Bootstrapping line defects with $O(2)$ global symmetry

Abstract

We use the numerical bootstrap to study conformal line defects with $O(2)$ global symmetry. Our results are very general and capture in particular conformal line defects originating from bulk CFTs with a continuous global symmetry, which can either be preserved or partially broken by the presence of the defect. We begin with an agnostic approach and perform a systematic bootstrap study of correlation functions between two canonical operators on the defect: the displacement and the tilt. We then focus on two interesting theories: a monodromy line defect and a localized magnetic field line defect. To this end, we combine the numerical bootstrap with the $\epsilon$-expansion, where we complement existing results in the literature with additional calculations. For the monodromy defect our numerical results are consistent with expectations, with known analytic solutions sitting inside our numerical bounds. For the localized magnetic field line defect our plots show a series of intriguing cusps which we explore.

54 pages, 11 figures

References in corpus (7)

• Generalized Global Symmetries
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• 3d Abelian Gauge Theories at the Boundary
• Critical behavior in the presence of an order-parameter pinning field