Conformal Field Theory Approach Research Articles

Time-dependent multipoint correlation functions of the nonlinear schrödinger model

A one-dimensional system of bosons, interacting via a delta-function potential, is analyzed by means of a conformal field theory approach. A systematic method for deriving the operator content of the critical Hamiltonian of the model is proposed. In the case of impenetrable bosons it is shown that the Hamiltonian consists of only two commuting parts and possesses an unsuspected symmetry. A number of new results for time-dependent multipoint correlators are presented.

PERCOLATION ON A FRACTAL WITH THE STATISTICS OF PLANAR FEYNMAN GRAPHS: EXACT SOLUTION

A new bond-percolation problem on a graph (fractal) randomly chosen from all planar Feynman graphs of zero-dimensional φ3 (or φ4) theory in the thermodynamical limit (infinite order of graphs) is solved exactly. At the percolation transition point pc the mean number of clusters per volume unit has the singularity (pc−p)4 log (pc−p) which corresponds to the critical exponent α=−2. This model is a particular example of Potts models on dynamical planar lattice1 and the result agrees with the formulae obtained in Ref. 2 by conformal field theory approach for Potts spins interacting with 2D quantum gravity.

Conformal field theory and the symmetries of string field theory

The two-dimensional conformal field theory representation of Witten's bosonic string field theory is discussed. The basic overlap equations, K n symmetry and BRST invariance are proved directly, without the usual expansion in oscillators. The conformal field theory approach naturally provides local overlap identities which (when integrated over half the string) can be used to verify properties of the cubic action. In particular, a recently proposed diffeomorphism invariance is shown to be free of anomalies. Finally, a new class of symmetries, including generalizations of the K n symmetries which are local in spacetime, are presented.