Decomposition of slc2,k ⊕ slc2,1 highest weight representations for generic level k and equivalence between two dimensional CFT models
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Decomposition of slc2,k ⊕ slc2,1 highest weight representations for generic level k and equivalence between two dimensional CFT models. / Hadasz, Leszek; Ruba, Błażej.
arXiv.org, 2023.Research output: Working paper › Preprint › Research
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TY - UNPB
T1 - Decomposition of slc2,k ⊕ slc2,1 highest weight representations for generic level k and equivalence between two dimensional CFT models
AU - Hadasz, Leszek
AU - Ruba, Błażej
N1 - 48 pages, 1 figure, PDFLaTeX
PY - 2023/12/22
Y1 - 2023/12/22
N2 - We construct highest weight vectors of ${\widehat{\mathfrak{sl}_2}}_{,k+1} \oplus \mathsf{Vir}$ in tensor products of highest weight modules of ${\widehat{\mathfrak{sl}_2}}_{,k}$ and ${\widehat{\mathfrak{sl}_2}}_{,1}$, and thus for generic weights we find the decomposition of the tensor product into irreducibles of ${\widehat{\mathfrak{sl}_2}}_{,k+1} \oplus \mathsf{Vir}$. The construction uses Wakimoto representations of ${\widehat{\mathfrak{sl}_2}}_{,k}$, but the obtained vectors can be mapped back to Verma modules. Singularities of this mapping are cancelled by a renormalization. A detailed study of ``degenerations'' of Wakimoto modules allowed to find the renormalization factor explicitly. The obtained result is a significant step forward in a proof of equivalence of certain two-dimesnional CFT models.
AB - We construct highest weight vectors of ${\widehat{\mathfrak{sl}_2}}_{,k+1} \oplus \mathsf{Vir}$ in tensor products of highest weight modules of ${\widehat{\mathfrak{sl}_2}}_{,k}$ and ${\widehat{\mathfrak{sl}_2}}_{,1}$, and thus for generic weights we find the decomposition of the tensor product into irreducibles of ${\widehat{\mathfrak{sl}_2}}_{,k+1} \oplus \mathsf{Vir}$. The construction uses Wakimoto representations of ${\widehat{\mathfrak{sl}_2}}_{,k}$, but the obtained vectors can be mapped back to Verma modules. Singularities of this mapping are cancelled by a renormalization. A detailed study of ``degenerations'' of Wakimoto modules allowed to find the renormalization factor explicitly. The obtained result is a significant step forward in a proof of equivalence of certain two-dimesnional CFT models.
KW - hep-th
KW - math-ph
KW - math.MP
M3 - Preprint
BT - Decomposition of slc2,k ⊕ slc2,1 highest weight representations for generic level k and equivalence between two dimensional CFT models
PB - arXiv.org
ER -
ID: 382552975