Conformal perturbation theory confronts lattice results in the vicinity of a critical point

We study the accuracy and predictive power of conformal perturbation theory by a comparison with lattice results in the neighborhood of the finite-temperature deconfinement transition of SU(2) Yang-Mills theory, assuming that the infrared properties of this non-Abelian gauge theory near criticality can be described by the Ising model. The results of this comparison show that conformal perturbation theory yields quantitatively accurate predictions in a broad temperature range. We discuss the implications of these findings for the description of the critical point (belonging to the same universality class) of another strongly coupled, nonsupersymmetric non-Abelian gauge theory: the critical end point in the phase diagram of QCD at finite temperature and finite quark chemical potential.

Figure 1

Logarithmic plot of our results for the two-point correlation function of Polyakov loops $G(R)$ in the SU(2) gauge theory at the deconfinement temperature, as a function of the distance $R$.

Figure 2

Example of results for the Polyakov-loop two-point correlation function (in logarithmic scale), plotted against the spatial separation $R$ (in linear scale), for different temperatures $T$ off $T_{\mathrm{c}}$. These results were obtained from simulations on lattices with $N_t=10$ lattice spacings in the Euclidean-time direction. The inset (in which both axes are in a linear scale) shows an enlargement of the region where the correlators at $T>T_{\mathrm{c}}$ were fitted to the CPT prediction, Eq. (14), as discussed in the text.