FZZT Brane Relations in the Presence of Boundary Magnetic Fields

Atkin M, Zohren S. FZZT Brane Relations in the Presence of Boundary Magnetic Fields. Journal of High Energy Physics. 2012;2012(11): 163.We show how a boundary state different from the (1,1) Cardy state may berealised in the (m,m+1) minimal string by the introduction of an auxiliarymatrix into the standard two hermitian matrix model. This boundary is a naturalgeneralisation of the free spin boundary state in the Ising model. Theresolvent for the auxiliary matrix is computed using an extension of thesaddle-point method of Zinn-Justin to the case of non-identical potentials. Thestructure of the saddle-point equations result in a Seiberg-Shih like relationbetween the boundary states which is valid away from the continuum limit, inaddition to an expression for the spectral curve of the free spin boundarystate. We then show how the technique may be used to analyse boundary statescorresponding to a boundary magnetic field, thereby allowing us to generalisethe work of Carroll et al. on the boundary renormalisation flow of the Isingmodel, to any (m,m+1) model