Notes on parafermionic QFT's with boundary interaction

Abstract

The main result of these notes is an analytical expression for the partition function of the circular brane model for arbitrary values of the topological angle. The model has important applications in condensed matter physics. It is related to the dissipative rotator (Ambegaokar-Eckern-Schon) model and describes a ``weakly blocked'' quantum dot with an infinite number of tunneling channels under a finite gate voltage bias. A numerical check of the analytical solution by means of Monte Carlo simulations has been performed recently. To derive the main result we study the so-called boundary parafermionic sine-Gordon model. The latter is of certain interest to condensed matter applications, namely as a toy model for a point junction in the multichannel quantum wire.

55 pages, 6 figures

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• Dirichlet sigma models and mean curvature flow
• ODE/IM correspondence for the Fateev model
• Integrable Kondo problems
• Universal scaling behavior of the single electron box in the strong tunneling limit
• Lattice regularisation of a non-compact boundary conformal field theory
• Critical interfaces of the Ashkin-Teller model at the parafermionic point
• Suzuki equations and integrals of motion for supersymmetric CFT
• ODE/IM correspondence and supersymmetric affine Toda field equations
• On the ODE/IM correspondence for minimal models
• Elementary functions in Thermodynamic Bethe Ansatz
• Kondo line defects and affine Gaudin models
• Anisotropic Kondo line defect and ODE/IM correspondence
• ODE/IQFT correspondence for the generalized affine $\mathfrak{sl}(2)$ Gaudin model
• The ODE/IM Correspondence between $C(2{)}^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT