Boundaries and interfaces with localized cubic interactions in the O(N) model
Sabine Harribey, Igor R. Klebanov, Zimo Sun
Abstract
A bstract We explore a new approach to boundaries and interfaces in the O ( N ) model where we add certain localized cubic interactions. These operators are nearly marginal when the bulk dimension is 4 − ϵ , and they explicitly break the O ( N ) symmetry of the bulk theory down to O ( N − 1). We show that the one-loop beta functions of the cubic couplings are affected by the quartic bulk interactions. For the interfaces, we find real fixed points up to the critical value N crit ≈ 7, while for N > 4 there are IR stable fixed points with purely imaginary values of the cubic couplings. For the boundaries, there are real fixed points for all N , but we don’t find any purely imaginary fixed points. We also consider the theories of M pairs of symplectic fermions and one real scalar, which have quartic OSp(1|2 M ) invariant interactions in the bulk. We then add the Sp(2 M ) invariant localized cubic interactions. The beta functions for these theories are related to those in the O ( N ) model via the replacement of N by 1 − 2 M . In the special case M = 1, there are boundary or interface fixed points that preserve the OSp(1|2) symmetry, as well as other fixed points that break it.