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Bosonization, cocycles, and the D1-D5 CFT on the covering surface
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abstract
We consider the D1-D5 CFT near the orbifold point, specifically the computation of correlators involving twist sector fields using covering surface techniques. As is well known, certain twists introduce spin fields on the cover. Here we consider the bosonization of fermions to facilitate computations involving the spin fields. We find a set of cocycle operators that satisfy constraints coming from various $SU(2)$ symmetries, including the $SU(2)_L\times SU(2)_R$ R-symmetry. Using these cocycles, we consider the correlator of four spin fields on the cover, and show that it is invariant under all of the $SU(2)$ symmetries of the theory. We consider the mutual locality of operators, and compute several three-point functions. These computations lead us to a notion of radial ordering on the cover that is inherited from the original computation before lifting. Further, we note that summing over orbifold images sets certain branch-cut ambiguous correlators to zero.
Forward citations
Cited by 2 Pith papers
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Covering space maps for $n$-point functions with three long twists
Explicit covering-space maps for three long twists plus any number of twist-2 operators are constructed, yielding closed-form four- and five-point bare twist correlators in the ΔN=1,2 cases.
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Fortuity beyond counting: an explicit construction
Explicit construction of BPS states in (h,j)=(1,0) sector of D1D5 CFT shows non-vanishing three-point coupling between monotone and fortuitous states, indicating the sectors are dynamically connected.
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