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arXiv 0908.3624hep-th
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SU(2,2)的极小酉表示及其作为无质量共形场的变形和超对称扩张

Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions

Sudarshan Fernando, Murat Gunaydin

摘要:

本文研究了三元函数Hilbert空间上SO(4,2)的极小酉表示(minrep),它是通过量子化其在五维空间上的拟共形作用而得到的. SO(4,2)的最小表示与类似构造的SU(2,2)的最小表示一致,对应于四维时空中的无质量共形标量。存在SU(2,2)的minrep的单参数形变族。对于变形参数的正(负)整数值,得到对应于SL(2,C)子群的(0,λ/2)((-λ/2,0))表示的无质量共形场的正能量酉不可约表示.我们构造了SU(2,2)极小表示的超对称扩张及其对SU(2,2)极小表示的变形|N)。SU(2,2)的最小酉超多重态|4),在未变形的情况下,简单地对应于无质量的N = 4的杨-米尔斯超多重态在四维。对于每一个给定的非零整数值,我们得到一个唯一的高自旋无质量共形场的超多重态。对于SU(2,2| 4)这些超多重态只是在arXiv:hep-th/9806042中研究的双重超多重态。

英文摘要:

We study the minimal unitary representation (minrep) of SO(4,2) over an Hilbert space of functions of three variables, obtained by quantizing its quasiconformal action on a five dimensional space. The minrep of SO(4,2), which coincides with the minrep of SU(2,2) similarly constructed, corresponds to a massless conformal scalar in four spacetime dimensions. There exists a one-parameter family of deformations of the minrep of SU(2,2). For positive (negative) integer values of the deformation parameter ζone obtains positive energy unitary irreducible representations corresponding to massless conformal fields transforming in (0,ζ/2) ((-ζ/2,0)) representation of the SL(2,C) subgroup. We construct the supersymmetric extensions of the minrep of SU(2,2) and its deformations to those of SU(2,2|N). The minimal unitary supermultiplet of SU(2,2|4), in the undeformed case, simply corresponds to the massless N=4 Yang-Mills supermultiplet in four dimensions. For each given non-zero integer value of ζ, one obtains a unique supermultiplet of massless conformal fields of higher spin. For SU(2,2|4) these supermultiplets are simply the doubleton supermultiplets studied in arXiv:hep-th/9806042.

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