Exact Solutions For Correlation Functions In Some 1+1 D Field Theories With Boundary

Abstract

We consider 1+1 D theories which are free everywhere except for cosine and magnetic interactions on the boundary. These theories arise in dissipative quantum systems, open string theory, and, in special cases, tunneling in quantum Hall systems. These boundary systems satisfy an approximate SL(2,Z) symmetry as a function of flux per unit cell and dissipation. At special multicritical points, they also satisfy a set of reparametrization Ward identities and have homogeneous, piecewise-linear correlation functions in momentum space. In this paper, we use these symmetries to find exact solutions for some of the correlation functions. We also comment on the form of the correlation functions in general, and verify that the SL(2,Z) duality transformation between different critical points is satisfied exactly in all cases where the full solution is known.