Iterative structure of the N=4 SYM spin chain

作者：Zwiebel Benjamin I^*

来源：The Journal of High Energy Physics, 2008, (7): 114.

• supersymmetric gauge theory
• AdS-CFT correspondence
• Bethe ansatz

We develop algebraic methods for finding loop corrections to the N = 4 SYM dilatation generator, within the noncompact psu( 1, 1 vertical bar 2) sector. This sector gives a 't Hooft coupling lambda-dependent representation of psu(1, 1 vertical bar 2) x psu(1 vertical bar 1)(2). At first working independently of the representation, we present an all-order algebraic ansatz for the lambda-dependence of this Lie algebra's generators. The ansatz solves the symmetry constraints if an auxiliary generator, h, satisfies certain simple commutation relations with the Lie algebra generators. Applying this to the psu(1, 1 vertical bar 2) sector leads to an iterative solution for the planar three-loop dilatation generator in terms of leading order symmetry generators and h, which passes a thorough set of spectral tests. We argue also that this algebraic ansatz may be applicable to the nonplanar theory as well.

• 出版日期2008-7