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arXiv 1306.5242hep-th
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诱导高自旋规范理论的AdS描述

AdS Description of Induced Higher-Spin Gauge Theory

Simone Giombi, Igor R. Klebanov, Silviu S. Pufu, Benjamin R. Safdi, Grigory Tarnopolsky

备注：
62 pages, 1 figure; v2 refs added, minor improvements; v3 refs added, minor improvements
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摘要：

本文研究了由Δ维自旋s单迹算符构造的双迹算符对三维大N个CFTs的形变.这些理论都具有UV不动点，我们计算了三球自由能δF= F_{UV} - F_{IR}的变化.为了使用对偶AdS_4空间描述UV不动点，我们修改了体相中自旋s场的边界条件;这种方法产生的δF与场论计算一致。如果自旋s算符是守恒流，则不动点由诱导宇称不变的共形自旋s规范理论描述。低自旋的例子是QED_3（s=1）和三维诱导共形引力（s=2）。当原CFT是N个共形复标量场或费米子场时，在自旋s无质量规范场上，在交替边界条件下，诱导三维规范理论的U（N）单重扇区与AdS_4中的Vasiliev理论是对偶的.我们通过计算大N时δF中的首项来检验这种对应性。我们证明了δF中的（1/2）\log N系数等于自旋s-1规范场中作用于自旋s规范场的规范参数的个数.我们讨论这些结果的推广到3-d规范理论，包括陈-西蒙斯条款和理论，其中s是半整数。我们还论证了在偶数维d中共形自旋s理论的Weyl反常a系数，如d=4的Weyl平方引力理论的Weyl反常a系数，可以用AdS_{d+1}中的无质量自旋s场在交替边界条件下有效地计算。利用这种方法，我们导出了d=4的Fradkin-Tseytlin共形高自旋规范场的Weyl反常a系数的一个简单公式。同样地，在AdS_3中使用交替边界条件，我们再现了二维引力中bc鬼的著名的中心荷c=-26，以及它的高自旋推广。

英文摘要：

We study deformations of three-dimensional large N CFTs by double-trace operators constructed from spin s single-trace operators of dimension Δ. These theories possess UV fixed points, and we calculate the change of the 3-sphere free energy δF= F_{UV}- F_{IR}. To describe the UV fixed point using the dual AdS_4 space we modify the boundary conditions on the spin s field in the bulk; this approach produces δF in agreement with the field theory calculations. If the spin s operator is a conserved current, then the fixed point is described by an induced parity invariant conformal spin s gauge theory. The low spin examples are QED_3 (s=1) and the 3-d induced conformal gravity (s=2). When the original CFT is that of N conformal complex scalar or fermion fields, the U(N) singlet sector of the induced 3-d gauge theory is dual to Vasiliev's theory in AdS_4 with alternate boundary conditions on the spin s massless gauge field. We test this correspondence by calculating the leading term in δF for large N. We show that the coefficient of (1/2)\log N in δF is equal to the number of spin s-1 gauge parameters that act trivially on the spin s gauge field. We discuss generalizations of these results to 3-d gauge theories including Chern-Simons terms and to theories where s is half-integer. We also argue that the Weyl anomaly a-coefficients of conformal spin s theories in even dimensions d, such as that of the Weyl-squared gravity in d=4, can be efficiently calculated using massless spin s fields in AdS_{d+1} with alternate boundary conditions. Using this method we derive a simple formula for the Weyl anomaly a-coefficients of the d=4 Fradkin-Tseytlin conformal higher-spin gauge fields. Similarly, using alternate boundary conditions in AdS_3 we reproduce the well-known central charge c=-26 of the bc ghosts in 2-d gravity, as well as its higher-spin generalizations.

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