Conformal Invariant Theory Research Articles

Conformal invariance and critical behavior of the O(n) model on the honeycomb lattice.

A seven-vertex model on the honeycomb lattice is solved exactly by the Bethe ansatz method. The vertex model is equivalent to the critical O(n) model on the honeycomb lattice. The equivalence is made exact for lattices wrapped on a cylinder with one finite and one infinite direction, by the introduction of a seam into the vertex model. Thus asymptotic finite-size amplitudes of the critical O(n) model are obtained exactly. Applications of the theory of conformal invariance, which relate these amplitudes to the central charge and critical exponents, confirm the existing results and conjectures for these quantities. The finite-size amplitude corresponding to the temperature exponent was not obtained from the exact solution. However, this amplitude was accurately determined from numerical finite-size results obtained by the transfer-matrix method. This result also agrees with recent predictions.

CORRELATION FUNCTIONS OF σ FIELDS WITH VALUES IN A HYPERBOLIC SPACE

It is shown that the functional integral for a σ field with values in the Poincare upper half-plane (and some other hyperbolic spaces) can be performed explicitly resulting in a conformal invariant noncanonical field theory in two dimensions.

Conformal anomaly and scaling dimensions of the O(n) model from an exact solution on the honeycomb lattice.

The critical $\mathrm{O}(n)$ model on a finite honeycomb lattice is solved by the Bethe-Ansatz method. Amplitudes of the dominant finite-size corrections to part of the eigenspectrum are obtained analytically. A comparison with Cardy's predictions from the theory of conformal invariance leads to the exact results for the conformal anomaly and scaling dimensions.

The (1+1)DO(2) model: a finite lattice analysis

Finite-size methods and the theory of conformal invariance are applied to the (1+1)DO(2) or X-Y planar model. The critical point is found to be xc approximately=2.0, the value sigma =0.501+or-0.005 is obtained for the index governing the critical divergence of the correlation length and the conformal anomaly is confirmed to be c=1. The Kosterlitz-Thouless features of a low-temperature phase with zero spontaneous magnetisation but algebraic decay of correlations, together with a standard high-temperature phase, are observed. The critical exponent eta is determined as a function of coupling constant and compared with theoretical expectations.

Operator approach to conformal invariant quantum field theories and related problems

Conformal quantum field theory is analysed from a global point of view. The use of the covering transformations leads to a global decomposition theory in which the basic building blocks are nonlocal quantum fields which live on each light cone separately. As an application of the new formalism arbitrary order-disorder mixed n -point functions of the Ising field theory are explicitly calculated.

Weyl fields, quantum integrability and conformal invariant field theories

We show that some Weyl field theories arise as a quantum “linear” problem associated to some Kac-Moody algebras. We relate this quantum “linear” problem to the conformal invariant field theories studied by Dashen and Frishman and to the WZW field theory.

Einstein gravity as spontaneously broken Weyl gravity

We study the locally conformal invariant Weyl theory of gravitation and introduce a conformally coupled scalar field. Einstein gravity is induced by spontaneous breaking of the local conformal symmetry in an effective long range approximation. The effective potential for the scalar field is calculated at the one-loop level up to curvature squared in order in an arbitrary curved background. The non-zero vacuum expectation value of the scalar field induces the dimensional Einstein's gravitational coupling constant stably in case ofR > 0. ForR < 0, the phase transition occurs from the symmetric phase to the broken phase as the curvature decreases. This theory may be an attractive candidate for the primordial inflationary universe scenario.

Operator content of the ADE lattice models

The author computes the scaling dimensions of order parameters in ADE lattice models. Some connection is made between the lattice algebra and the operator algebra in conformal invariant theories.

The A-D-E classification of minimal andA 1 (1) conformal invariant theories

We present a detailed and complete proof of our earlier conjecture on the classification of minimal conformal invariant theories. This is based on an exhaustive construction of all modular invariant sesquilinear forms, with positive integral coefficients, in the characters of the Virasoro or of theA1(1) Kac-Moody algebras, which describe the corresponding partition functions on a torus. A remarkable correspondence emerges with simply laced Lie algebras.

