By Olivier Piguet, Klaus Sibold (auth.)

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**Additional resources for Renormalized Supersymmetry: The Perturbation Theory of N = 1 Supersymmetric Theories in Flat Space-Time**

**Example text**

3) and is characterized by the fact that the F-component of a chiral field acquires a vacuum expectation value, hence the spinor W in its multiplet transforms inhomogeneously. Obviously the other possibility is that the O-component of a vector superfield acquires a vacuum expectation value and its partner A transforms as a Goldstone spinor. 66) a linear term O. Parity is now broken explicitly, but by a dimension 2 term only. 53). 75) * The prime indicates spontaneous breaking of the respective symmetry.

E. 52) for the same range of k. 60) (b n- 2b 1 + bn- 3b2 + •.. 53) is shown in appendix C. 42). As the result we give now the anwsers to the questions posed before: (1) One can consistently continue the transformation law to all orders in the fields. 63) this undetermined part anbo(¢n), we may write more precisely in components: 51 (n) L a sU:(. ) (c+-<:+). ¢ . . ¢. 64) . are invariant tensors under the group G completely 11 1 ···1 n ) symmetric in (il ... i ), 51(n) is the number of such tensors and a n are n* w arbitrary parameters.

E. at most these and DODD, DODD are independent. e. 7) PL projects to a chiral field, PL to an anti-chiral, PT to a real one. 8) one has to identify PT* with the transverse part of and hence PL <1>, PL I"lith the longitudinal parts. J. 11) are gauge invariant. J = iOOOO(f\-f\) = iDOODf\ = iO[OO,O]f\ - Do30f\ O. e. 6]. We now wish to quantize the theory, in particular to calculate the propagator for ¢. e. to add to the invariant action a gauge fixing term. Since the construction of the physical state space depends on the gauge chosen we always give also the equation of motion satisfied by the ghosts. *