N ═ 2 Super Symmetric Approach to the String Theory Treatment of Three Dimensional Ising M0del
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Date
1990-06
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Addis Ababa University
Abstract
In this work a string theoretic approach is made to
the calculation of ihe critical exponents a and B of the
30 lsi n9 Model. Thi s approach ~/hi c<h has been pursued b'Y
polyakov and collaborators has been pushed upto N • I
supersymmetry (SUSY) of the world sheet. No realistic
.. . /
results have been obtained for N ~ I SUSV. Since it is now
known that SUSY in space~time is g1~n by N = 2 SUSV in
world sheet, an N = 2 supersymmetric approach has been
pu~sued in this work. Polyakov has given arguments showing
the identity of the ~tring theory away from the critical
dimension and 20 superconformal field theory. It has been
found here that for N = 2 SUSV the gauge coupling of the
20 super conformal field theory (or the Wess-Zumino-Witten
model) with the induced 20 super gravity does not renormalise.
This enable~ an ans"a tz to be made for a and B in terms of
the conformal dimensions of ·20 superconformal field theory.
The latter are known now and the ans"a tz, which is analogous
to Polyakov's ansatz for y, seem to give excellent values
for q and B
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Keywords
Theory Treatment of Three Dimensional