Fermion Flavours and the Dynamics of Gauge Theories
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Number of fermion flavours dictates the existence of asymptotic
freedom in QCD. There are indications that below this critical value
lies a conformal window where the asymptotically free QCD shows no
confinement and chiral symmetry breaking. QED3 also exhibits a similar
phase transition. A critical value of the number of flavours lies at
the boundary of its chirally symmetric-confined and asymmetric/deconfined
phases. Is there a generality associated with this behaviour? Do
other gauge theories exhibit a similar pattern? In this talk we take
up the example of QED4 and show that for a fixed interaction strength, it
also has a critical number of flavours above which fermions cease to have
dynamical masses. We find this statement independent of the model one
chooses for the photon propagator in the study of the
Schwinger-Dyson equations. Even an all order resummation of the leading
logarithms conserves this pattern.
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