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Consistency of Couplings in Supergravity Theory with Propagating Lorentz Connexion

H. Nishino

1982
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Progress of theoretical physics
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1765 Our theory of supergravity with propagating Lorentz connexion wprs is a supersymmetric extension of the "massless case" of Poincare gauge theory. In such a case, it is necessary to verify the consistency of couplings between wprs (or the vierbein epm) and spinor fields in the theory. We will show that in our supersymmetric theory the coupling consistency between wprs and its spinor partner ,lars is in fact guaranteed up to the trilinear interaction order. § 1. Introduction Poincare gauge
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... on Poincare gauge theoryl)-IO) and supergravity theories I 1)-21) are regarded as extensions of the general relativity theory based on the gauge principle of gravitational interactions. The attempt to combine and unify these two gauge theories now seems to be of great interest. To this end, we have presented some models of supergravity (SG) with propagating Lorentz connexion (LC) in our previous papers. 22 ),23)*) In our theory the total Lagrangian .L is divided into two parts: .L =.L SGa +.L LCa, 22) where .L SGa is the Lagrangian of SG and .L LCa is that of the multiplet of LC. 22 ) It was shown that .L SGa is a supersymmetric extension of the "massless case" in Poincare gauge theory,IO) while .L LCa contains the kinetic term of LC, w/,rs. The simplest example of .LLca was already given by Breitenlohner,16) which is a supersymmetric extension of the Yang-Mills type kinetic term: -+ eR/,vrs(w)R/,vrs(w). We named this Lagrangian .LLcaJ. 22 ) As was noticed in I, theories with Lagrangians in the "massless case" may. generally have a problem of inconsistency of couplings between w/,rs and spin or fields. 22 ) A remarkable fact for the supersymmetric total Lagrangian .L =.L SGa +.L LCal is that the couplings of w/,rs to its spinor partner ;lars are shown to be consistent to all orders in spite of the "masslessness" of .L SGa. 22) We regard this as a consequence of local supersymmetric covariance of our theory. We encountered, however, the problem of negative energy ghosts in .L LCal. To circumvent this difficulty we proposed second models with Lagrangians .L LCa2 and .L LCa3 expressed in superspace as 22 )

doi:10.1143/ptp.68.1765
fatcat:iqlm47eta5adnm7nlsky2jgsoe