18 research outputs found
Massive-Conformal Dictionary
The finite-volume spectrum of an integrable massive perturbation of a
rational conformal field theory interpolates between massive multi-particle
states in infinite volume (IR limit) and conformal states, which are approached
at zero volume (UV limit). Each state is labeled in the IR by a set of `Bethe
Ansatz quantum numbers', while in the UV limit it is characterized primarily by
the conformal dimensions of the conformal field creating it. We present
explicit conjectures for the UV conformal dimensions corresponding to any IR
state in the -perturbed minimal models and . The
conjectures, which are based on a combinatorial interpretation of the
Rogers-Ramanujan-Schur identities, are consistent with numerical results
obtained previously for low-lying energy levels.Comment: 18/11 pages in harvmac, Tel-Aviv preprint TAUP 2109/9
Sine-Gordon =/= Massive Thirring, and Related Heresies
By viewing the Sine-Gordon and massive Thirring models as perturbed conformal
field theories one sees that they are different (the difference being
observable, for instance, in finite-volume energy levels). The UV limit of the
former (SGM) is a gaussian model, that of the latter (MTM) a so-called {\it
fermionic} gaussian model, the compactification radius of the boson underlying
both theories depending on the SG/MT coupling. (These two families of conformal
field theories are related by a ``twist''.) Corresponding SG and MT models
contain a subset of fields with identical correlation functions, but each model
also has fields the other one does not, e.g. the fermion fields of MTM are not
contained in SGM, and the {\it bosonic} soliton fields of SGM are not in MTM.
Our results imply, in particular, that the SGM at the so-called ``free-Dirac
point'' is actually a theory of two interacting bosons with
diagonal S-matrix , and that for arbitrary couplings the overall sign of
the accepted SG S-matrix in the soliton sector should be reversed. More
generally, we draw attention to the existence of new classes of quantum field
theories, analogs of the (perturbed) fermionic gaussian models, whose partition
functions are invariant only under a subgroup of the modular group. One such
class comprises ``fermionic versions'' of the Virasoro minimal models.Comment: 50 pages (harvmac unreduced), CLNS-92/1149, ITP-SB-92-3
Quasi-Particles, Conformal Field Theory, and -Series
We review recent results concerning the representation of conformal field theory characters in terms of fermionic quasi-particle excitations, and describe in detail their construction in the case of the integrable three-state Potts chain. These fermionic representations are q-series which are generalizations of the sums occurring in the Rogers-Ramanujan identities
The Many Faces of a Character
We prove an identity between three infinite families of polynomials which are
defined in terms of `bosonic', `fermionic', and `one-dimensional configuration'
sums. In the limit where the polynomials become infinite series, they give
different-looking expressions for the characters of the two integrable
representations of the affine algebra at level one. We conjecture yet
another fermionic sum representation for the polynomials which is constructed
directly from the Bethe-Ansatz solution of the Heisenberg spin chain.Comment: 14/9 pages in harvmac, Tel-Aviv preprint TAUP 2125-9
On the Scaling Limit of the 1D Hubbard Model at Half Filling
The dispersion relations and S-matrix of the one-dimensional Hubbard model at
half filling are considered in a certain scaling limit. (In the process we
derive a useful small-coupling expansion of the exact lattice dispersion
relations.) The resulting scattering theory is consistently identified as that
of the SU(2) chiral-invariant Thirring (or Gross-Neveu) field theory,
containing both massive and massless sectors.Comment: 14 pages in harvmac, Tel-Aviv preprint TAUP 2203-9
Rg Flows in the -Series of Minimal Cfts
Using results of the thermodynamic Bethe Ansatz approach and conformal
perturbation theory we argue that the -perturbation of a unitary
minimal -dimensional conformal field theory (CFT) in the -series of
modular invariant partition functions induces a renormalization group (RG) flow
to the next-lower model in the -series. An exception is the first model in
the series, the 3-state Potts CFT, which under the \ZZ_2-even
-perturbation flows to the tricritical Ising CFT, the second model
in the -series. We present arguments that in the -series flow
corresponding to this exceptional case, interpolating between the tetracritical
and the tricritical Ising CFT, the IR fixed point is approached from ``exactly
the opposite direction''. Our results indicate how (most of) the relevant
conformal fields evolve from the UV to the IR CFT.Comment: 30 page
Kinks in Finite Volume
A (1+1)-dimensional quantum field theory with a degenerate vacuum (in
infinite volume) can contain particles, known as kinks, which interpolate
between different vacua and have nontrivial restrictions on their
multi-particle Hilbert space. Assuming such a theory to be integrable, we show
how to calculate the multi-kink energy levels in finite volume given its
factorizable -matrix. In massive theories this can be done exactly up to
contributions due to off-shell and tunneling effects that fall off
exponentially with volume. As a first application we compare our analytical
predictions for the kink scattering theories conjectured to describe the
subleading thermal and magnetic perturbations of the tricritical Ising model
with numerical results from the truncated conformal space approach. In
particular, for the subleading magnetic perturbation our results allow us to
decide between the two different -matrices proposed by Smirnov and
Zamolodchikov.Comment: 48/28 pages + 10 figs, 4 in pictex, the rest in postscript files
attached at the en