Narrow Results

A general concept of the long-range elastic interactions in continuous medium is proposed. The interaction is determined as a consequence of symmetry breaking of the elastic field distribution produced by the topological defect as isolated inclusions. It is proposed to treat topological defects as the source of elastic field that can be described in terms of this field. The source is considered as a nonlinear object which determines the effective charge of the field at large distances in the linear theory. The models of the nonlinear source are proposed.

In this paper, we study topological defect lines in two character rational conformal field theories. Among them one set of two character theories are commutant pairs in $E_{8,1}$ conformal field theory. Using these defect lines, we construct defect partition function in the $E_8$ theory. We find that the defects preserve only a part of the $E_8$ current algebra symmetry. We also determine the defect partition function in $c=24$ CFTs using these defects lines of two character theories and we find that, with appropriate choice of commutant pairs, these defects preserve all current algebra symmetries of $c=24$ CFTs.

In this paper we describe how relativistic field theories containing defects are equivalent to a class of boundary field theories. As a consequence previously derived results for boundaries can be directly applied to defects, these results include reduction formulas, the Coleman–Thun mechanism and Cutcosky rules. For integrable theories the defect crossing unitarity equation can be derived and defect operator found. For a generic purely transmitting impurity we use the boundary bootstrap method to obtain solutions of the defect Yang–Baxter equation. The groundstate energy on the strip with defects is also calculated.

We perform canonical quantization of the WZW model with defects and permutation branes. We establish symplectomorphism between phase space of WZW model with N defects on cylinder and phase space of Chern–Simons theory on annulus times R with N Wilson lines, and between phase space of WZW model with N defects on strip and Chern–Simons theory on disk times R with N + 2 Wilson lines. We obtained also symplectomorphism between phase space of the N-fold product of the WZW model on strip with boundary conditions specified by permutation branes, and phase space of Chern–Simons theory on sphere times R with N holes and two Wilson lines.

Using the AdS/CFT correspondence, we study the anisotropic charge transport properties of both supersymmetric and nonsupersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional "heat bath." We focus on the cases of a finite external background magnetic field, finite net charge density and finite mass and their combinations. In this context, we also discuss the limitations due to operator mixing that appears in a few situations and that we ignore in our analysis. At high frequencies, we discover a spectrum of quasiparticle resonances due to the magnetic field and finite density and at small frequencies, we perform a Drude-like expansion around the DC limit. Both of these regimes display many generic features and some features that we attribute to strong coupling, such as a minimum DC conductivity and an unusual behavior of the "cyclotron" and plasmon frequencies, which become related to the resonances found in the conformal case in an earlier paper. We further study the hydrodynamic regime and the relaxation properties, from which the system displays a set of different possible transitions to the collisionless regime. The mass dependence can be cast in two regimes: a generic relativistic behavior dominated by the UV and a nonlinear hydrodynamic behavior dominated by the IR. In the massless case, we furthermore extend earlier results from the literature to find an interesting selfduality under a transformation of the conductivity and the exchange of density and magnetic field.

In this paper, we analyze the Cardy–Lewellen equation in general diagonal model. We show that in these models it takes a simple form due to some general properties of conformal field theories, like pentagon equations and OPE associativity. This implies that the Cardy–Lewellen equation has a simple form also in nonrational diagonal models. We specialize our finding to the Liouville and Toda field theories. In particular, we prove that recently conjectured defects in Toda field theory indeed satisfy the cluster equation. We also derive the Cardy–Lewellen equation in all sl(n) Toda field theories and prove that the form of boundary states found recently in sl(3) Toda field theory holds in all sl(n) theories as well.