P. Fendley

Scattering and thermodynamics of fractionally-charged supersymmetric solitons

Abstract We show that there are solitons with fractional fermion number in integrable N = 2 supersymmetric models. We obtain the soliton S -matrix for the minimal, N = 2 supersymmetric theory perturbed in the least relevant chiral primary field, the φ (1,3) superfield. The perturbed theory has a nice Landau-Ginzburg description with a Chebyshev polynomial superpotential. We show that the S -matrix is a tensor product of an associated ordinary ADE minimal model S -matrix with a supersymmetric part. We calculate the ground-state energy in these theories and in the analogous N = 1 case and SU(2) coset models. In all cases, the ultraviolet limit is in agreement with the conformal field theory.

Scattering and thermodynamics in integrable N=2 theories

Abstract We study N = 2 supersymmetric integrable theories with spontaneously-broken Z n symmetry. They have exact soliton masses given by the affine SU( n ) Toda masses and fractional fermion numbers given by multiples of 1 n . The basic such N = 2 integrable theory is the A n -type N = 2 minimal model perturbed by the most relevant operator. The soliton content and exact S -matrices are obtained using the Landau-Ginzburg description. We study the thermodynamics of these theories and calculate the ground-state energies exactly, verifying that they have the correct conformal limits. We conjecture that the soliton content and S -matrices in other integrable Z n N = 2 theories are given by the tensor product of the above N =2 Z n scattering theory with various N = 0 theories. In particular, we consider integrable perturbations of N = 2 Kazama-Suzuki models described by generalized Chebyshev potentials, CP n −1 sigma models, and N = 2 sine-Gordon and its affine Toda generalizations.

N = 2 supersymmetry, Painlevé III and exact scaling functions in 2D polymers

We discuss in this paper various aspects of the off-critical O(n) model in two dimensions. We find the ground-state energy conjectured by Zamolodchikov for the unitary minimal models, and extend the results to some non-unitary minimal cases. These results are applied to the discussion of scaling functions for polymers on a cylinder. Using the underlying N = 2 supersymmetry, the scaling function for one non-contractible polymer loop around the cylinder is shown to be simply related to the solution of the Painleve III differential equation. We also find the ground-state energy for a single polymer on the cylinder. These results are checked by numerically simulating the polymer system. The flow to the dense polymer phase is also analyzed numerically. We find there surprising results, with a ceff function that is not monotonically decreasing and seems to have a roaming behavior, getting very close to the value 8170 and 710 between its UV and IR values of 1.

Excited state thermodynamics

Abstract In the last several years, the Casimir energy for a variety of (1 + 1)-dimensional integrable models has been determined from the exact S-matrix. It is shown here how to modify the boundary conditions to project out the lowest-energy state, which enables one to find excited-state energies. This is done by calculating thermodynamic expectation values of operators which generate discrete symmetries. This is demonstrated with a number of perturbed conformal field theories, including the Ising model, the three-state Potts model, Z n parafermions, Toda S-matrices, and massless goldstinos.

MASSLESS FLOWS II: THE EXACT S-MATRIX APPROACH

We study the spectrum, the massless S matrices and the ground-state energy of the flows between successive minimal models of conformal field theory, and within the sine-Gordon model with imaginary coefficient of the cosine term (related to the minimal models by “truncation”). For the minimal models, we find exact S matrices which describe the scattering of massless kinks, and show using the thermodynamic Bethe ansatz that the resulting non-perturbative c function (defined by the Casimir energy on a cylinder) flows appropriately between the two theories, as conjectured earlier. For the nonunitary sine-Gordon model, we find unusual behavior. For the range of couplings we can study analytically, the natural S matrix deduced from the minimal one by “undoing” the quantum-group truncation does not reproduce the proper c function with the TBA. It does, however, describe the correct properties of the model in a magnetic field.

Kinks in the Kondo problem

We find the exact quasiparticle spectrum, elastic [ital S] matrix, and free energy for the continuum Kondo problem of [ital k] species of electrons coupled to an impurity of spin [ital S]. Here, the impurity becomes an immobile quasiparticle sitting on the boundary. The particles are kinks, which can be thought of as field configurations interpolating between adjacent wells of a potential with [ital k]+1 degenerate minima. For the overscreened case [ital k][gt]2[ital S], the impurity in the continuum is a kink as well, which explains the noninteger number of boundary states.

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” trF(−1)F follows from the Painleve III differential equation, and is shown to have simple poles in this phase. These poles are interpreted as occurring 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. These results and points of view are used in the following paper to discuss the appropriate exact S matrices and the resulting Casimir energies.

Exact N=2 Landau-Ginzburg flows

Abstract We find exactly solvable N = 2-supersymmetric flows whose infrared fixed point sare the N = 2 minimal models. The exact S -matrices and the Casimir energy (a c -function) are determined along the entire renormalization-group trajectory. The c -functions run from c = 3 (asymptotically) to the N = 2 minimal-model values, leading us to interpret these theories as the Landau-Ginzburg models with superpotential X k +2 . The calculation of the elliptic genus is consistent with this interpretation. We also find an integrable model in this hierarchy with spontaneously broken supersymmetry and superpotential X , and a series of integrable models with (0,2) supersymmetry. The flows exhibit interesting behavior in the UV, including a relation to the N = 2 super sine-Gordon model. We speculate about the relation between the kinetic term and the cigar target-space metric.

Central charges without finite-size effects

We show how to obtain the ultraviolet central charge from the exact S-matrix for a wide variety of models with a U(1) symmetry. This is done by coupling the U(1) current J to a background field. In an N=2 superconformal theory with J the fermion number current, the OPE of J with itself and hence the free energy are proportional to c. By deforming the supersymmetry into affine quantum-group symmetry, this result can be generalized to many U(1)-invariant theories, including the N=0 and N=1 sine-Gordon models and the SU(2)kWZW models. This provides a consistency check on a conjectured S-matrix completely independent of the finite-size effects expressed in terms of dilogarithms resulting from the thermodynamic Bethe ansatz.