178 research outputs found
Coulomb Gas Representation of the SU(2) WZW Correlators at Higher Genera
We express the correlation functions of the SU(2) WZW conformal field theory
on Riemann surfaces of genus >1 by finite dimensional integrals.Comment: 9 pages, late
Field condensations and Noncritical String for c>1
Quantum theory of 2d gravity for is examined as a non-critical string
theory by taking account of the loop-correction of open strings whose end
points are on the 2d world surface of the closed string. This loop-correction
leads to a conformal anomaly, and we obtain a modified target-space action
which implies a new phase of the non-critical closed-string. In this phase, the
dual field of the gauge field, which lives on the boundary, condenses and the
theory can be extended to without any instability.Comment: 17 pages, Latex, no figur
On the validity of ADM formulation in 2D quantum gravity
We investigate 2d gravity quantized in the ADM formulation, where only the
loop length is retained as a dynamical variable of the gravitation, in
order to get an intuitive physical insight of the theory. The effective action
of is calculated by adding scalar fields of conformal coupling, and the
problems of the critical dimension and the time development of are
addressed.Comment: 12 page
Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems
We work out finite-dimensional integral formulae for the scalar product of
genus one states of the group Chern-Simons theory with insertions of Wilson
lines. Assuming convergence of the integrals, we show that unitarity of the
elliptic Knizhnik-Zamolodchikov-Bernard connection with respect to the scalar
product of CS states is closely related to the Bethe Ansatz for the commuting
Hamiltonians building up the connection and quantizing the quadratic
Hamiltonians of the elliptic Hitchin system.Comment: 24 pages, latex fil
Elliptic Wess-Zumino-Witten Model from Elliptic Chern-Simons Theory
This letter continues the program aimed at analysis of the scalar product of
states in the Chern-Simons theory. It treats the elliptic case with group
SU(2). The formal scalar product is expressed as a multiple finite dimensional
integral which, if convergent for every state, provides the space of states
with a Hilbert space structure. The convergence is checked for states with a
single Wilson line where the integral expressions encode the Bethe-Ansatz
solutions of the Lame equation. In relation to the Wess-Zumino-Witten conformal
field theory, the scalar product renders unitary the
Knizhnik-Zamolodchikov-Bernard connection and gives a pairing between conformal
blocks used to obtain the genus one correlation functions.Comment: 18 pages, late
The Block Spin Renormalization Group Approach and Two-Dimensional Quantum Gravity
A block spin renormalization group approach is proposed for the dynamical
triangulation formulation of two-dimensional quantum gravity. The idea is to
update link flips on the block lattice in response to link flips on the
original lattice. Just as the connectivity of the original lattice is meant to
be a lattice representation of the metric, the block links are determined in
such a way that the connectivity of the block lattice represents a block
metric. As an illustration, this approach is applied to the Ising model coupled
to two-dimensional quantum gravity. The correct critical coupling is
reproduced, but the critical exponent is obscured by unusually large finite
size effects.Comment: 10 page
Quasi-Spin-Charge Separation and the Spin Quantum Hall Effect
We use quantum field theory methods to study the network model for the spin
quantum hall transition. When the couplings are fine tuned in a certain way,
the spin and charge degrees of freedom, corresponding to the supercurrent
algebras su(2) and osp(2|2) respectively, decouple in the renormalization group
flow. The infrared fixed point of this simpler theory is the coset
osp(4|4)/su(2) which is closely related to the current algebra osp(2|2) but not
identical. Some critical exponents are computed and shown to agree with the
recent predictions based on percolation.Comment: 20 pages, two figures, Some subtleties in implementing the coset are
pointed out, so that the resulting fixed point theory is not precisely the
osp(2|2) current algebra. This modifies the comparison with percolatio
Localization-delocalization transition of disordered d-wave superconductors in class CI
A lattice model for disordered d-wave superconductors in class CI is
reconsidered. Near the band-center, the lattice model can be described by Dirac
fermions with several species, each of which yields WZW term for an effective
action of the Goldstone mode. The WZW terms cancel out each other because of
the four-fold symmetry of the model, which suggests that the quasiparticle
states are localized. If the lattice model has, however, symmetry breaking
terms which generate mass for any species of the Dirac fermions, remaining WZW
term which avoids the cancellation can derive the system to a delocalized
strong-coupling fixed point.Comment: 4 pages, revte
Phase diagram of a 1 dimensional spin-orbital model
We study a 1 dimensional spin-orbital model using both analytical and
numerical methods. Renormalization group calculations are performed in the
vicinity of a special integrable point in the phase diagram with SU(4)
symmetry. These indicate the existence of a gapless phase in an extended region
of the phase diagram, missed in previous studies. This phase is SU(4) invariant
at low energies apart from the presence of different velocities for spin and
orbital degrees of freedom. The phase transition into a gapped dimerized phase
is in a generalized Kosterlitz-Thouless universality class. The phase diagram
of this model is sketched using the density matrix renormalization group
technique.Comment: 11 pages, 5 figures, new references adde
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