Long-range psu(2,2|4) Bethe Ansatze for gauge theory and strings

By N. Beisert, M. Staudacher. 2005

719 citations recorded by the source corpus.

We generalize various existing higher-loop Bethe ansatze for simple sec- tors 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, compar- ison 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 AdS5 × S 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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/eb3c99f5646561d24c3e6b3c2617811aadffe1d3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4 (2014, methodology): “We can rewrite these unitarity constraints as the constraints on bosonic Dynkin labels and with respect to ABA-diagram: all Dynkin labels except q2 are integers satisfying q1 ≥ 2 q3 ≥ 2 , r1 ≥ 0, r2 ≥ 2 , r3 ≥ 0 , ABA− diagram (C.16) while generically non-integer q2 satisfies q2 ≤ −(q1 + q3 + ∑ i ri”
Transcendentality and crossing (2006, methodology): “It was constructed to possibly describe gauge theory at four loops and beyond in [5], in analogy with an earlier proposal for the su(2) sector [26].”
Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions (2014, methodology): “We shall first report the physical S-matrix which was extracted from the analysis of the spectral equations for the fermionic excitations of the Gubser-Klebanov-Polyakov string [12] using the underlying integrable spin-chain description [13].”
The AdS 5 ×S 5 superstring worldsheet S matrix and crossing symmetry (2006, background): “In fact, in a remarkable series of papers [24, 25] the S-matrix in various sectors was uncovered.”
Gauge-string duality for (non)supersymmetric deformations of N=4 super-Yang–Mills theory (2005, background): “One may also hope that the analysis of the string Bethe equations will shed light on the structure of the dressing factor that appears in the Bethe ansatz for quantum strings [48, 49, 50] (in the deformed case the dressing factor may depend on γi and that may lead to an additional consistency condit”
Wrapping interactions at strong coupling: The giant magnon (2007, background): “ble worldsheet theory of the superstring in AdS 5 ×S5 on the plane. The full exact S-matrix is now believed to be known. Initially its structure in various subsectors of the theory has been uncovered [8, 9], which culminated with [10] where the su(2|2) × su(2|2) ⊂ psu(2,2|4) symmetry has been exploi”
The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations (2006, methodology): “pectral parameter as x → 2πP +x/ √ λ. This rescaling should be contrasted to the rescaling x → 4π(J + M)x/ √ λ performed in [44], in order to achieve the comparison with the gauge theory Bethe ansatz [16]. Then, it is easy to see that after the rescaling, the set of equations (8.21), (8.22), (8.23) ”