Theta dependence of SU(N) gauge theories

By Luigi Del Debbio, H. Panagopoulos, E. Vicari. 2002

147 citations recorded by the source corpus.

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 $b_2=O(1/N^2)$.

Subfields: Nuclear and High Energy Physics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/bad462a685bb705391cb1ea2a5c1e670a4f20701

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In Nuclear and High Energy Physics

  1. Rainer Sommer
  2. Stefan Schaefer
  3. Francesco Virotta
  4. M. Luscher
  5. M. Morte
  6. G. Herdoiza
  7. Stephen R. Sharpe
  8. U. Wenger

In Radiology, Nuclear Medicine and Imaging

  1. Francesco Virotta
  2. M. Luscher
  3. Rainer Sommer
  4. Stefan Schaefer

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