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In this chapter we extend some of the general results of Chap. 2 to the supersymmetric NLSM. Though our presentation is self-contained, we would like to mention some basic references about supersymmetry [121, 122, 123, 124, 125, 126, 127, 128], supergravity [129, 130, 131], and superspace [132, 133, 134, 135, 136, 137], as well as some reviews [138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148]. A supersymmetry algebra in d dimensions is the Z 2 graded extension of the Poincaré algebra. In addition to the even Poincaré generators, it has odd supersymmetry generators that transform in a spinor representation of the Lorentz group. A simple supersymmetry has only one irreducible spinor representation of minimal dimension. If there are N such spinors, one has the N-extended supersymmetry. In two dimensions, a generic (p, q) supersymmetry algebra can have p chiral and q anti-chiral real spinor generators. The minimal 2d non-chiral supersymmetry is N = (1, 1), while the real chiral (1,0) supersymmetry in 2d is often called heterotic.
KeywordsInternal Line Group Manifold Bosonic Case Spinor Derivative Field Redefinition
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