Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings

TL;DR

This paper extends Bethe ansatz equations to the full psu(2,2|4) symmetry of N=4 Super Yang-Mills, providing tests, deriving S-matrices, and proposing all-order equations for gauge and string theories.

Contribution

It generalizes higher-loop Bethe ansatz equations to the full symmetry and proposes asymptotic all-order equations for the gauge/string duality.

Findings

Conjectured all-order S-matrices for subsectors.

Validated equations through multiple tests.

Proposed asymptotic Bethe equations for string theory.

Abstract

We generalize various existing higher-loop Bethe ansaetze for simple sectors of the integrable long-range dynamic spin chain describing planar N=4 Super Yang-Mills Theory to the full psu(2,2|4) 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 su(1|2) 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 su(1|2) and su(1,1|2) subsectors, and show that they satisfy the Yang-Baxter equation. Throughout the paper, we muse about the idea that quantum string theory on AdS_5xS^5 is also described by a psu(2,2|4) 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.