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Exact Solution of a Boundary Conformal Field Theory

Curtis G. Callan·Igor R. Klebanov·Andreas W. W. Ludwig·Juan M. Maldacena
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Abstract

We study the conformal field theory of a free massless scalar field living on the half line with interactions introduced via a periodic potential at the boundary. An SU(2) current algebra underlies this system and the interacting boundary state is given by a global SU(2) rotation of the left-moving fields in the zero-potential (Neumann) boundary state. As the potential strength varies from zero to infinity, the boundary state interpolates between the Neumann and the Dirichlet values. The full S-matrix for scattering from the boundary, with arbitrary particle production, is explicitly computed. To maintain unitarity, it is necessary to attribute a hidden discrete ``soliton'' degree of freedom to the boundary. The same unitarity puzzle occurs in the Kondo problem, and we anticipate a similar solution.

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Curtis G. Callan, Igor R. Klebanov, Andreas W. W. Ludwig, Juan M. Maldacena. 2003-05-25. Exact Solution of a Boundary Conformal Field Theory. https://doi.org/10.1016/0550-3213(94)90440-5

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