AdS/CFT中的格和弦世界单：数值研究
Lattice and string worldsheet in AdS/CFT: a numerical study
摘要：
我们考虑了IIB超弦规范固定的格林-施瓦茨（二维）σ模型作用量的一种可能的离散化，并用它来测量从弦论导出的平面$\mathcal{N}=4$ SYM的尖点反常维数。我们进行晶格模拟采用有理混合蒙特卡罗（RHMC）算法和威尔逊式费米子离散化。在这个初步的研究中，我们比较我们的结果与预期的行为非常大的值的$g=\frac{\sqrtλ}{4π}$，这是微扰制度的西格玛模型，并找到一个定性的协议在有限的晶格间距。对于较小的$g$，连续极限被发散所阻碍。我们还检测到一个阶段的费米子行列式，其起源，我们解释，这对于小$g$导致一个符号的问题，不能通过标准的reweighting治疗。本文给出的结果在~ \cite{toappear}中进行了详细讨论。
英文摘要：
We consider a possible discretization for the gauge-fixed Green-Schwarz (two-dimensional) sigma-model action for the Type IIB superstring and use it for measuring the cusp anomalous dimension of planar $\mathcal{N}=4$ SYM as derived from string theory. We perform lattice simulations employing a Rational Hybrid Monte Carlo (RHMC) algorithm and a Wilson-like fermion discretization. In this preliminary study, we compare our results with the expected behavior for very large values of $g=\frac{\sqrtλ}{4π}$, which is the perturbative regime of the sigma-model, and find a qualitative agreement at finite lattice spacing. For smaller $g$ the continuum limit is obstructed by a divergence. We also detect a phase in the fermion determinant, whose origin we explain, which for small $g$ leads to a sign problem not treatable via standard reweigthing. Results presented here are discussed thoroughly in~\cite{toappear}.
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