N=2 boundary supersymmetry in integrable models and perturbed boundary conformal field theory

Abstract

Boundary integrable models with N = 2 supersymmetry are considered. For the simplest boundary N = 2 superconformal minimal model with a Chebyshev bulk perturbation we show explicitly how fermionic boundary degrees of freedom arise naturally in the boundary perturbation in order to maintain integrability and N = 2 supersymmetry. A new boundary reflection matrix is obtained for this model and N = 2 boundary superalgebra is studied. A factorized scattering theory is proposed for a N = 2 supersymmetric extension of the boundary sine-Gordon model with either (i) fermionic or (ii) bosonic and fermionic boundary degrees of freedom. Exact results are obtained for some quantum impurity problems: the boundary scaling Lee-Yang model, a massive deformation of the anisotropic Kondo model at the filling values g = 2/(2n + 3) and the boundary Ashkin-Teller model..

Integrability of the boundary sine-Gordon model

“…Comparable boundary Lagrangians have thereafter been adopted in different ways in [2] and [3,4] in the context of supersymmetric integrable boundary field theories. For a construction of the boundary structure relying on a boundary quantum group see [9,10]. As mentioned in the introduction, the approach following [2,4] has also recently appeared in a string theory context, compare for example with [21,22].…”

Boundary fermions and the plane wave

“…In the following we will derive the relations (13), (14) between the N = (2, 2) worldsheet supersymmetry and the spacetime supercharges from the Green-Schwarz formulation. This will in particular also lead to an explicit confirmation of the related group theoretical discussion in [23].…”

“…implicitly using the negative SO(8) chiralities of the spinors S, S. In a similar way one expresses the remaining supersymmetries as linear combinations of the spacetime charges as given in (13), (14). To relate this result to the discussion of section 5 in [23], we only have to note that the condition (10) requires η to be the bottom state discussed in [23], whereas η * is the corresponding top-state as established beforehand at the end of the last section.…”

“…The choice of a trigonometric superpotential W (z) ∼ cos z in the solutions of [11] leads to the integrable N = 2 supersymmetric sine-Gordon model on the worldsheet, whereas the exponential W (z) ∼ e z gives rise to the N = 2 Liouville theory. In the context of boundary fermions these theories have been discussed in [4,14,15] and [16].…”

Integrability + Supersymmetry + Boundary: Life on the Edge Is Not So Dull After All!

“…where L 0 is given by (24), a ± are Fermionic boundary degrees of freedom which anticommute with ψ ± andψ ± , and B(ϕ + , ϕ − ), f ± (ϕ ± ) are boundary potentials. Imposing both integrability (as in Eq.…”