Abstract
We study half-BPS line defects in mathcal{N} = 2 superconformal theories using the bootstrap approach. We concentrate on local excitations constrained to the defect, which means the system is a 1d defect CFT with osp(4∗|2) symmetry. In order to study correlation functions we construct a suitable superspace, and then use the Casimir approach to calculate a collection of new superconformal blocks. Special emphasis is given to the displacement operator, which controls deformations orthogonal to the defect and is always present in a defect CFT. After setting up the crossing equations we proceed with a numerical and analytical bootstrap analysis. We obtain numerical bounds on the CFT data and compare them to known solutions. We also present an analytic perturbative solution to the crossing equations, and argue that this solution captures line defects in mathcal{N} = 2 gauge theories at strong coupling.
Highlights
Defects are important observables in quantum field theory: they serve as probes that allow to extract physics otherwise inaccessible from the study of local operators
In the supersymmetric setup we are considering, the displacement sits in a supermultiplet whose highest weight is a scalar. This means that after taking into account all the constraints coming from supersymmetry, our analysis will be similar to the 1d bosonic bootstrap
This standard property of the covariant derivative ensures that shortening conditions constructed with it are invariant under supersymmetry
Summary
We study perturbations around the bosonic mean-field solution (4.22), similar to the analysis of section 6 in [17]. From the correlator it is possible to extract the first-order corrections to the anomalous dimensions and OPE coefficients of the operators in the spectrum. This function can be expressed in a superblocklike expansion. The solution to crossing we want to perturb around has OPE coefficients given in equation (4.23) with ξ = 1, and the spectrum of dimensions is. Where R(z) and P (z) are a priory completly arbitrary functions Comparing this with the block expansion we obtain. The one-dimensional bosonic blocks g∆ = g∆0,0 of equation (4.1) have clean transformation properties under braiding. See [29] for a careful analysis in the BCFT setup
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