{"paper":{"title":"Bounds on free energy in QCD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","hep-th"],"primary_cat":"hep-lat","authors_text":"Axel Maas, Daniel Zwanziger","submitted_at":"2013-01-15T22:32:22Z","abstract_excerpt":"We derive some exact bounds on the free energy $W(J)$ in QCD, where $J_\\mu^b$ is a source for the gluon field $A_\\mu^b$ in the minimal Landau gauge, and $W(J)$ is the generating functional of connected gluon correlators. Among other results, we show that for a static source $J(x) = h$ the free energy vanishes, $W(h) = 0$, together with its first derivative, ${\\partial W(h) \\over \\partial h} = 0,$ for all $h$, no matter how strong. Thus the system does not respond to a static color probe. We also present numerical evaluations of the free energy $W(J)$ and find that the bounds are well satisfied"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3520","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}