Freiburg 1998 – scientific programme

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T: Teilchenphysik

T 302: QCD III

T 302.5: Talk

Tuesday, March 24, 1998, 17:20–17:35, HS B

Yang-Mills Theory in the Polyakov Gauge — •M. Engelhardt, K. Langfeld, H. Reinhardt, and O. Tennert — Institut für theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen

We investigate Yang-Mills theory in the Polyakov gauge. This gauge is a variant of ’t Hooft’s abelian gauges and is characterized by a time-independent, color-diagonal temporal component of the gauge field. Such gauges generically display magnetic monopoles as a consequence of gauge-fixing ambiguities. We identify the magnetic monopole configurations and the associated string and sheet singularities. In the Polyakov gauge, it proves to be possible to give a relation between the Pontryagin index of the gauge field and its monopole charge content [1]. The magnetic monopoles are sufficient to account for the non-trivial topological structure of the theory.

The Polyakov gauge is also well-suited for a study of the finite temperature properties of Yang-Mills theory. In the Polyakov gauge, the Polyakov loop order parameter distinguishing the confined and deconfined phases of Yang-Mills theory takes a particularly simple form. One can directly obtain the effective potential for this order parameter by integrating out the vector fields in the Yang-Mills partition function in some approximation. We specifically investigate the one-loop approximation of the effective action to second order in a derivative expansion [2]. The kinetic term contains centrifugal barriers which modify the mean field value of the Polyakov loop in such a way as to induce confinement at sufficiently low temperatures.

We corroborate this result by carrying out lattice measurements of the effective potential for the Polyakov loop. We recover the centrifugal barriers found in the one-loop calculation. The centrifugal barriers inducing confinement appear to be a generic consequence of the metric on the gauge group, largely independent of the details of the vector field dynamics.

[1] H.Reinhardt, preprint hep-th/9702049, Nucl. Phys. B, in press

[2] M.Engelhardt and H.Reinhardt, preprint hep-th/9709115

Supported by Deutsche Forschungsgemeinschaft under contract DFG Re 856 / 1–3