In $D$-dimensional gauge theory with a kinetic term based on the p-form tensor gauge field, we introduce a gauge invariant operator associated with the composite formed from a electric $(p-1)$-brane and a magnetic $(q-1)$-brane in $D=p+q+1$ spacetime dimen

Theexoticstatistics,anyonsandfermion-bosontransmutationforthecompositestateofapointchargeandamagneticvortexhasbeendiscussedbyWilczek[1].In(2+1)dimensionalspacetime,theanyonshaveawell-knownphysicalrealizationwheremagnetic uxtubesareattachedtochargedparticlesandtheAharonov-Bohmphaseresultingfromadiabatictransportofthecompositesgivethemfractionalexchangestatistics.ItwasgeneralizedtothefactthatthecompositeofaclosedNambuchargedstringandapointvortexpresentedtheunusalstatisticsin(3+1)dimensions[2].

Also,Polyakovshowedthefermion-bosontransmutationin(2+1)dimensionsbyinvestigatingthesmallmomentumbehaviorofascalar eldinteractingwithtopo-logicalChern-simonsterm[3].ThisChern-Simonsmechanismofstatisticaltransmu-tationwasshowntoholdforstring-likeobjectinteractingwithtopologicalBFtermin(3+1)dimensions[4][5].Thetopologicalquantum eldtheorywhichgivestheappropriategeneralizationtohigherdimensionshasbeenstudied[6].Chern-Simonstheorygivestherepresentationsoflinkingnumbersofcurvesin3dimensions,BFtheoriesprovidethepathintegralrepresentationsofthelinkingandintersectionnumbersofgenericsurfacesinDdimensions[5][6].

Inthesestatisticalphenomenalikefermion-bosontransmutation,eventhoughthetopologicalterm(Chern-SimonstermorBFterminhigherdimensions)playsanessentialrole,suchtopologicalcontributionsmayarisefromthegaugetheorywiththekinetictermaselectromagnetism[7].InWilczek’swork[1],iftwocompositesofachargedparticleandapointvortexareinterchanged,anadditionalphasefactorappearsinallgaugeinvariantobservables,thisisbecauseeachcompositeshouldbecovariantlytransportedinthegaugepotentialoftheother.Sothecompositeshavetheunusualstatistics.

Recentlytherehasincreasinglybeenthetheoreticalevidencefortheextended