Broken Global Symmetries and Defect Conformal Manifolds

The Tilting Space of Boundary Conformal Field Theories

“…It is often challenging to perform the integrals, and various techniques have been developed to simplify and streamline the procedure [15,16]. Indeed, [1,17] have already employed the method of [15] in computing the curvature for line and surface defects. Here however we are able to proceed directly.…”

“…These results give a simple illustration of the salient features of conformal manifolds while generalising to interacting and more intricate setups. Our work was inspired by [1].…”

“…Finding exactly marginal parameters for CFTs that are neither supersymmetric nor two dimensional has historically been a challenge. Recently, however, it was pointed out [1] that defect and boundary conformal field theories with global symmetry, where the defect or boundary breaks the global symmetry, naturally have such couplings. The role of conserved currents in providing exactly marginal operators has long been known in boundary two dimensional CFT and supersymmetric CFTs in higher dimensions [5,6].…”

“…In contrast to ref. [1] where the focus was on line and surface defects, the goal of this letter is to investigate the nature of these couplings in boundary conformal field theories (bCFTs). We focus on two particularly simple examples: N free massless scalar or spinor fields where the coupling acts by changing the boundary conditions.…”

“…Here is an instance of the more general insight of ref. [1] for the particular case of a U (1) global symmetry. In the absence of a defect, Noether's Theorem implies the existence of a corresponding conserved current J µ (x).…”