Massless Flows I: the sine-Gordon and O(n) models

The massless flow between successive minimal models of conformal field theory is related to a flow within the sine-Gordon model when the coefficient of the cosine potential is imaginary. This flow is studied, partly numerically, from three different points of view. First we work out the expansion close to the Kosterlitz-Thouless point, and obtain roaming behavior, with the central charge going up and down in between the UV and IR values of $c=1$. Next we analytically continue the Casimir energy of the massive flow (i.e. with real cosine term). Finally we consider the lattice regularization provided by the O(n) model in which massive and massless flows correspond to high- and low-temperature phases. A detailed discussion of the case $n=0$ is then given using the underlying N=2 supersymmetry, which is spontaneously broken in the low-temperature phase. The ``index'' \tr F(-1)^F follows from the Painleve III differential equation, and is shown to have simple poles in this phase. These poles are interpreted as occuring from level crossing (one-dimensional phase transitions for polymers). As an application, new exact results for the connectivity constants of polymer graphs on cylinders are obtained.Comment: 39 pages, 7 uuencoded figures, BUHEP-93-5, USC-93/003, LPM-93-0

Differential equations and duality in massless integrable field theories at zero temperature

Functional relations play a key role in the study of integrable models. We argue in this paper that for massless field theories at zero temperature, these relations can in fact be interpreted as monodromy relations. Combined with a recently discovered duality, this gives a way to bypass the Bethe ansatz, and compute directly physical quantities as solutions of a linear differential equation, or as integrals over a hyperelliptic curve. We illustrate these ideas in details in the case of the $c=1$ theory, and the associated boundary sine-Gordon model.Comment: 18 pages, harvma

Boundary flows in minimal models

We discuss in this paper the behaviour of minimal models of conformal theory perturbed by the operator $\Phi_{13}$ at the boundary. Using the RSOS restriction of the sine-Gordon model, adapted to the boundary problem, a series of boundary flows between different set of conformally invariant boundary conditions are described. Generalizing the "staircase" phenomenon discovered by Al. Zamolodchikov, we find that an analytic continuation of the boundary sinh-Gordon model provides a flow interpolation not only between all minimal models in the bulk, but also between their possible conformal boundary conditions. In the particular case where the bulk sinh-Gordon coupling is turned to zero, we obtain a boundary roaming trajectory in the $c=1$ theory that interpolates between all the possible spin $S$ Kondo models.Comment: 13pgs, harvmac, 2 fig

Critical exponents of domain walls in the two-dimensional Potts model

We address the geometrical critical behavior of the two-dimensional Q-state Potts model in terms of the spin clusters (i.e., connected domains where the spin takes a constant value). These clusters are different from the usual Fortuin-Kasteleyn clusters, and are separated by domain walls that can cross and branch. We develop a transfer matrix technique enabling the formulation and numerical study of spin clusters even when Q is not an integer. We further identify geometrically the crossing events which give rise to conformal correlation functions. This leads to an infinite series of fundamental critical exponents h_{l_1-l_2,2 l_1}, valid for 0 </- Q </- 4, that describe the insertion of l_1 thin and l_2 thick domain walls.Comment: 5 pages, 3 figures, 1 tabl

A comment on finite temperature correlations in integrable QFT

I discuss and extend the recent proposal of Leclair and Mussardo for finite temperature correlation functions in integrable QFTs. I give further justification for its validity in the case of one point functions of conserved quantities. I also argue that the proposal is not correct for two (and higher) point functions, and give some counterexamples to justify that claim.Comment: 11 page

Thermodynamics of the Complex su(3) Toda Theory

We present the first computation of the thermodynamic properties of the complex su(3) Toda theory. This is possible thanks to a new string hypothesis, which involves bound states that are non self-conjugate solutions of the Bethe equations. Our method provides equivalently the solution of the su(3) generalization of the XXZ chain. In the repulsive regime, we confirm that the scattering theory proposed over the past few years - made only of solitons with non diagonal S-matrices - is complete. But we show that unitarity does not follow, contrary to early claims, eigenvalues of the monodromy matrix not being pure phases. In the attractive regime, we find that the proposed minimal solution of the bootstrap equations is actually far from being complete. We discuss some simple values of the couplings, where, instead of the few conjectured breathers, a very complex structure (involving E_6, or two E_8) of bound states is necessary to close the bootstrap.Comment: 6 pages, 2 figures; some minor changes; accepted for publication in Phys. Lett.

Correlations in one dimensional quantum impurity problems with an external field

We study response functions of integrable quantum impurity problems with an external field at $T=0$ using non perturbative techniques derived from the Bethe ansatz. We develop the first steps of the theory of excitations over the new, field dependent ground state, leading to renormalized (or ``dressed'') form-factors. We obtain exactly the low frequency behaviour of the dynamical susceptibility $\chi''(\omega)$ in the double well problem of dissipative quantum mechanics (or equivalently the anisotropic Kondo problem),and the low frequency behaviour of the AC noise $S_t(\omega)$ for tunneling between edges in fractional quantum Hall devices. We also obtain exactly the structure of singularities in $\chi''(\omega)$ and $S_t(\omega)$. Our results differ significantly from previous perturbative approaches.Comment: harvmac, epsf, 37pgs, 2figs. modified some reference