Chern-Simons theory with vector fermion matter
Chern-Simons theory with vector fermion matter
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DOI：
10.1140/epjc/s10052-012-2112-0
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发表时间：
2012-08-01
影响因子：
4.4
通讯作者：
Yin, Xi
中科院分区：
文献类型：
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作者：
Giombi, Simone;Minwalla, Shiraz;Yin, Xi
我们研究了在k能级上由U(N) chen - simons理论描述的三维共形场理论与基本表示中的无质量费米子耦合。通过在光锥规范下求解Schwinger-Dyson方程，我们计算了该理论在R-2上有限温度下的精确平面自由能，它是t- Hooft耦合λ = N/k的函数。采用降维正则化方案，我们发现自由能在垂直线处消失，垂直线= 1；垂杆的保形理论不存在垂杆的保形理论不存在。我们利用异常守恒关系分析了高自旋电流下的算子谱，并特别证明了高自旋电流在1/N阶上不会产生异常维数。我们提出了一个积分方程，其解原则上决定了这些电流在1/N阶的所有相关器，并给出了所有三点函数到两个回路的显式微扰结果。我们还讨论了该理论的光锥哈密顿公式，其中出现了w -∞代数。我们的理论的最大超对称版本是ABJ模型，其中一个规范群取为U(1)，证明了纯高自旋规范理论作为弦理论的极限而出现。
We study three-dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in light-cone gauge, we compute the exact planar free energy of the theory at finite temperature on R-2 as a function of the 't Hooft coupling lambda = N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at vertical bar lambda vertical bar = 1; the conformal theory does not exist for vertical bar lambda vertical bar > 1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three-point functions up to two loops. We also discuss a light-cone Hamiltonian formulation of this theory where a W-infinity algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory.