A note on the S-matrix bootstrap for the 2d O(N) bosonic model
A note on the S-matrix bootstrap for the 2d O(N) bosonic model
复制标题
关于 2d O(N) 玻色子模型的 S 矩阵自举的注释
DOI：
10.1007/jhep11(2018)093
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发表时间：
2018
影响因子：
5.4
通讯作者：
M. Kruczenski
中科院分区：
文献类型：
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作者：
Yifei He;Andrew Irrgang;M. Kruczenski
在这项工作中，我们应用S-矩阵bootstrap最大化程序的二维玻色子O（N）可积模型，其中有N种标量粒子的质量m和没有束缚态。由于在之前的研究中，理论是通过最大化粒子及其束缚态之间的耦合来定义的，因此主要问题似乎是找到可以使用哪些其他泛函来定义该模型。相反，我们认为，这个可积模型的定义属性是，它驻留在由酉性和交叉约束确定的凸空间的顶点。因此，可积模型可以通过最大化任何线性泛函来找到，该线性泛函的梯度指向顶点的一般方向，即在由在顶点处相交的面的法线确定的圆锥内。这是应用数学中的一个标准问题，与半定规划有关，可通过快速可用的数值算法求解。数值解提供的信息足以在不使用可积性的情况下重现已知的解析解，即杨-巴克斯特方程。这种情况看起来很普遍，所以我们期望其他没有连续参数的理论也可以通过最大化允许的S-矩阵的凸空间中的线性泛函来找到。
In this work we apply the S-matrix bootstrap maximization program to the 2d bosonic O (N) integrable model which has N species of scalar particles of mass m and no bound states. Since in previous studies theories were defined by maximizing the coupling between particles and their bound states, the main problem appears to be to find what other functional can be used to define this model. Instead, we argue that the defining property of this integrable model is that it resides at a vertex of the convex space determined by the unitarity and crossing constraints. Thus, the integrable model can be found by maximizing any linear functional whose gradient points in the general direction of the vertex, namely within a cone determined by the normals to the faces intersecting at the vertex. This is a standard problem in applied mathematics, related to semi-definite programming and solvable by fast available numerical algorithms. The information provided by the numerical solution is enough to reproduce the known analytical solution without using integrability, namely the Yang-Baxter equation. This situation seems quite generic so we expect that other theories without continuous parameters can also be found by maximizing linear functionals in the convex space of allowed S-matrices.