Andrea Cappelli, Giuseppe D'Appollonio, Maxim Zabzine
Landau-Ginzburg Description of Boundary Critical Phenomena in Two Dimensions
Preprint series: ESI preprints

MSC:

81T15 Perturbative methods of renormalization

81T30 String and superstring theories; other extended objects , See also {83E30}

81T40 Two-dimensional field theories, conformal field theories, etc.

PACS: 11.25.-w,11.25.Hf,11.10.Hi
Abstract: The Virasoro minimal models with boundary are described in the
Landau-Ginzburg theory by introducing
a boundary potential, function of the boundary field value.
The ground state field configurations become non-trivial and are found to
obey the soliton equations.
The conformal invariant boundary conditions are characterized by
the reparametrization-invariant data of the boundary potential,
that are the number and degeneracies of the stationary points.
The boundary renormalization group flows are obtained by varying
the boundary potential while keeping the bulk critical:
they satisfy new selection rules and correspond to real
deformations of the Arnold simple singularities of $A_k$ type.
The description of conformal boundary conditions in terms of boundary
potential and associated ground state solitons is extended to the
$N=2$ supersymmetric case, finding agreement with the analysis
of $A$-type boundaries by Hori, Iqbal and Vafa.

Keywords: D-branes, Conformal Field Models in String Theory, Boundary Quantum Field Theory