Heidelberg 1999 – wissenschaftliches Programm

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T: Teilchenphysik

T 306: Feldtheorie

T 306.4: Vortrag

Dienstag, 16. März 1999, 14:55–15:10, TE7

Ward Identities for Yang-Mills Theory in Abelian Gauges — •M. Quandt and H. Reinhardt — Institut f"ur Theoretische Physik, Universit"at T"ubingen, Auf der Morgenstelle 14, D-72076 T"ubingen

Recent lattice calculations in Abelian gauges indicate that the Yang-Mills ground state realises confinement by the dual Meissner effect. This conclusion is largely based on the phenomenon of Abelian (and monopole) dominance, i.e. the string tension can be entirely obtained from an effective Abelian theory.

We have studied Abelian gauges in the framework of continuum field theory. In the Abelian sector, a new set of Ward identities can be derived, which are valid to all orders in perturbation theory. These relations resemble the ones found in QED and are considerably less involved than the usual Slavnov-Taylor identities associated with the full BRST symmetry. Moreover, the new Ward identities lead to powerful non-renormalisation theorems with profound consequences for the effective Abelian theory [1]. The coupling constant is renormalised only through the Abelian two-point function, implying that in all Abelian gauges asymptotic freedom can be understood from an effective Abelian theory alone (Abelian dominance in the high energy regime) [1]. This observation is not only a formal aspect of the new Ward identities, but it also offers great simplifications e.g. for the actual calculation of the β-function in Yang-Mills theory. In fact, all diagrams with charged external legs (and in particular all vertex corrections) are irrelevant for the calculation. At one loop level and in the special case of the maximal Abelian gauge, this fact can be confirmed explicitly [2].

[1] M. Quandt, H. Reinhardt, Phys. Lett. B424 (1998) 115.

[2] M. Quandt, H. Reinhardt, Int. J. Mod. Phys. A13 (1998) 4049.