BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time

TL;DR

This paper introduces a new family of supersymmetric Wilson loops in N=4 SYM theory, focusing on hyperbolic submanifolds of space-time, revealing their properties, duals, and special cases including a novel half-BPS hyperbolic line.

Contribution

It presents new supersymmetric Wilson loops on hyperbolic submanifolds, analyzes their properties, and explores their string duals, including a previously unstudied half-BPS hyperbolic line.

Findings

Most loops preserve two supercharges.

Special cases include a half-BPS hyperbolic line.

String duals often involve complexified AdS_5 x S^5 or de-Sitter space.

Abstract

In this paper we present a family of supersymmetric Wilson loops of N=4 supersymmetric Yang-Mills theory in Minkowski space. Our examples focus on curves restricted to hyperbolic submanifolds, H_3 and H_2, of space-time. Generically they preserve two supercharges, but in special cases more, including a case which has not been discussed before, of the hyperbolic line, conformal to the straight line and circle, which is half-BPS. We discuss some general properties of these Wilson loops and their string duals and study special examples in more detail. Generically the string duals propagate on a complexification of AdS_5 x S^5 and in some specific examples the compact sphere is effectively replaced by a de-Sitter space.