论文标题
具有边界的2D O（N）骨模型的R-Matrix引导程序
The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary
论文作者
论文摘要
S-Matrix引导程序扩展到具有$ O（N）$对称性的1+1D理论，并且在我们称为R-Matrix Bootstrap中的边界，因为感兴趣的数量是反射矩阵（R-Matrix）。给定批量S-矩阵，允许的R-Matrices的空间是一个无限的尺寸凸空间，我们从中绘制了由2D平面上的凸形域给出的二维截面。在某些情况下，在域的边界处，我们发现与没有自由参数的可集成R-Matrices相对应的顶点。在其他情况下，当有一个可集成的R-Matrices家族家族时，整个边界代表可综合的理论。我们还考虑了在物理切割以外的扩展区域中进行分析的R-膜，因此禁止该区域的极点（共振）。在某些模型中，这大大降低了R型的允许空间，导致新的顶点再次与综合理论相对应。我们还解决了双重问题，尤其是在扩展分析性的情况下，每当单位性饱和时，双重函数都会在物理线上切断。对于零传输的周期性杨巴克斯特解决方案，我们最初使用bootstrap计算了R-Matrix，然后得出了其先前未知的分析形式。
The S-matrix bootstrap is extended to a 1+1d theory with $O(N)$ symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space of allowed R-matrices is an infinite dimensional convex space from which we plot a two dimensional section given by a convex domain on a 2d plane. In certain cases, at the boundary of the domain, we find vertices corresponding to integrable R-matrices with no free parameters. In other cases, when there is a one-parameter family of integrable R-matrices, the whole boundary represents integrable theories. We also consider R-matrices which are analytic in an extended region beyond the physical cuts, thus forbidding poles (resonances) in that region. In certain models, this drastically reduces the allowed space of R-matrices leading to new vertices that again correspond to integrable theories. We also work out the dual problem, in particular in the case of extended analyticity, the dual function has cuts on the physical line whenever unitarity is saturated. For the periodic Yang-Baxter solution that has zero transmission, we computed the R-matrix initially using the bootstrap and then derived its previously unknown analytic form.
