Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model

Abstract 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...

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Bibliographic Details
Published inProgress of theoretical and experimental physics Vol. 2021; no. 4
Main Author Sasakura, Naoki
Format Journal Article
LanguageEnglish
Published Oxford Oxford University Press 01.04.2021
Subjects
Gravity
Lie groups
Spacetime
Symmetry
Theoretical physics
Theory of relativity
B83
A13
E05
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Summary:Abstract 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.
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ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptab034