Seiberg duality and e+e- experiments Page: 2 of 24
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1 Introduction
In the last few years, remarkable progress has been made on understanding
supersymmetric gauge theories. An important part of the progress is the
so-called Seiberg duality [1], which states that two distinct supersymmetric
gauge theories describe the same physics in the infrared limit. In some cases
both theories are in the non-Abelian Coulomb phase, with scale-invariant
dynamics and no particle interpretation, i.e., asymptotic states cannot be
defined. In two-dimensions, there are techniques developed in conformal
field theories which allow the calculation of correlation functions of conformal
fields exactly, thanks to the infinite-dimensional extension of the conformal
symmetry. Unfortunately, much less is known about four-dimensional scale-
invariant theories.
We attempt to extract some physical quantities from the proposed dual
supersymmetric scale-invariant theories. Since there is no particle interpre-
tation for conformal fields, one cannot discuss S-matrices among quarks and
gluons in these theories. This situation is somewhat similar to the real-
world QCD, where quarks and gluons cannot appear as asymptotic states,
even though the reason for failure here is the color confinement rather than
scale-invariant dynamics. The similarity suggests the study of "e+e-" cross
sections, which have direct physical meaning even in the absence of the pre-
cise knowledge of the excitations in the dynamics, and are known to be useful
in studies of QCD. The problem then is to develop a technique to calculate
these total cross sections exactly in scale-invariant supersymmetric theories.
We point out that the NSVZ beta-function allows us to determine the
vacuum polarization amplitudes with global symmetry current operators ex-
actly in the infrared limit for these theories, thanks to scale invariance. By
analytically continuing them to the time-like region, we obtain the exact
"e+c-" cross sections even if the theory is strongly-coupled. This allows us
to compare results in the electric and magnetic theories and check the duality
assumption. We find that the "e+e-" cross sections indeed agree between
the proposed dual theories. We then show that the agreement between the
total cross sections is guaranteed by the anomaly matching condition, which
was required in [1] to determine if the two theories are dual.
On the other hand, checking that both theories yield the same "e+c-"
total cross sections is not enough to guarantee that the two theories in ques-
tions are dual: all physical processes have to agree in the infrared limit. We
next investigate the "yy -- '" and "WW -> WW" scattering amplitudes1
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De Gouvea, Andre; Friedland, Alexander & Murayama, Hitoshi. Seiberg duality and e+e- experiments, article, October 2, 1998; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc782649/m1/2/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.