双对数矩阵模型和正则张量模型中的对称性增强
Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model
摘要：
本文研究了实对称矩阵的一个矩阵模型，其势是两个对数函数与一个调和函数之和。该双对数矩阵模型是玩具波函数的绝对平方范数，该玩具波函数是通过用矩阵替换正则张量模型（CTM）的波函数的张量自变量而获得的。我讨论了这种矩阵模型的对称性增强现象，并表明，对称性和涌现空间的尺寸是稳定的，只有在一个阶段，专门存在于积极的宇宙学常数的情况下，在CTM的意义。这暗示了宇宙学常数的正性在CTM的涌现现象中的重要性。
英文摘要：
I 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. I 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.
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