On the abundance of supersymmetric strings in AdS3 × S × S × S describing BPS line operators

We study supersymmetric open strings in type IIB AdS3 × S × S × S with mixed R-R and NS-NS fields. We focus on strings ending along a straight line at the boundary of AdS3, which can be interpreted as line operators in a dual CFT2. We study both classical configurations and quadratic fluctuations around them. We find that strings sitting at a fixed point in S × S × S, i.e. satisfying Dirichlet boundary conditions, are 1/2 BPS. We also show that strings sitting at different points of certain submanifolds of S × S × S can still share some fraction of the supersymmetry. This allows to define supersymmetric smeared configurations by the superposition of them, which range from 1/2 BPS to 1/8 BPS. In addition to the smeared configurations, there are as well 1/4 BPS and 1/8 BPS strings satisfying Neumann boundary conditions. All these supersymmetric strings are shown to be connected by a network of interpolating BPS boundary conditions. Our study reveals the existence of a rich moduli of supersymmetric open string configurations, for which the appearance of massless fermionic fields in the spectrum of quadratic fluctuations is crucial. ar X iv :2 10 8. 09 38 0v 2 [ he pth ] 3 S ep 2 02 1