Tensor renormalization group and the volume independence in 2D U(N) and SU(N) gauge theories

Journal of High Energy Physics

Mitsuaki Hirasawa¹  Jun Nishimura¹  Atis Yosprakob¹  Akira Matsumoto¹ 

[1] Department of Particle and Nuclear Physics, School of High Energy Accelerator Science, Graduate University for Advanced Studies (SOKENDAI);

关键词: Lattice Quantum Field Theory;    1/N Expansion;   

DOI  :  10.1007/JHEP12(2021)011

来源: DOAJ

【 摘 要 】

Abstract The tensor renormalization group method is a promising approach to lattice field theories, which is free from the sign problem unlike standard Monte Carlo methods. One of the remaining issues is the application to gauge theories, which is so far limited to U(1) and SU(2) gauge groups. In the case of higher rank, it becomes highly nontrivial to restrict the number of representations in the character expansion to be used in constructing the fundamental tensor. We propose a practical strategy to accomplish this and demonstrate it in 2D U(N) and SU(N) gauge theories, which are exactly solvable. Using this strategy, we obtain the singular-value spectrum of the fundamental tensor, which turns out to have a definite profile in the large-N limit. For the U(N) case, in particular, we show that the large-N behavior of the singular-value spectrum changes qualitatively at the critical coupling of the Gross-Witten-Wadia phase transition. As an interesting consequence, we find a new type of volume independence in the large-N limit of the 2D U(N) gauge theory with the θ term in the strong coupling phase, which goes beyond the Eguchi-Kawai reduction.

【 授权许可】

Unknown