The analytic bootstrap for large N Chern-Simons vector models
The analytic bootstrap for large N Chern-Simons vector models
复制标题
大 N Chern-Simons 向量模型的解析引导
DOI：
10.1007/jhep08(2018)166
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发表时间：
2018
影响因子：
5.4
通讯作者：
Ran Yacoby
中科院分区：
文献类型：
--
作者：
O. Aharony;L. Alday;A. Bissi;Ran Yacoby
一个抽象的三维chen - simons矢量模型在大N极限下显示出近似的高自旋对称性。它们的单线算符由一个弱断裂电流塔和一个近似扭转为1或2的标量σ组成。利用解析自举技术，研究了1/N展开式σ的四点相关器的交叉对称性。对于1/N阶，我们证明交叉对称固定了电流塔的贡献，提供了马尔达西纳和日勃多夫著名结果的另一种推导。当σ的扭数为1时，由于存在边际六性耦合，它的OPE接收到σ本身与任意系数交换的贡献。我们开发了一种机制来确定由于这种情况对双迹算子的OPE数据的修正，以及类似的交换。这反过来又允许我们将相关器完全固定到三个已知的交叉截断解。然后我们继续研究1/N2阶的问题。我们发现交叉暗示了奇扭双迹算子的出现，并计算了它们在大自旋展开中的OPE系数。此外，令人惊讶的是，在1/N2阶上交叉，意味着偶数双迹算子的非平凡O（1/N）异常维数，即使这种贡献没有出现在1/N阶的四点函数中（在没有标量交换的情况下）。我们认为这种现象是由于操作员混合而产生的。最后，我们分析了没有规范相互作用的六性耦合玻色子矢量模型，并确定了扭转-2双迹算子维度的1/N2阶修正。
A bstractThree-dimensional Chern-Simons vector models display an approximate higher spin symmetry in the large N limit. Their single-trace operators consist of a tower of weakly broken currents, as well as a scalar σ of approximate twist 1 or 2. We study the consequences of crossing symmetry for the four-point correlator of σ in a 1/N expansion, using analytic bootstrap techniques. To order 1/N we show that crossing symmetry fixes the contribution from the tower of currents, providing an alternative derivation of well-known results by Maldacena and Zhiboedov. When σ has twist 1 its OPE receives a contribution from the exchange of σ itself with an arbitrary coefficient, due to the existence of a marginal sextic coupling. We develop the machinery to determine the corrections to the OPE data of double-trace operators due to this, and to similar exchanges. This in turns allows us to fix completely the correlator up to three known truncated solutions to crossing. We then proceed to study the problem to order 1/N2. We find that crossing implies the appearance of odd-twist double-trace operators, and calculate their OPE coefficients in a large spin expansion. Also, surprisingly, crossing at order 1/N2, implies non-trivial O(1/N) anomalous dimensions for even-twist double-trace operators, even though such contributions do not appear in the four-point function at order 1/N (in the case where there is no scalar exchange). We argue that this phenomenon arises due to operator mixing. Finally, we analyse the bosonic vector model with a sextic coupling without gauge interactions, and determine the order 1/N2 corrections to the dimensions of twist-2 double-trace operators.