Exact results for ABJ Wilson loops and open-closed duality

TL;DR

This paper derives exact relations linking ABJ theory's partition functions and Wilson loops, revealing an open-closed duality and connecting open and closed string amplitudes via topological string theory.

Contribution

It introduces new exact relations between partition functions and Wilson loops in ABJ theory, enabling predictions of large N expansions and elucidating open-closed duality through topological string connections.

Findings

Exact relations between partition functions and Wilson loops in ABJ theory.

Open-closed duality interpreted as a back-reaction effect.

Explicit relations between open and closed string amplitudes.

Abstract

We find new exact relations between the partition function and vacuum expectation values (VEVs) of 1/2 BPS Wilson loops in ABJ theory, which allow us to predict the large N expansions of the 1/2 BPS Wilson loops from known results of the partition function. These relations are interpreted as an open-closed duality where the closed string background is shifted by the insertion of Wilson loops due to a back-reaction. Using the connection between ABJ theory and the topological string on local P1 x P1, we explicitly write down non-trivial relations between open and closed string amplitudes.