arXivDaily arXiv每日学术速递 周一至周五更新
北美退伍军人节（Veterans Day），12 日无更新
arXiv 2007.00154hep-thcond-mat.stat-mechhep-latnlin.SI
收藏

关于Sinh-Gordon模型自对偶点的探讨

Approaching the Self-Dual Point of the Sinh-Gordon model

Robert Konik, Márton Lájer, Giuseppe Mussardo

备注：
84 pages, 23 figures, 1 table
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

sinh-Gordon模型（ShG）最引人注目但又最神秘的性质之一是它的$S$ -矩阵的$b \rightarrow 1/b$自对偶性，在它的拉格朗日公式中没有它的踪迹。这里$b$是出现在模型的拉格朗日量$\cosh(bϕ)$中的ependical双曲余弦中的耦合。在本文中，我们发展截断谱方法（TSM）研究在有限体积的sinh-Gordon模型，我们改变耦合常数。我们得到了$b \ll 1$和$b$的中间值的预期结果，但是当接近自对偶点$b=1$时，TSM对ShG的基本应用中断了。我们发现，TSM给出了一个强大的截止$E_c$依赖性，这只会消失根据一个非常缓慢的幂律在$E_c$的结果。标准的重整化群策略--无论是数值的还是解析的--也无法改善这里的问题。因此，我们探索三种策略，以解决在$b=1$附近的TSM的基本限制。在第一部分中，我们专注于小体积光谱。我们试图了解有多少物理的ShG编码在零模式的哈密顿量的一部分，在本质上如何“量子力学”与“量子场论”的问题。在第二，我们确定的分歧存在于微扰理论，并使用超波莱尔近似进行重新确认。在第三种方法中，我们使用模型的精确形状因子来将$b$的一个值处的ShG视为不同耦合处的ShG的扰动。根据这一工作，我们认为模型的拉格朗日表述的强耦合相$b > 1$可能不同于从它的$S$ -矩阵中简单地推断出的强耦合相.特别是，我们提出了一个论点，该理论是无质量的$b>1$。

英文摘要：

One of the most striking but mysterious properties of the sinh-Gordon model (ShG) is the $b \rightarrow 1/b$ self-duality of its $S$-matrix, of which there is no trace in its Lagrangian formulation. Here $b$ is the coupling appearing in the model's eponymous hyperbolic cosine present in its Lagrangian, $\cosh(bϕ)$. In this paper we develop truncated spectrum methods (TSMs) for studying the sinh-Gordon model at a finite volume as we vary the coupling constant. We obtain the expected results for $b \ll 1$ and intermediate values of $b$, but as the self-dual point $b=1$ is approached, the basic application of the TSM to the ShG breaks down. We find that the TSM gives results with a strong cutoff $E_c$ dependence, which disappears according only to a very slow power law in $E_c$. Standard renormalization group strategies -- whether they be numerical or analytic -- also fail to improve upon matters here. We thus explore three strategies to address the basic limitations of the TSM in the vicinity of $b=1$. In the first, we focus on the small-volume spectrum. We attempt to understand how much of the physics of the ShG is encoded in the zero mode part of its Hamiltonian, in essence how `quantum mechanical' vs `quantum field theoretic' the problem is. In the second, we identify the divergencies present in perturbation theory and perform their resummation using a supra-Borel approximate. In the third approach, we use the exact form factors of the model to treat the ShG at one value of $b$ as a perturbation of a ShG at a different coupling. In the light of this work, we argue that the strong coupling phase $b > 1$ of the Lagrangian formulation of model may be different from what is naïvely inferred from its $S$-matrix. In particular, we present an argument that the theory is massless for $b>1$.

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。

↑