Modular invariant partition functions in two dimensions

We present a systematic study of modular invariance of partition functions, relevant both for two-dimensional minimal conformal invariant theories and for string propagation on a SU(2) group manifold. We conjecture that all solutions are labelled by simply laced Lie algebras.

Two-dimensional critical systems labelled by Dynkin diagrams

We define two-dimensional critical integrable models. They generalise the RSOS models and are labelled by Dynkin diagrams. These models are candidates for describing unitary conformal invariant theories.

Two-dimensional conformal invariant theories on a torus

The study of unitary conformal invariant theories on a torus reveals two important properties: the partition function and correlation functions may be expressed in terms of free (gaussian) field modes, and the modular invariance dictates the operator content of the theory: for a generic value of the central charge c = 1−/ m( m + 1), there exist at least two distinct models depending whether m = 0,3 mod or m = 1,2 mod 4. The case of non-unitary c < 1 theories is also briefly discussed.

Classical and quantum field theories overS 3×S 1

Conformal invariant field theories are studied using a different approach to the conventional one. The difference lies in the fact that we consider a new time related to the conformal invariance properties of the theory. We study the Green’s functions for different scalar theories and finally we give Feynman’s rules on a compact manifold, conformally flat to Minkowski space: the so-calledS3×S1 hypertorus.

Dynamic critical behaviour of semi-infinite systems: conformal invariance and mirror theory

The critical dynamics of the d-dimensional semi-infinite systems is studied at bulk critical temperature. As a result of the conformal invariance, the dynamic response and correlation functions depend only on the 'real' distance r, the 'image' distance r and the time t (mirror theory). Assuming the non-conserved order parameter with O(n) symmetry, the authors evaluate the response and correlation functions exactly in the large-n limit and also to first order in epsilon =4-d. The authors' results satisfy the mirror theory for the various types of the phase transitions including the ordinary, special, anisotropic special and extraordinary transitions.

Integrable model of Yang-Mills theory and quasi-instantons

Within the framework of Euclidean conformal invariant Yang-Mills theory with a scalar field, a two-dimensional Hamiltonian system integrable for a definite relation between the coupling constants is considered. A particular solution of the Hamilton-Jacobi equation leads to a system of first-order equations providing a nonself-dual instanton-like solution of the model concerned. As a generalization of the system, a quasi-self-duality equation is suggested which is integrated by means of the 't Hooft ansatz and results in quasi-self-dual instantons (quasi-instantons).

Group Theoretic Analysis of Conformal Invariant Field Theories

Various issues associated with field theoretic realization of conformal symmetry in 2 dimensions are discussed. A method of constructing primary fields for a class of conformal algebras which are based upon level-2 representations of current algebra are presented. Realizations of twisted current algebra are also discussed. 16 refs.

Dynamics of conformal gravity with merons

We investigate the semi-classical stability of a fully conformal invariant theory with gravity around the meron solutions. Using a new definition of stability for merons, we find that stability depends on the cosmological constant. We also investigate the potential of the model in Minkowski domain with cosmological time background and draw physical consequences about the dynamics of the model.

Spinor exponents for the two-dimensional Potts model.

The spinor operator in the two-dimensional Ising model can be readily generalized to other self-dual models as the product of the order parameter and its dual image, the disorder operator. Recently, the exponent of this and other operators in the $q$-state Potts model received renewed attention, as the theory of conformal invariance produces complete lists of critical exponents for some of these models. In this paper we calculate the critical and tricritical indices of the spinor operator in the two-dimensional $q$-state Potts model, via a well-known mapping into a solid-on-solid model. Our results give a physical identification for the exponents predicted by the conformal theory.

Instantons in a two-dimensional conformal invariant model with a liouville term

We obtain the instanton solutions to a class of two-dimensional conformal invariant field theories with a Liouville term. The invariance and stability properties of the solutions are discussed.

Four-point correlation functions and the operator algebra in 2D conformal invariant theories with central charge C≤1

Four-point correlation functions are calculated for the basic operators in 2D conformal invariant theories with the central charge of the corresponding Virasoro algebra C≤1. Based on these results, explicit expressions are found for structure constants of the operator product expansions in these theories.