340 research outputs found
Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model
We discuss conserved currents and operator product expansions (OPE's) in the
context of a invariant conformal field theory. Using OPE's we find
explicit expressions for the first few terms in suitable short-distance limits
for various four-point functions involving the fundamental -component scalar
field , . We propose an alternative
evaluation of these four-point functions based on graphical expansions.
Requiring consistency of the algebraic and graphical treatments of the
four-point functions we obtain the values of the dynamical parameters in either
a free theory of massless fields or a non-trivial conformally invariant
vector model in , up to next-to-leading order in a
expansion. Our approach suggests an interesting duality property of the
critical invariant theory. Also, solving our consistency relations we
obtain the next-to-leading order in correction for which
corresponds to the normalisation of the energy momentum tensor two-point
function.Comment: 45 pages Latex + 2 uuencoded PostScript figures, DAMTP 94/1
Finite-Size Effects and Operator Product Expansions in a CFT for d>2
The large momentum expansion for the inverse propagator of the auxiliary
field in the conformally invariant O(N) vector model is calculated
to leading order in 1/N, in a strip-like geometry with one finite dimension of
length for . Its leading terms are identified as contributions from
itself and the energy momentum tensor, in agreement with a
previous calculation based on conformal operator product expansions. It is
found that a non-trivial cancellation takes place by virtue of the gap
equation. The leading coefficient of the energy momentum tensor contribution is
shown to be related to the free energy density.Comment: 10 pages LaTeX 2 eps figures, minor changes in text. Revised version
to be published in Phys.Lett. B. email: [email protected]
[email protected]
Renormalization Group Flow and Thermodynamics of Conformal Field Theories
We discuss the free-energy density of bosonic and fermionic theories
possessing strongly coupled critical points in D=3. We construct a stationary
renormalization group trajectory which interpolates between the free massless
theory of N scalars and a class of interacting theories including both bosons
and fermions. At a special point of this trajectory the free-energy density is
5/4 times the free-energy density of the O(N) vector model at its nontrivial
critical point. Our method could in principle be useful in the study of other
theories with strongly coupled fixed points, such as {\cal N}=4 SYM in D=4.Comment: 13 pages, RevTeX, 1 figure, version to appear in JHE
On the Free-Energy of Three-Dimensional CFTs and Polylogarithms
We study the O(N) vector model and the U(N) Gross-Neveu model with fixed
total fermion number, in three dimensions. Using non-trivial polylogarithmic
identities, we calculate the large-N renormalized free-energy density of these
models, at their conformal points in a ``slab'' geometry with one finite
dimension of length L. We comment on the possible implications of our results.Comment: Latex, 13 pages, 2 eps figures; v2 typos corrected; v3 Expanded
discussion of the results, added reference
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