Tachyon Potential in a Magnetic Field with Anomalous Dimensi(6)

Products defined in the context of noncommutative gauge theory allow for an interpolation between exact results on tachyon potentials at zero and large background B-fields. Techniques for computations of effective actions are transposed from the framework

Asdiscussedabove,theonlycontractionsinthecomputationsof[4]thatcontributeinourbosonicframeworkarethosebetweenscalars.WearegoingtomapthecomputationoftheWess–Zuminocouplingstoourcontext,

dτdθDφµAµ(φ)→T(X(τ))dτ,

byreplacingthe eldstrengthsFµνinthosecouplingswithtachyon eldsT,andcancellinganytermthatdoesnotcarrytwozero-modesforeach eldstrength(sincethoseinvolvefermions).Finally,wehavetoreplaceanyproductoffermioniczero-modesby1,thusdestroyingthegradedstructureandallowingfortermsofarbitrarilyhighdegreeinT.

Thesimpli cationthatoccurs,duetothequadraticnatureofthetachyon eld,comesfromthelownumberofderivativesthatcanactonit.Acorrectionoforderninuµνnamelyhastocomefromtheexpansionatorderninthetachyon eld,withtwoderivativesactingoneachofthefactors,as:

p 1dσi

p≥2i=1

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