Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-06-10
JHEP 0308 (2003) 041
Physics
High Energy Physics
High Energy Physics - Theory
25 pages
Scientific paper
10.1088/1126-6708/2003/08/041
We develop a Coulomb gas formalism for boundary conformal field theory having a $W$ symmetry and illustrate its operation using the three state Potts model. We find that there are free-field representations for six $W$ conserving boundary states, which yield the fixed and mixed physical boundary conditions, and two $W$ violating boundary states which yield the free and new boundary conditions. Other $W$ violating boundary states can be constructed but they decouple from the rest of the theory. Thus we have a complete free-field realization of the known boundary states of the three state Potts model. We then use the formalism to calculate boundary correlation functions in various cases. We find that the conformal blocks arising when the two point function of $\phi_{2,3}$ is calculated in the presence of free and new boundary conditions are indeed the last two solutions of the sixth order differential equation generated by the singular vector.
Caldeira Alexandre F.
Kawai Shinsuke
Wheater John F.
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