2003/09/30 by Jun Nishimura, Toshiyuki Okubo, Fumihiko Sugino
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum chaos and dynamical systems #Quantum many-body systems #hep-th
paper · pdf · doi:10.1088/1126-6708/2003/10/057
published as JHEP 0310 (2003) 057 · 30 pages, 15 figures, LaTeX; added references for section 1
arxiv created 2003/10/08 · openalex publication_date 2003/10/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Gaussian expansion has been developed since early 80s as a powerful analytical method, which enables nonperturbative studies of various systems using `perturbative' calculations. Recently the method has been used to suggest that 4d space-time is generated dynamically in a matrix model formulation of superstring theory. Here we clarify the nature of the method by applying it to exactly solvable one-matrix models with various kinds of potential including the ones unbounded from below and of the double-well type. We also formulate a prescription to include a linear term in the Gaussian action in a way consistent with the loop expansion, and test it in some concrete examples. We discuss a case where we obtain two distinct plateaus in the parameter space of the Gaussian action, corresponding to different large-N solutions. This clarifies the situation encountered in the dynamical determination of the space-time dimensionality in the previous works.