Supergravity one-loop corrections on AdS7 and AdS3, higher spins and AdS/CFT
Supergravity one-loop corrections on AdS7 and AdS3, higher spins and AdS/CFT
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AdS7 和 AdS3 上的超重力单环修正、更高的旋转和 AdS/CFT
DOI：
10.1016/j.nuclphysb.2015.01.014
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
A. Tseytlin
中科院分区：
文献类型：
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作者：
M. Beccaria;G. Macorini;A. Tseytlin
如前所述，AdS 5× S 5 上 10d 超重力的单环修正对应于真空能和 4d 边界共形异常的贡献，减去一个 N= 4 麦克斯韦超多重态的值，从而再现了对偶 SU (N) SYM 理论中 N 2− 1 系数中的次主导项。我们在 AdS 7× S 4 上的 11d 超重力和 AdS 3× S 3× T 4 上的 10d 超重力中执行类似的单循环计算。在 AdS 7 情况下，我们发现对 6d 共形异常 a 系数和真空能量的修正再次减去一 (2, 0) 张量多重态的修正，表明对偶 (2, 0) 理论的总 a 异常系数为4 N 3− 9/4 N− 7/4，因此当 N= 1 时消失。在 AdS 3 情况下，对真空能量或 2d 中心电荷的单环校正结果等于一个自由 (4, 4) 标量多重态的单环校正，即 c=+ 6。这再现了描述去耦的双 2d CFT 的中心电荷 c= 6 (Q 1 Q 5+ 1) 中的副主项D5-D1系统的限制。我们还提出了 AdS 7 中一般对称高自旋场的 6d a 反常系数和真空能量贡献的表达式，并考虑将它们应用到以自由标量、旋量或 2 阶反对称张量为代表的边界共形 6d 理论的矢量 AdS/CFT 测试中。
As was shown earlier, the one-loop correction in 10d supergravity on AdS 5× S 5 corresponds to the contributions to the vacuum energy and 4d boundary conformal anomaly which are minus the values for one N= 4 Maxwell supermultiplet, thus reproducing the subleading term in the N 2− 1 coefficient in the dual SU (N) SYM theory. We perform similar one-loop computations in 11d supergravity on AdS 7× S 4 and 10d supergravity on AdS 3× S 3× T 4. In the AdS 7 case we find that the corrections to the 6d conformal anomaly a-coefficient and the vacuum energy are again minus the ones for one (2, 0) tensor multiplet, suggesting that the total a-anomaly coefficient for the dual (2, 0) theory is 4 N 3− 9/4 N− 7/4 and thus vanishes for N= 1. In the AdS 3 case the one-loop correction to the vacuum energy or 2d central charge turns out to be equal to that of one free (4, 4) scalar multiplet, ie is c=+ 6. This reproduces the subleading term in the central charge c= 6 (Q 1 Q 5+ 1) of the dual 2d CFT describing decoupling limit of D5–D1 system. We also present the expressions for the 6d a-anomaly coefficient and vacuum energy contributions of general-symmetry higher spin field in AdS 7 and consider their application to tests of vectorial AdS/CFT with the boundary conformal 6d theory represented by free scalars, spinors or rank-2 antisymmetric tensors.