# Massive fluctuations in deconfining SU(2) Yang-Mills thermodynamics

## TL;DR

This paper investigates the behavior of loop corrections in SU(2) Yang-Mills thermodynamics, demonstrating that higher-loop contributions dominate at high temperatures and that the loop expansion does not terminate at finite order, requiring resummation techniques.

## Contribution

It provides a detailed analysis of loop corrections, disproves the finite termination conjecture, and introduces an all-loop resummation method for bubble diagrams in deconfining SU(2) Yang-Mills theory.

## Key findings

- Higher-loop contributions dominate at high temperatures.
- Loop expansion does not terminate at finite order.
- Resummation yields an analytic continuation across temperatures.

## Abstract

We review how vertex constraints inherited from the thermal ground state strongly reduce the integration support of loop four-momenta associated with massive quasi-particles in bubble diagrams constituting corrections to the free thermal quasi-particle pressure. In spite of the observed increasingly suppressing effect when increasing 2-particle-irreducible (2PI) loop order, a quantitative analysis enables us to disprove the conjecture voiced in hep-th/0609033 that the loop expansion would terminate at a finite order. This reveals the necessity to investigate exact expressions of (at least some) higher-loop order diagrams. Explicit calculation shows that although the behaviour of the 2PI three-loop contribution at low temperatures displays hierarchical suppression compared to lower loop-orders, its high-temperature expression instead dominates all lower orders. However, an all-loop-order resummation of a class of 2PI bubble diagrams is shown to yield an analytic continuation of the low-temperature hierarchy to all temperatures in the deconfining phase.