Long-range image Bethe ansätze for gauge theory and strings Original Research Article

We generalize various existing higher-loop Bethe ansätze for simple sectors of the integrable long-range dynamic spin chain describing planar image super-Yang–Mills theory to the full image symmetry and, asymptotically, to arbitrary loop order. We perform a large number of tests of our conjectured equations, such as internal consistency, comparison to direct three-loop diagonalization and expected thermodynamic behavior. In the special case of the image subsector, corresponding to a long-range t–J model, we are able to derive, up to three loops, the S-matrix and the associated nested Bethe ansatz from the gauge theory dilatation operator. We conjecture novel all-order S-matrices for the image and image subsectors, and show that they satisfy the Yang–Baxter equation. Throughout the paper, we muse about the idea that quantum string theory on image is also described by a image spin chain. We propose asymptotic all-order Bethe equations for this putative “string chain”, which differ in a systematic fashion from the gauge theory equations.