四次矩阵场论的组合戴森-施温格方程
Combinatorial Dyson-Schwinger Equations of Quartic Matrix Field Theory
AI总结：
该研究针对四次矩阵场论，依托微扰重整化的霍普夫代数结构分析组合戴森-施温格方程，验证其与重整化的兼容性，揭示其与定域量子场论模型方程的相似性，为非微扰结构推广提供组合层面的理论支撑。
摘要：
矩阵场论是一种组合非定域场论，近期被发现是一类非平凡但可解的量子场论（QFT）范例。为将这类非微扰结构推广到其他模型，深入理解戴森-施温格方程及其解的组合性质具有重要意义。为此，我们研究了明确依托微扰重整化霍普夫代数结构的组合戴森-施温格方程。研究发现，这些方程与重整化完全兼容，仅依赖于表观发散图（即平面带状图，也称为去完备对偶组合映射）。此外，它们与定域QFT实际模型中的方程类型相似，尤其具备无穷多基本图以及依赖于图的组合因子。
英文摘要：
Matrix field theory is a combinatorially non-local field theory which has recently been found to be a non-trivial but solvable QFT example. To generalize such non-perturbative structures to other models, a more combinatorial understanding of Dyson-Schwinger equations and their solutions is of high interest. To this end we consider combinatorial Dyson-Schwinger equations manifestly relying on the Hopf-algebraic structure of perturbative renormalization. We find that these equations are fully compatible with renormalization, relying only on the superficially divergent diagrams which are planar ribbon graphs, i.e. decompleted dual combinatorial maps. Still, they are of a similar kind as in realistic models of local QFT, featuring in particular an infinite number of primitive diagrams as well as graph-dependent combinatorial factors.
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