# Thermal Ground State in Yang-Mills Thermodynamics

## Abstract

We derive an a useful priori estimate for the thermal ground state of deconfining phase of SU(2) Yang-Mills thermodynamics in four-dimensional, flat spacetime and discuss its implications. Upon a selfconsistent spatial coarse-graining over noninteracting, trivial-holonomy (BPS saturated)(anti)calorons of unit topological charge modulus an inert, adjoint scalar field |{phi}| and an effective pure-gauge configuration a{sub {mu}}{sup gs} emerge. The modulus |{phi}|>0 defines the maximal resolution in the coarse-grained theory and induces dynamical gauge-symmetry breaking. Thanks to perturbative renormalizability and the fact that |{phi}| can not absorb or emit energy-momentum the effective action is local and simple. The temperature dependence of the effective coupling is a consequence of thermodynamical consistency and describes the Coulomb screening of a static test charge due to short-lived monopole-antimonopole pairs. The latter occur unresolvably as small-holonomy excitations of (anti)calorons by the absorption of propagating fundamental gauge fields.

- Authors:

- ITP, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany)

- Publication Date:

- OSTI Identifier:
- 21611614

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1389; Journal Issue: 1; Conference: ICNAAM 2011: Conference on numerical analysis and applied mathematics, Halkidiki (Greece), 19-25 Sep 2011; Other Information: DOI: 10.1063/1.3636820; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ABSORPTION; ACTION INTEGRAL; COUPLING; EXCITATION; FOUR-DIMENSIONAL CALCULATIONS; GAUGE INVARIANCE; GROUND STATES; PERTURBATION THEORY; POLARIZATION; QUANTUM FIELD THEORY; RENORMALIZATION; SCALAR FIELDS; SPACE-TIME; SYMMETRY BREAKING; TEMPERATURE DEPENDENCE; THERMODYNAMICS; TOPOLOGY; YANG-MILLS THEORY; ENERGY LEVELS; ENERGY-LEVEL TRANSITIONS; FIELD THEORIES; INTEGRALS; INVARIANCE PRINCIPLES; MATHEMATICS; SORPTION

### Citation Formats

```
Hofmann, Ralf.
```*Thermal Ground State in Yang-Mills Thermodynamics*. United States: N. p., 2011.
Web. doi:10.1063/1.3636820.

```
Hofmann, Ralf.
```*Thermal Ground State in Yang-Mills Thermodynamics*. United States. doi:10.1063/1.3636820.

```
Hofmann, Ralf. Thu .
"Thermal Ground State in Yang-Mills Thermodynamics". United States. doi:10.1063/1.3636820.
```

```
@article{osti_21611614,
```

title = {Thermal Ground State in Yang-Mills Thermodynamics},

author = {Hofmann, Ralf},

abstractNote = {We derive an a useful priori estimate for the thermal ground state of deconfining phase of SU(2) Yang-Mills thermodynamics in four-dimensional, flat spacetime and discuss its implications. Upon a selfconsistent spatial coarse-graining over noninteracting, trivial-holonomy (BPS saturated)(anti)calorons of unit topological charge modulus an inert, adjoint scalar field |{phi}| and an effective pure-gauge configuration a{sub {mu}}{sup gs} emerge. The modulus |{phi}|>0 defines the maximal resolution in the coarse-grained theory and induces dynamical gauge-symmetry breaking. Thanks to perturbative renormalizability and the fact that |{phi}| can not absorb or emit energy-momentum the effective action is local and simple. The temperature dependence of the effective coupling is a consequence of thermodynamical consistency and describes the Coulomb screening of a static test charge due to short-lived monopole-antimonopole pairs. The latter occur unresolvably as small-holonomy excitations of (anti)calorons by the absorption of propagating fundamental gauge fields.},

doi = {10.1063/1.3636820},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1389,

place = {United States},

year = {2011},

month = {9}

}