Integrable spin chain in superconformal Chern-Simons theory
Integrable spin chain in superconformal Chern-Simons theory
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DOI：
10.1088/1126-6708/2008/10/053
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发表时间：
2008-07
影响因子：
5.4
通讯作者：
D. Bak;S. Rey
中科院分区：
文献类型：
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作者：
D. Bak;S. Rey
在AdS4⊗cp3上提出了N = 6超共形chen - simons理论作为对IIA型弦理论的规范理论对偶。从平面极限单迹算子的共形维谱出发，研究了理论的可积性。在强't Hooft耦合下，谱由OSp(6|4； R)/SO（3,1） × SU(3) × U(1)超集上的自由超弦激发能得到。我们利用关于对称空间上sigma模型的著名结果，回顾了世界表理论的经典可积性。利用r -对称群SU(4)，我们还求解了带有单迹算子的自旋链系统的相关Yang-Baxter方程。根据解，构造了包含4和4之间三位点相互作用的交替自旋链哈密顿量。在弱t - Hooft耦合下，对规范理论进行了摄动研究，并计算了膨胀算子对单迹算子的作用，最大可达两个环。为了确保一致性，我们计算了所有与扩张算子相关的费曼图。我们发现所得的自旋链哈密顿量与由Yang- Baxter方程得到的哈密顿量相匹配。进一步研究了最短规范不变算子TrY I Y†J =(15,1)所引起的新问题。我们观察到“包裹相互作用”的存在，计算了真实的光谱，发现光谱与超对称的预测一致。我们还发现，由交替自旋链哈密托年计算的标度维与真实谱相吻合。我们求解了少量激发态的Bethe ansatz方程，发现了4和4激发态之间的相关性和介子（44）束缚态不存在的迹象。
N = 6 superconformal Chern-Simons theory was proposed as gauge theory dual to Type IIA string theory on AdS4 ⊗ CP 3 . We study integrability of the theory from conformal dimension spectrum of single trace operators at planar limit. At strong 't Hooft coupling, the spectrum is obtained from excitation energy of free superstring on OSp(6|4; R)/SO(3,1) × SU(3) × U(1) supercoset. We recall that the worldsheet theory is integrable classically by utilizing well-known results concerning sigma model on symmetric space. With R-symmetry group SU(4), we also solve relevant Yang-Baxter equation for a spin chain system associated with the single trace operators. From the solution, we con- struct alternating spin chain Hamiltonian involving three-site interactions between 4 and 4. At weak 't Hooft coupling, we study gauge theory perturbatively, and calculate action of dilatation operator to single trace operators up to two loops. To ensure consistency, we computed all relevant Feynman diagrams contributing to the dilatation opeator. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from Yang- Baxter equation. We further study new issues arising from the shortest gauge invariant operators TrY I Y † J = (15,1). We observe that 'wrapping interactions' are present, compute the true spectrum and find that the spectrum agrees with prediction from supersymmetry. We also find that scaling dimension computed naively from alternating spin chain Hamilto- nian coincides with the true spectrum. We solve Bethe ansatz equations for small number of excitations, and find indications of correlation between excitations of 4's and 4's and of nonexistence of mesonic (44) bound-state.