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arXiv 1207.4485hep-th
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ABJ三重性：从高自旋场到弦

ABJ Triality: from Higher Spin Fields to Strings

Chi-Ming Chang, Shiraz Minwalla, Tarun Sharma, Xi Yin

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摘要：

我们证明了一个超对称和宇称违反版本的瓦西里耶夫的更高的自旋规范理论在AdS $_4$承认边界条件，保持${\cal N}=0,1,2,3,4$或6超对称。特别地，我们证明了在大$N,k$和有限$M$的极限下，具有U（M）Chan-Paton和${\cal N}=6$边界条件的Vasiliev理论与2+1维$U(N)_k\times U(M)_{-k}$ ABJ理论是全息对偶的.在这个系统中，所有的体高自旋场都在U（M）规范群的伴随中变换，其体t 'Hooft耦合是$\frac{M}{N}$。通过对Vasiliev理论中边界条件的分析，我们可以确定Vasiliev理论的宇称破缺相位与Chern-Simons矢量模型中两点和三点函数系数在大$N$下的精确关系。我们的图像表明，超对称Vasiliev理论可以作为AdS $_4\times \mathbb{CP}^3$中IIA型弦理论的极限而得到，而非阿贝尔Vasiliev理论在强体t Hooft耦合下可以平滑地转变为弦场论.基本弦是瓦西里耶夫的高自旋粒子通过U（M）规范相互作用结合在一起的单重束缚态。这是说明了热分配功能的自由ABJ理论上的两个球在大$M$和$N$即使在分析易处理的自由限制。在这个系统中，低温相的痕迹或串在U（M）解禁闭相变的阶数单位分解成它们的瓦西里耶夫微粒成分。在$T=\sqrt{\frac{N}{M}}$阶的更高温度下，瓦西里耶夫的更高自旋场本身在U（N）解除限制温度下分裂成更多的基本成分，这一过程在本体中被描述为黑洞成核。

英文摘要：

We demonstrate that a supersymmetric and parity violating version of Vasiliev's higher spin gauge theory in AdS$_4$ admits boundary conditions that preserve ${\cal N}=0,1,2,3,4$ or 6 supersymmetries. In particular, we argue that the Vasiliev theory with U(M) Chan-Paton and ${\cal N}=6$ boundary condition is holographically dual to the 2+1 dimensional $U(N)_k\times U(M)_{-k}$ ABJ theory in the limit of large $N,k$ and finite $M$. In this system all bulk higher spin fields transform in the adjoint of the U(M) gauge group, whose bulk t'Hooft coupling is $\frac{M}{N}$. Analysis of boundary conditions in Vasiliev theory allows us to determine exact relations between the parity breaking phase of Vasiliev theory and the coefficients of two and three point functions in Chern-Simons vector models at large $N$. Our picture suggests that the supersymmetric Vasiliev theory can be obtained as a limit of type IIA string theory in AdS$_4\times \mathbb{CP}^3$, and that the non-Abelian Vasiliev theory at strong bulk 't Hooft coupling smoothly turn into a string field theory. The fundamental string is a singlet bound state of Vasiliev's higher spin particles held together by U(M) gauge interactions. This is illustrated by the thermal partition function of free ABJ theory on a two sphere at large $M$ and $N$ even in the analytically tractable free limit. In this system the traces or strings of the low temperature phase break up into their Vasiliev particulate constituents at a U(M) deconfinement phase transition of order unity. At a higher temperature of order $T=\sqrt{\frac{N}{M}}$ Vasiliev's higher spin fields themselves break up into more elementary constituents at a U(N) deconfinement temperature, in a process described in the bulk as black hole nucleation.

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