arXiv 1402.53962014-02hep-th

高自旋AdS_{d+1} /CFT_d的配分函数和Casimir能

Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d

Simone Giombi, Igor R. Klebanov, Arkady A. Tseytlin

备注：: 43 pages. v3: minor changes, references added. Version published in PRD
发表信息：: Phys. Rev. D 90, 024048 (2014)
DOI：: 10.1103/PhysRevD.90.024048

摘要：

最近，在欧几里得AdS_{d+1}中计算了高自旋（HS）理论的单圈自由能，并与S^d边界上的大N“矢量”标量CFT自由能中的阶N^0项匹配。在这里，我们将这种匹配扩展到定义在S^1 × S^{d-1}上的边界理论，其中S^1的长度可以解释为温度的倒数。结果表明，在N个自由复标量的CFT的U（N）单重区中，S^1 × S^2上的配分函数的大N极限与AdS_4中Vasiliev理论的单圈热配分函数相匹配，而在N个实标量的CFT的O（N）单重区中，它与只包含偶自旋的极小理论相匹配.我们将这种匹配扩展到所有维度d。我们还计算了各种维度下自由费米子CFT的单重态扇区的配分函数，并将它们与适当定义的高自旋理论相匹配，其中d>3包含具有混合对称性的无质量规范场。在零温度情形R x S^{d-1}中，我们计算了标量或费米子CFT中的卡西米尔能量，并将其与全局AdS_{d+1}中的单圈修正相匹配。对于任何奇维CFT的卡西米尔能量必须消失的一般理由，我们表明，HS的能量服从这一点。在U（N）对称情形下，我们证明了在AdS_{d+1}中对偶HS理论的正则化单圈Casimir能量的消失。在最小HS理论中，对于奇数d，真空能量为零，而对于偶数d，真空能量等于R x S^{d-1}中单个共形标量的卡西米尔能量，这再次与AdS/CFT一致，前提是最小HS耦合常数为~ 1/（N-1）。我们证明了类似的结果单重态部门的N狄拉克或马约拉纳费米子的理论。我们还讨论了在U（N）或O（N）的基本表示中含有N_f味的CFT的扩展。

英文摘要：

Recently, the one-loop free energy of higher spin (HS) theories in Euclidean AdS_{d+1} was calculated and matched with the order N^0 term in the free energy of the large N "vectorial" scalar CFT on the S^d boundary. Here we extend this matching to the boundary theory defined on S^1 x S^{d-1}, where the length of S^1 may be interpreted as the inverse temperature. It has been shown that the large N limit of the partition function on S^1 x S^2 in the U(N) singlet sector of the CFT of N free complex scalars matches the one-loop thermal partition function of the Vasiliev theory in AdS_4, while in the O(N) singlet sector of the CFT of N real scalars it matches the minimal theory containing even spins only. We extend this matching to all dimensions d. We also calculate partition functions for the singlet sectors of free fermion CFT's in various dimensions and match them with appropriately defined higher spin theories, which for d>3 contain massless gauge fields with mixed symmetry. In the zero-temperature case R x S^{d-1} we calculate the Casimir energy in the scalar or fermionic CFT and match it with the one-loop correction in the global AdS_{d+1}. For any odd-dimensional CFT the Casimir energy must vanish on general grounds, and we show that the HS duals obey this. In the U(N) symmetric case, we exhibit the vanishing of the regularized 1-loop Casimir energy of the dual HS theory in AdS_{d+1}. In the minimal HS theory the vacuum energy vanishes for odd d while for even d it is equal to the Casimir energy of a single conformal scalar in R x S^{d-1} which is again consistent with AdS/CFT, provided the minimal HS coupling constant is ~ 1/(N-1). We demonstrate analogous results for singlet sectors of theories of N Dirac or Majorana fermions. We also discuss extensions to CFT's containing N_f flavors in the fundamental representation of U(N) or O(N).

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文