# 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.

## Key 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.