Exploring the Tan contact term in Yang-Mills theory

Reliably computing the free energy in a gauge theory like QCD is a challenging and resource-demanding endeavor. We explore the possibility to obtain the associated thermodynamic anomaly from two-point functions based on a conjectured relation. This conjecture is triggered by the relation to the Tan contact in condensed matter systems. For this investigation we use state-of-the-art results for the Yang-Mills gluon two-point function from the lattice and the functional renormalization group, as well as novel Dyson-Schwinger results at (mite temperature computed in the present work. This allows for a first, qualitative, test of this conjecture. The results from all methods reveal the same nontrivial temperature behavior of the subleading large momentum dependence of the gluon propagator relevant for the conjectured relation. The comparison with the expected behavior for SU(2) Yang-Mills theory is encouraging to further pursue this approach.

Automated summary

Reliably computing the free energy in gauge theories like QCD is challenging, but the study shows promising results in obtaining the thermodynamic anomaly from two-point functions. Using advanced techniques and novel results, the research reveals consistent behavior of the gluon propagator at large momentum, encouraging further exploration of this approach for SU(2) Yang-Mills theory.