On higher spin partition functions
On higher spin partition functions
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关于更高自旋配分函数
DOI：
10.1088/1751-8113/48/27/275401
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发表时间：
2015
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：
M. Beccaria;A. Tseytlin
我们观察到所有自由无质量较高自旋集合的配分函数S=0，1，2，3，…在平面空间中等于1：幽灵行列式抵消‘物理’行列式，或者，等价地，(正则化的)自由度总数为零。这反映了大的潜在规范对称性，并暗示了与超对称或拓扑理论的相似之处。Z=1性质也扩展到ADS背景，即Vasiliev理论的1环真空配分函数等于1(假设自旋上的和的特定正则化)；这在前面被注意为矢量ADS/CFT对偶性的一致性要求。我们发现Z=1在共形高自旋理论(具有高导数∂2 S？>；动力学项)在平坦或共形平坦S4背景附近扩展时也是正确的。我们还考虑了平坦四维空间中对称无迹秩位S张量场的自由共形理论的配分函数，该张量场具有二阶导数动力项，但只具有标量规范不变性。该非么正理论在弯曲背景下具有Weyl不变作用，与AdS5中的“部分无质量”场相对应。我们详细讨论了S=2(或‘共形引力子’)的特例，计算了相应的共形反常系数，并将它们与已有的四维共形群的一般表示式进行了比较。
We observe that the partition function of the set of all free massless higher spins s = 0, 1, 2, 3,... in flat space is equal to one: the ghost determinants cancel against the ‘physical’ ones or, equivalently, the (regularized) total number of degrees of freedom vanishes. This reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory. The Z = 1 property extends also to the AdS background, i.e. the 1-loop vacuum partition function of Vasiliev theory is equal to 1 (assuming a particular regularization of the sum over spins); this was noticed earlier as a consistency requirement for the vectorial AdS/CFT duality. We find that Z = 1 is true also in the conformal higher spin theory (with higher-derivative ∂ 2 s ?> kinetic terms) expanded near flat or conformally flat S4 background. We also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2-derivative kinetic term but only scalar gauge invariance in flat 4d space. This non-unitary theory has Weyl-invariant action in curved background and it corresponds to ‘partially massless’ field in AdS5. We discuss in detail the special case of s = 2 (or ‘conformal graviton’), compute the corresponding conformal anomaly coefficients and compare them with previously found expressions for generic representations of conformal group in 4 dimensions.