arXiv 1408.36202014-08hep-th

巨引力子和$β$中几何极限的出现--${\cal N}=4$ SYM的形变

Giant gravitons and the emergence of geometric limits in $β$-deformations of ${\cal N}=4$ SYM

David Berenstein, Eric Dzienkowski

备注：: 1 Table
DOI：: 10.1007/JHEP01(2015)126

摘要：

我们研究具有$U(1)^3$对称性的${\cal N}=4$ SYM的超对称边缘变形的一个参数族，称为$β$ -变形，以理解其对偶$AdS\times X$几何，其中$X$是$g_{YM}^2N\to \infty$极限中的大型经典几何。我们认为，我们可以确定是否$X$是几何的，通过研究巨大的引力子状态之间的开弦的频谱，在场论中的运营商所代表的，因为我们把$N\to\infty$在某些双标度限制。我们研究的条件下，这些开放的字符串可以产生大量的国家与能源远远低于字符串规模。$β$的数论性质非常重要。当$\exp(iβ)$是单位根时，空间$X$是一个轨道。当$\exp(iβ)$接近双标度极限意义下的单位根时，$X$对应于轨道的有限变形。最后，如果$β$是无理数，则可以存在零星的光态。

英文摘要：

We study a one parameter family of supersymmetric marginal deformations of ${\cal N}=4$ SYM with $U(1)^3$ symmetry, known as $β$-deformations, to understand their dual $AdS\times X$ geometry, where $X$ is a large classical geometry in the $g_{YM}^2N\to \infty$ limit. We argue that we can determine whether or not $X$ is geometric by studying the spectrum of open strings between giant gravitons states, as represented by operators in the field theory, as we take $N\to\infty$ in certain double scaling limits. We study the conditions under which these open strings can give rise to a large number of states with energy far below the string scale. The number-theoretic properties of $β$ are very important. When $\exp(iβ)$ is a root of unity, the space $X$ is an orbifold. When $\exp(iβ)$ close to a root of unity in a double scaling limit sense, $X$ corresponds to a finite deformation of the orbifold. Finally, if $β$ is irrational, sporadic light states can be present.

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摘要：

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