John Wheater

Abstract:

The Veneziano-Yankielowicz glueball superpotential for an arbitrary N=1 SUSY pure gauge theory with classical gauge group is derived using an approach following recent work of Dijkgraaf, Vafa and others. These non-perturbative terms, which had hitherto been included by hand in the above approach, are thus seen to arise naturally, and the approach is rendered self-contained. By minimising the glueball superpotential for theories with fundamental matter added, the expected vacuum structure with gaugino condensation and chiral symmetry breaking is obtained. Various possible extensions are also discussed.

Abstract:

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.