The four-fermi coupling of the supersymmetric non-linear sigma-model on G/S\otimesU(1)^k

Abstract

The reducible Kähler coset space G/S\otimesU(1)^k is discussed in a geometrical approach. We derive the formula which expresses the Riemann curvature of the reducible Kähler coset space in terms of its Killing vectors. The formula manifests the group structure of G. On the basis of this formula we establish an algebraic method to evaluate the four-fermi coupling of the supersymmetric non-linear sigma-model on G/S\otimesU(1)^k at the low-energy limit. As an application we consider the supersymmetric non-linear sigma-model on E_7/SU(5)\otimesU(1)^3 which contains the three families of {10} + {5^*} + {1} of SU(5) as the pseudo NG fermions. The four-fermi coupling constants among diffferent families of the fermions are explicitly given at the low-energy limit.

33 pages, 1 figure, to appear in Nuclear Physics B

References in corpus (1)

• Large Lepton Mixing in a Coset-space Family Unification on $E_7/SU(5)\times U(1{)}^3$

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• Fuzzy Algebrae of the General Kaehler Coset Space G/H\otimesU(1)^k
• Consistently Constrained SL(N) WZWN Models and Classical Exchange Algebra
• Killing scalar of non-linear sigma models on G/H realizing the classical exchange algebra
• The Berkovits Method for Conformally Invariant Non-linear Sigma-models on G/H