By Lucchini A.
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Additional resources for (2, 3, k)-generated groups of large rank
Zumino, 1974, ‘‘Supergauge Invariance and the Gell-Mann-Low Eigenvalue,’’ Nucl. Phys. B 77, 413–419. , H. P. Nilles, J. Polchinski, S. Raby, and L. Susskind, 1981, ‘‘Vanishing Renormalization of the D-term in Supersymmetric U(1) Theories,’’ Phys. Rev. Lett. 47, 757–759. Giudice, G. , and R. Rattazzi, 1998, ‘‘Theories with Gauge Mediated Supersymmetry Breaking,’’ eprint hep-ph/9801271. , and J. Schwarz, 1984, ‘‘Anomaly Cancellations in Supersymmetric D ϭ 10 Gauge Theory Require SO(32),’’ Phys. Lett.
As an example consider an SO(7) gauge group with five matter multiplets transforming in the spinor representation. The theory possesses an SU(5) global symmetry and a U(1) R under which all matter fields are neutral. The gauge invariant composites transform as an antisymmetric tensor A and antifundamental ¯F of the global symmetry. The quantum constraint is ¯ 4 ϭ⌳ 10. A 5 ϩAF (123) ˜ and F Coupling all gauge invariants to gauge singlets A and implementing the constraint through the Lagrange multiplier we find ˜ AϩFF ¯ ϩ ͑ A 5 ϩAF ¯ 4 Ϫ⌳ 10 ͒ , WϭA (124) and obviously SUSY is broken.
In Sec. B we argue that this is often a signal of unbroken supersymmetry. It is easy to find the supersymmetric vacua in this model. In terms of the meson fields they are given by M ij ϭ ͓ det͑ m ͒ ⌳ 3N c ϪN f ͔ 1/N c ͩ ͪ 1 . m ij (A24) It is also worth noting that if some number of matter fields are massive they decouple from the low-energy theory and can be integrated out. Solving the equations of motion for the massive fields one can find the superpotential of Eq. (A15) and the solution (A24) for the VEV’s of the remaining light fields.
(2, 3, k)-generated groups of large rank by Lucchini A.
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