We study a one-matrix model of a real symmetric matrix with a potential which is a sum of two logarithmic functions and a harmonic one. This two-logarithm matrix model is the absolute square norm of a toy wave function which is obtained by replacing the tensor argument of the wave function of the canonical tensor model (CTM) with a matrix. We discuss a symmetry enhancement phenomenon in this matrix model and show that symmetries and dimensions of emergent spaces are stable only in a phase which exists exclusively for the positive cosmological constant case in the sense of CTM. This would imply the importance of the positivity of the cosmological constant in the emergence phenomena in CTM.

中文翻译：

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二对数矩阵模型和规范张量模型中的对称性增强

我们研究了一个实对称矩阵的单矩阵模型，其势是两个对数函数和一个调和函数之和。这个二对数矩阵模型是玩具波函数的绝对平方范数，它是通过用矩阵替换规范张量模型（CTM）的波函数的张量参数而获得的。我们讨论了该矩阵模型中的对称性增强现象，并表明涌现空间的对称性和维度仅在仅在 CTM 意义上的正宇宙学常数情况下存在的相中是稳定的。这意味着宇宙学常数的正性在 CTM 的出现现象中的重要性。