits conformal symmetry,
it is natural to ask whether an analogous symmetry can be defined for the
figure eight. We find that, unlike in the case of a manifold, the action plus
boundary conditions for the network are not invariant under separate conformal
transformations associated with left- and right-movers. Instead, the system is,
at best, invariant under only a single set of transformations. Its conserved
current is also found to satisfy Kirchhoff's law at the junction. We obtain the
associated conserved charges, and show that they generate a Virasoro algebra.
Its conformal anomaly (central charge) is computed for special values of the
parameters characterizing the network.Comment: 39 pages; Latex with 1 figure included in encapsulated postscript
format. psbox.tex require