New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5

TL;DR

This paper derives an integrable two-dimensional fermionic system from superstrings on AdS_5 x S^5, revealing a new Hamiltonian structure and confirming its integrability through a Lax pair construction.

Contribution

It introduces a novel integrable fermionic Hamiltonian from string theory in AdS_5 x S^5, with explicit Lax representation and connections to gauge theory operators.

Findings

Hamiltonian expressed as a polynomial in 1/J and √λ'

Agreement of energy shifts with gauge theory results

Explicit Lax pair demonstrating integrability

Abstract

We consider classical superstrings propagating on AdS_5 x S^5 space-time. We consistently truncate the superstring equations of motion to the so-called su(1|1) sector. By fixing the uniform gauge we show that physical excitations in this sector are described by two complex fermionic degrees of freedom and we obtain the corresponding Lagrangian. Remarkably, this Lagrangian can be cast in a two-dimensional Lorentz-invariant form. The kinetic part of the Lagrangian induces a non-trivial Poisson structure while the Hamiltonian is just the one of the massive Dirac fermion. We find a change of variables which brings the Poisson structure to the canonical form but makes the Hamiltonian nontrivial. The Hamiltonian is derived as an exact function of two parameters: the total S^5 angular momentum J and string tension \lambda; it is a polynomial in 1/J and in \sqrt{\lambda'} where \lambda'=\frac{\lambda}{J^2} is the effective BMN coupling. We identify the string states dual to the gauge theory operators from the closed su(1|1) sector of N=4 SYM and show that the corresponding near-plane wave energy shift computed from our Hamiltonian perfectly agrees with that recently found in the literature. Finally we show that the Hamiltonian is integrable by explicitly constructing the corresponding Lax representation.