正交和辛随机张量模型的对偶性

IF 1.5 Q2 PHYSICS, MATHEMATICAL Annales de l Institut Henri Poincare D Pub Date : 2023-10-09 DOI:10.4171/aihpd/177
Razvan Gurau, Hannes Keppler
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引用次数: 2

摘要

组$\mathrm{O}(N)$和$\mathrm{Sp}(N)$通过解析延拓与$N$, $\mathrm{O}(-N)\simeq\mathrm{Sp}(N)$的负值相关联。这种对偶性已经研究了向量模型,$\mathrm{SO}(N)$和$\mathrm{Sp}(N)$规范理论,以及一些随机矩阵系综。我们将这种对偶性推广到具有四次相互作用且指标置换下不对称的任意阶的真实随机张量模型$D$。在摄动理论中,对于配分函数、自由能和连通两点函数,$N$到$-N$的对偶性可以一个图接一个图地保持到所有阶。
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Duality of orthogonal and symplectic random tensor models
The groups $\mathrm{O}(N)$ and $\mathrm{Sp}(N)$ are related by an analytic continuation to negative values of $N$, $\mathrm{O}(-N)\simeq\mathrm{Sp}(N)$. This duality has been studied for vector models, $\mathrm{SO}(N)$ and $\mathrm{Sp}(N)$ gauge theories, as well as some random matrix ensembles. We extend this duality to real random tensor models of arbitrary order $D$ with no symmetry under permutation of the indices and with quartic interactions. The $N$ to $-N$ duality is shown to hold graph by graph to all orders in perturbation theory for the partition function, the free energy and the connected two-point function.
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CiteScore
2.30
自引率
0.00%
发文量
16
期刊最新文献
A vertex model for supersymmetric LLT polynomials Duality of orthogonal and symplectic random tensor models Second order cumulants: Second order even elements and $R$-diagonal elements Fluctuations of dimer heights on contracting square-hexagon lattices Reflection of stochastic evolution equations in infinite dimensional domains
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