Duality and Reversal of Renormalization Group Flow.

The coupling of a boundary spin operator to the two dimensional Ising model is known to lead to renormalization group flow to a theory with fixed or Dirichlet boundary conditions at large distance from the boundary. Using the fact that spin and disorder operators are dual under a Kramers--Wannier or T-duality transformation, we show that coupling a boundary disorder operator results in an RG flow to free or Neumann boundary conditions. It seems that RG flow is reversed under the duality transformation. We reconcile this result with the conventional wisdom about RG flow and with the g-theorem of Affleck and Ludwig by noting that there are different possible definitions of free or fixed boundary conditions in the Ising theory, with different ground state degeneracies. In the two dual calculations, we show that the RG flow is restricted to different (dual) sectors of the theory with different free and fixed boundary states. Within each sector, the flow is always towards the conformally in..