Abstract
We consider the critical O(N) model in the presence of an external magnetic field localized in space. This setup can potentially be realized in quantum simulators and in some liquid mixtures. The external field can be understood as a relevant perturbation of the trivial line defect, and thus triggers a defect Renormalization Group (RG) flow. In agreement with the g-theorem, the external localized field leads at long distances to a stable nontrivial defect CFT (DCFT) with g < 1. We obtain several predictions for the corresponding DCFT data in the epsilon expansion and in the large N limit. The analysis of the large N limit involves a new saddle point and, remarkably, the study of fluctuations around it is enabled by recent progress in AdS loop diagrams. Our results are compatible with results from Monte Carlo simulations and we make several predictions that can be tested in the future.
Highlights
Distances one expects to typically find a critical line operator
In this note we explore a particular class of renormalization group flows on line defects which correspond to activating external fields
Since gIR < 1 and the infrared defect is nontrivial, it must have two protected defect operators: the displacement operator of dimension 2 and since the O(N ) symmetry is explicitly broken to O(N − 1) symmetry by the defect it must have a “tilt” operator in the vector representation of O(N − 1) of dimension 1
Summary
The main aim of this paper is to shed light on the infrared properties of the defect (1.3). For the large N limit in generic d we find that the line operator (1.3) leads to a new classical RG trajectory which we analyze in great detail, including the fluctuations around this new classical trajectory This leads to an explicit determination of several scaling dimensions and one-point functions of the DCFTIR. There we show that, in d = 3, the defect coupling is marginally irrelevant and leads to a logarithmic correction to the one-point function of the bulk order parameter, as well as to other defect correlators These findings might be relevant for future Monte Carlo studies utilizing symmetry breaking defects as in [10, 11]. In appendix A we discuss the case of a non-conformal ordered bulk, while appendix B contains technical details on the calculation of the g-function in 4 − ε dimensions
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