On partition function and Weyl anomaly of conformal higher spin fields
On partition function and Weyl anomaly of conformal higher spin fields
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共形高自旋场的配分函数和Weyl反常
DOI：
10.1016/j.nuclphysb.2013.10.009
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Tseytlin
中科院分区：
文献类型：
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作者：
A. Tseytlin
我们研究了推广Weyl引力子和共形引力子的4维高导数共形高自旋(CHS)场。特别是在ADS/CFT语境中，它们似乎是“诱导”理论。我们考虑它们在弯曲的爱因斯坦空间背景上的配分函数，如(A)DS或球面和Ricci-平坦空间。值得注意的是，玻色子(整数自旋S)CHS配分函数似乎是由标准二阶导数“部分无质量”S场的配分函数的乘积给出的，推广了先前已知的单圈Weyl引力子(S=2)配分函数的表达式。我们计算了相应的自旋S Weyl反常系数a S和c S。我们对S的结果用ADS/CFT所暗示的间接方法(将S 4上CHS场的配分函数与ADS 5中已知的无质量高自旋场配分函数之比与交替边界条件相联系)，重现了最近在arxiv：1306.5242中发现的表达式。对于费米子CHS场，我们也得到了类似的结果。在半整数S的情况下，(A)DS背景上的CHS配分函数是由“部分无质量”的自旋S配分函数的平方与一个对应于特殊质量共形不变自旋S场的额外因子的乘积给出的。在Arxiv：1306.5242中注意到，当用ζ函数正则化计算时，所有S的玻色子a S系数之和为零，我们观察到同样的性质在费米子情况下也是正确的。
We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A) dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s) CHS partition function appears to be given by a product of partition functions of the standard 2nd-derivative “partially massless” spin s fields, generalizing the previously known expression for the 1-loop Weyl graviton (s= 2) partition function. We compute the corresponding spin s Weyl anomaly coefficients a s and c s. Our result for a s reproduces the expression found recently in arXiv: 1306.5242 by an indirect method implied by AdS/CFT (which relates the partition function of a CHS field on S 4 to a ratio of known partition functions of massless higher-spin field in AdS 5 with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS partition function on (A) dS background is given by the product of squares of “partially massless” spin s partition functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in arXiv: 1306.5242 that the sum of the bosonic a s coefficients over all s is zero when computed using the ζ-function regularization, and we observe that the same property is true also in the fermionic case.