Decomposition of slc2,k ⊕ slc2,1 highest weight representations for generic level k and equivalence between two dimensional CFT models

Research output: Working paper › Preprint › Research

Standard

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

Harvard

Hadasz, L & Ruba, B 2023 'Decomposition of slc2,k ⊕ slc2,1 highest weight representations for generic level k and equivalence between two dimensional CFT models' arXiv.org.

APA

Hadasz, L., & Ruba, B. (2023). Decomposition of slc2,k ⊕ slc2,1 highest weight representations for generic level k and equivalence between two dimensional CFT models. arXiv.org.

Vancouver

Hadasz L, Ruba B. Decomposition of slc2,k ⊕ slc2,1 highest weight representations for generic level k and equivalence between two dimensional CFT models. arXiv.org. 2023 Dec 22.

Author

Hadasz, Leszek ; Ruba, Błażej. / Decomposition of slc2,k ⊕ slc2,1 highest weight representations for generic level k and equivalence between two dimensional CFT models. arXiv.org, 2023.

Bibtex

@techreport{3ad8552619fa47eaa857edf34a4b197e,
title = "Decomposition of slc2,k ⊕ slc2,1 highest weight representations for generic level k and equivalence between two dimensional CFT models",
abstract = " 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. ",
keywords = "hep-th, math-ph, math.MP",
author = "Leszek Hadasz and B{\l}a{\.z}ej Ruba",
note = "48 pages, 1 figure, PDFLaTeX",
year = "2023",
month = dec,
day = "22",
language = "English",
publisher = "arXiv.org",
type = "WorkingPaper",
institution = "arXiv.org",

}

RIS

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