Volume 220, number 4 PHYSICS LETTERSB 13 April 1989 ON THE SPECTRUM OF EXCITATIONS IN SOME STRONG COUPLING GAUGE MODELS V.P. GUSYNIN, V.A. KUSHNIR Institutefor TheoreticalPhysics, 252 130 Kiev 130, USSR and V.A. MIRANSKY l Department of Physics, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan Received 12 December 1988; revised manuscript received 28 January 1989 The spectrumof spinlessexcitations in (3 + 1)-dimensionalladder QED with additional four-fermion interaction and in (2 + 1)- dimensional QED is considered. Recently, there has been considerable interest in strong coupling gauge theories. On the one hand, non- asymptotically free (NAF) gauge theories with the bare coupling c~ t°l in the supercritical (c~~°) > ac~ 1 ) phase can lead to a new class of four-dimensional continuum field theories with non-trivial S-matrix [ 1-4 ] (for a recent discussion of this possibility see ref. [ 5 ] ). On the other hand, both NAF and asymp- totically free (AF) gauge theories in the dynamical regime with a "walking" near-critical [a(q2) - c~. << 1 ] coupling can find their application in techn- icolour dynamics [6-9] (for a recent discussion see ref. [10]). Also, there are similarities [ 11-14] between the non-perturbative dynamics in four-dimensional strong coupling QED and that in (2+ 1)-dimen- sional QED with four-component spinors [ 15 ]. The last model may be important [ 14 ] for some attempts to understand theoretically the recently discovered high temperature superconductors. In the large majority of papers dealing with strong coupling gauge theories the approximate (usually ladder) Schwinger-Dyson (SD) equation for the fer- Permanent address: Institute for Theoretical Physics, 252 130 Kiev 130, USSR. mion propagator is studied. From the Ward identi- ties for the chiral currents, it follows that such a method is equivalent to looking for solutions of the approximate Bethe-Salpeter equations for the corre- sponding massless Goldstone bosons. The aim of the present paper is to study the spectrum of spinless ex- citations in such models, i.e., we want to describe not only massless but also massive spinless ferrnion-an- tifermion bound states there. The emphasis will be on the study of four-dimensional ladder QED with additional four-fermion interaction. This model has recently attracted considerable interest both from the point of view of the existence of non-trivial contin- uum NAF theories and that of its application to the technicolour dynamics [ 3,16-19 ]. We shall also consider the spectrum of the radial excitations of Goldstone bosons in (2 + 1 )-dimensional QED. The main results of the present paper are the following. We show that in the massless ladder QED with ad- ditional chiral-invariant four-fermion interaction, AL= ½G(°) [ ( ~ / / ) 2__ (~e~IS ~/,/)2], ( 1 ) the form of the spectrum ofspinless excitations in the non-perturbative phase with chiral symmetry break- down essentially depends on the values of the gauge 0370-2693/89/$ 03.50 © Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division ) 635