Hubert Saleur

Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing ab initio analytical and numerical computations of their characteristics. In this work, topological defects are investigated in nonunitary conformal field theories using appropriate variations of the restricted solid-on-solid models. The relevant impurity models and the corresponding defect operators are constructed for the lattice system. Numerical computations are performed for the energy spectrum, eigenvalues of the defect operators, as well as thermodynamic characteristics and compared with analytical predictions. Finally, renormalization group flows between the different fixed points are analyzed using numerical methods.

Using techniques of conformal bootstrap, we propose analytical expressions for a large class of two-point functions of bulk fields in critical loop models defined on the upper-half plane. Our results include the two-point connectivities in the Fortuin--Kasteleyn random cluster model with both free and wired boundary conditions. We link the continuum expressions to lattice quantities by computing universal ratios of amplitudes for the two-point connectivities, and find excellent agreement with transfer-matrix numerics.

Topological defect lines (TDLs) in two-dimensional conformal field theories (CFTs) are standard examples of generalized symmetries in quantum field theory. Integrable lattice incarnations of these TDLs, such as those provided by spin/anyonic chains, provide a crucial playground to investigate their properties, both analytically and numerically. Here, a family of parameter-dependent integrable lattice models is presented, which realize different TDLs in a given CFT as the parameter is varied. These models are based on the general quantum-inverse scattering construction, and involve inhomogeneities of the spectral parameter. Both defect hamiltonians and (defect) line operators are obtained in closed form. By varying the inhomogeneities, renormalization group flows between different TDLs (such as the Verlinde lines associated with the Virasoro primaries (1, s) and (r, 1) in diagonal minimal CFTs) are then studied using different aspects of the Bethe-ansatz as well as ab-initio numerical techniques. Relationships with the anisotropic Kondo model as well as its non-Hermitian version are briefly discussed.

Starting with the Ising model, statistical models with global symmetries provide fruitful approaches to interesting physical systems, for example percolation or polymers. These include the O(n) O ( n ) model (symmetry group O(n) O ( n ) ) and the Potts model (symmetry group S_Q S Q ). Both models make sense for n,Q∈ \mathbb{C} n , Q ∈ ℂ and not just n,Q∈ \mathbb{N} n , Q ∈ ℕ , and both give rise to a conformal field theory in the critical limit. Here, we study similar models based on the group PSU(n) P S U ( n ) . We focus on the two-dimensional case, where the models can be described either as gases of non-intersecting orientable loops, or as alternating spin chains. This allows us to determine their spectra either by computing a twisted torus partition function, or by studying representations of the walled Brauer algebra. In the critical limit, our models give rise to a CFT that exists for any n∈\mathbb{C} n ∈ ℂ and has a global PSU(n) P S U ( n ) symmetry. Its spectrum is similar to those of the O(n) O ( n ) and Potts CFTs, but a bit simpler. We conjecture that the O(n) O ( n ) CFT is a \mathbb{Z}_2 ℤ 2 orbifold of the PSU(n) P S U ( n ) CFT, where \mathbb{Z}_2 ℤ 2 acts as complex conjugation.

Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and analyzed in the case of the three-state Potts CFT. In particular, lattice versions for all the primitive defects are presented, with the remaining defects obtained from the fusion of the primitive ones. The defects are obtained by introducing modified interactions around two given sites of an otherwise homogeneous spin chain with periodic boundary condition. The various primitive defects are topological on the lattice except for one, which is topological only in the scaling limit. The lattice models are analyzed using a combination of exact diagonalization and density matrix renormalization group techniques. Low-lying energy spectra for different defect Hamiltonians as well as entanglement entropy of blocks located symmetrically around the defects are computed. The latter provides a convenient way to compute the g-function which characterizes various defects. Finally, the eigenvalues of the line operators in the “crossed channel” and fusion of different defect lines are also analyzed. The results are all in agreement with expectations from conformal field theory.