Cohomological BRST aspects of the massless tensor field with the mixed symmetry (k,k)

The main BRST cohomological properties of a free, massless tensor field that transforms in an irreducible representation of GL(D,R), corresponding to a rectangular, two-column Young diagram with k>2 rows are studied in detail. In particular, it is shown th

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002 ebF 92 1v710304/0ht-pe:hviXraCohomologicalBRSTaspectsofthemasslesstensor eldwiththemixedsymmetry(k,k)

C.C.Ciob rc a ,E.M.Cioroianu ,S.O.Saliu FacultyofPhysics,UniversityofCraiova13A.I.CuzaStr.,Craiova200585,Romania

February1,2008

Abstract

ThemainBRSTcohomologicalpropertiesofafree,masslesstensor eldthattransformsinanirreduciblerepresentationofGL(D,R),cor-respondingtoarectangular,two-columnYoungdiagramwithk>2rowsarestudiedindetail.Inparticular,itisshownthatanynon-trivialco-cyclefromthelocalBRSTcohomologygroupH(s|d)canbetakentostopeitheratantighostnumber(k+1)ork,itslastcomponentbelongingtothecohomologyoftheexteriorlongitudinalderivativeH(γ)andcontainingnon-trivialelementsfromthe(invari-ant)characteristiccohomologyHinv(δ|d).PACSnumber:11.10.Ef

1Introduction

Aninterestingclassof eldtheoriesisrepresentedbytensor eldsin“ex-otic”representationsoftheLorentzgroup,characterizedbyamixedYoungsymmetrytype[1,2,3,4,5],whichareknowntoappearinsuperstringtheories,supergravitiesorsupersymmetrichighspintheories.Thistype

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