2019/11/26 by Guillaume Valette, Valette, Guillaume, G Valette
Computer Science · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Opportunistic and Delay-Tolerant Networks #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.1911.11574
openalex publication_date 2019/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Large N matrix models play an important role in modern theoretical physics,\nranging from quantum chromodynamics to string theory and holography. However,\nthey remain a difficult technical challenge because in most cases it is not\nknown how to perform the sum over planar graphs, which dominate the models at\nlarge N. In this thesis, we study large D matrix models, which provide a\nframework to build new limits for matrix models in which the sum over planar\ngraphs simplifies when D is large. The basic degrees of freedom are real\nmatrices of size N\× N with r additional indices of range D. They can\nbe interpreted as a real tensor of rank R=r+2 with indices of different\nranges, making a compelling connection with tensor models. We define a new\nlarge D limit for the sum over Feynman graphs of fixed genus in matrix\nmodels, based on an enhanced large D scaling of the coupling constants. Then,\nwe show that the resulting large D expansion is well-defined and organized\naccording to a half-integer called the index. When N=D, the result provides a\nnew large N limit for general \O(N)R invariant tensor models. In the\nlarge D limit, the sum over planar graphs of large N matrix models\nsimplifies to a non-trivial sum over generalized melonic graphs. This class of\ngraphs extends the one obtained in tensor models with standard scaling and\nallows for a wider class of interactions, including all the maximally\nsingle-trace terms. The general classification of generalized melonic graphs\nremains an open problem. However, in the case of the complete interaction of\norder R+1 for R a prime number, we identify them in detail and demonstrate\nthat they exhibit the same important features as the SYK model with\nq=(R+1)-fold random interactions, including the emergent conformal symmetry\nin the infrared regime and maximal chaos.\n