Contour integrals and the modular $$ \mathcal{S} $$-matrix
We investigate a conjecture to describe the characters of large families of RCFT’s in terms of contour integrals of Feigin-Fuchs type. We provide a simple algorithm to determine the modular $$ \mathcal{S} $$ S -matrix for arbitrary numbers of characters as a sum over paths. Thereafter we focus on th...
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Veröffentlicht in: | The journal of high energy physics 2020-07, Vol.2020 (7), Article 45 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We investigate a conjecture to describe the characters of large families of RCFT’s in terms of contour integrals of Feigin-Fuchs type. We provide a simple algorithm to determine the modular
$$ \mathcal{S} $$
S
-matrix for arbitrary numbers of characters as a sum over paths. Thereafter we focus on the case of 2, 3 and 4 characters, where agreement between the critical exponents of the integrals and the characters implies that the conjecture is true. In these cases, we compute the modular
S
-matrix explicitly, verify that it agrees with expectations for known theories, and use it to compute degeneracies and multiplicities of primaries. We verify that our algorithm reproduces the correct
$$ \mathcal{S} $$
S
-matrix for SU (2)
k
for all
k ≤
18 which provides additional evidence for the original conjecture. On the way we note that the Verlinde formula provides interesting constraints on the critical exponents of RCFT in this context. |
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ISSN: | 1029-8479 1029-8479 |
DOI: | 10.1007/JHEP07(2020)045 |