Theta dependence of SU(N) gauge theories
read the original abstract
We study the $\theta$ dependence of four-dimensional SU($N$) gauge theories, for $N\geq 3$ and in the large-N limit. We use numerical simulations of the Wilson lattice formulation of gauge theories to compute the first few terms of the expansion of the ground-state energy $F(\theta)$ around $\theta=0$, $F(\theta)-F(0) = A_2 \theta^2 (1 + b_2 \theta^2 + ...)$. Our results support Witten's conjecture: $F(\theta)-F(0) = {\cal A} \theta^2 + O(1/N)$ for sufficiently small values of $\theta$, $\theta < \pi$. Indeed we verify that the topological susceptibility has a nonzero large-N limit $\chi_\infty=2 {\cal A}$ with corrections of $O(1/N^2)$, in substantial agreement with the Witten-Veneziano formula which relates $\chi_\infty$ to the $\eta^\prime$ mass. Furthermore, higher order terms in $\theta$ are suppressed; in particular, the $O(\theta^4)$ term $b_2$ (related to the $\eta^\prime - \eta^\prime$ elastic scattering amplitude) turns out to be quite small: $b_2=-0.023(7)$ for N=3, and its absolute value decreases with increasing $N$, consistently with the expectation $b_2=O(1/N^2)$.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
Unified Functional-Holographic Theory of the QCD Critical End Point
A coupled DSE-FRG-holographic model predicts the QCD critical end point at T_CEP approximately 130-135 MeV and mu_B,CEP approximately 600 MeV, with sensitivity to regulator and normalization choices.
-
Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
Out-of-equilibrium simulations with open-to-periodic boundary switching plus a tailored stochastic normalizing flow enable efficient topology sampling in the continuum limit of four-dimensional SU(3) Yang-Mills theory.
-
Topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory
High-precision lattice computation yields χ_top^{1/4} = 198.1(0.7)(2.7) MeV for SU(3) Yang-Mills after continuum and infinite-volume extrapolation from seven spacings and volumes.
-
FLAG Review 2024
The FLAG 2024 review provides updated averages of lattice QCD determinations for quark masses, decay constants, form factors, mixing parameters, and nucleon matrix elements.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.