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Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
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Riccardo
2020-10-20 19:29:13 +02:00
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sec/part1/fermions.tex
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@@ -4,9 +4,9 @@ As previously pointed out, the computation of quantities such as Yukawa coupling
After the analysis of the main contribution to amplitudes involving twist fields at the intersection of D-branes, we focus on the computation of correlators of (excited) spin fields.
This has been a research subject for many years until the formulation found in the seminal paper by Friedan, Martinec and Shenker~\cite{Friedan:1986:ConformalInvarianceSupersymmetry} based on bosonization.
In general the available techniques allow to compute only correlators involving Abelian configurations, that is configurations which can be factorized in sub-configurations having \U{1} symmetry.
Non Abelian cases have also been considered~\cite{Inoue:1987:NonAbelianOrbifolds,Inoue:1990:StringInteractionsNonAbelian,Gato:1990:VertexOperatorsNonabelian,Frampton:2001:ClassificationConformalityModels,Pesando:2016:FullyStringyComputation}, though their mathematical formulation is by far more complicated.
Non Abelian cases have also been considered~\cite{Inoue:1987:NonAbelianOrbifolds,Inoue:1990:StringInteractionsNonAbelian,Gato:1990:VertexOperatorsNonAbelian,Pesando:2016:FullyStringyComputation}, though their mathematical formulation is by far more complicated.
Despite the existence of an efficient method based on bosonization~\cite{Friedan:1986:ConformalInvarianceSupersymmetry} and old methods based on the Reggeon vertex~\cite{Sciuto:1969:GeneralVertexFunction,DellaSelva:1970:SimpleExpressionSciuto,Schwarz:1973:EvaluationDualFermion,DiVecchia:1990:VertexIncludingEmission,Nilsson:1990:GeneralNSRString,DiBartolomeo:1990:GeneralPropertiesVertices,Engberg:1993:AlgorithmComputingFourRamond,Petersen:1989:CovariantSuperreggeonCalculus}, we take into examination the computation of spin field correlators and propose a new method to compute them.
Despite the existence of an efficient method based on bosonization~\cite{Friedan:1986:ConformalInvarianceSupersymmetry} and old methods based on the Reggeon vertex~\cite{Sciuto:1969:GeneralVertexFunction,DiVecchia:1990:VertexIncludingEmission,Nilsson:1990:GeneralNSRString,DiBartolomeo:1990:GeneralPropertiesVertices,Petersen:1989:CovariantSuperreggeonCalculus}, we take into examination the computation of spin field correlators and propose a new method to compute them.
We hope to be able to extend this approach to correlators involving twist fields and non Abelian spin and twist fields.
We would also like to investigate the reason of the non existence of an approach equivalent to bosonization for twist fields.
At the same time we are interested to explore what happens to a \cft in presence of defects.