-1.5cm =22.5cm =16.5cm ‘=11 =by60 = \#1[[bsphack@filesw [ gtempa[auxout[ ]{}]{}]{}gtempa @nobreak esphack]{} eqnlabel[\#1]{}]{} eqnlabel vacuum \#1

hep-th/0411067

[**Loop Operators and the Kondo Problem**]{} .5cm

[Constantin Bachas$\ ^{1,2}$ and Matthias R. Gaberdiel$\ ^2$]{}

[$\ ^1$ *Laboratoire de Physique Th[é]{}orique de l’Ecole Normale Sup[é]{}rieure[^1]\
24 rue Lhomond, 75231 Paris cedex 05, France\
$\, $\
$\ ^2$ Institut für Theoretische Physik, ETH H[ö]{}nggerberg\
8093 Zürich, Switzerland\
$\, $\
[Email: bachas@lpt.ens.fr ; gaberdiel@itp.phys.ethz.ch]{}* ]{}

.7in

[**ABSTRACT** ]{}

> We analyse the renormalisation group flow for D-branes in WZW models from the point of view of the boundary states. To this end we consider loop operators that perturb the boundary states away from their ultraviolet fixed points, and show how to regularise and renormalise them consistently with the global symmetries of the problem. We pay particular attention to the chiral operators that only depend on left-moving currents, and which are attractors of the renormalisation group flow. We check (to lowest non-trivial order in the coupling constant) that at their stable infrared fixed points these operators measure quantum monodromies, in agreement with previous semiclassical studies. Our results help clarify the general relationship between boundary transfer matrices and defect lines, which parallels the relation between (non-commutative) fields 