N ═ 2 Super Symmetric Approach to the String Theory Treatment of Three Dimensional Ising M0del

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Addis Ababa University


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



Theory Treatment of Three Dimensional