Spatial correlators in strongly coupled plasmas

TL;DR

This study numerically investigates spatial correlators of scalar and pseudoscalar operators in SU(3) Yang-Mills theory at various temperatures, comparing results with free-field, operator-product expansion, and AdS/CFT predictions to understand plasma behavior.

Contribution

It provides the first lattice calculation of these correlators at finite temperature and compares them with multiple theoretical frameworks, revealing deviations from weak coupling expectations.

Findings

Correlators are stronger than vacuum at certain temperatures.

AdS/CFT semi-quantitatively matches the $F^2$ correlator in specific temperature ranges.

Strong fluctuations of $F\tilde F$ persist up to 2$T_c$.

Abstract

We numerically calculate the spatial correlators of the scalar and pseudoscalar operators $F^2$ and $F\tilde F$, in SU(3) Yang-Mills theory at zero and finite-temperature on the lattice. We compare the results over the distances $\frac{1}{2T}<r<\frac{3}{2T}$ to the free-field prediction, to the operator-product expansion as well as to the strongly coupled large-$N_c$ $\sN=4$ super-Yang-Mills theory, where results are obtained by AdS/CFT methods. For $T_c<T<1.15T_c$, both channels exhibit stronger spatial correlations than in the vacuum, and we give an explanation for this, using sum-rules and the operator-product expansion. The AdS/CFT calculation provides a semi-quantitatively successful description of the vacuum-subtracted $F^2$ correlator, renormalized in the 3-loop $\overline{\rm MS}$ scheme, in the interval of temperatures $1.2<T/T_c<1.9$, while the free-field prediction has the wrong sign. The $F\tilde F$ and $F^2$ correlators are predicted to have the same functional form both at weak coupling and in the strongly coupled SYM theory. The Yang-Mills plasma does not meet that expectation below $2T_c$. Instead we find that strong fluctuations of $F\tilde F$ are present at least up to that temperature. We discuss the impact of our results on our understanding of the quark-gluon plasma.