2020/04/16 by Hisayoshi Muraki, Muraki, Hisayoshi
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2004.07600
openalex publication_date 2020/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One-dimensional topological gravity is defined as a Gaussian integral as its partition function. The Gaussian integral supplies a toy model as a simpler version of one-matrix model that is well known to provide a description of two-dimensional topological gravity. The one-dimensional topological gravity inherits an integrable hierarchy structure as with two-dimensional topological gravity, yet it is the Burgers hierarchy rather than the Korteweg--de Vries hierarchy. Making use of this fact, an extension of the one-dimensional topological gravity to an analogue of two-matrix model is investigated and the associated partition function is shown to consist of a pair of partition functions of one-dimensional topological gravity intertwined via the Moyal--Weyl product, which enables to provide an explicit formula for its free energy. The extended system shows a hierarchy structure interpreted as a noncommutative extension of the Burgers hierarchy. The relation to noncommutative U(1) gauge theory is suggested.