Elliptic algebra, Frenkel-Kac construction and root of unity limit
| Autor: | Reiji Yoshioka, Hiroshi Itoyama, Takeshi Oota |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Physics High Energy Physics - Theory 010308 nuclear & particles physics Root of unity Block (permutation group theory) FOS: Physical sciences General Physics and Astronomy Statistical and Nonlinear Physics 01 natural sciences Algebra High Energy Physics::Theory High Energy Physics - Theory (hep-th) Modeling and Simulation Mathematics::Quantum Algebra 0103 physical sciences Virasoro algebra Gauge theory 010306 general physics Central charge Realization (systems) Mathematical Physics Special unitary group Boson |
| Popis: | We argue that the level-$1$ elliptic algebra $U_{q,p}(\widehat{\mathfrak{g}})$ is a dynamical symmetry realized as a part of 2d/5d correspondence where the Drinfeld currents are the screening currents to the $q$-Virasoro/W block in the 2d side. For the case of $U_{q,p}(\widehat{\mathfrak{sl}}(2))$, the level-$1$ module has a realization by an elliptic version of the Frenkel-Kac construction. The module admits the action of the deformed Virasoro algebra. In a $r$-th root of unity limit of $p$ with $q^2 \rightarrow 1$, the $\mathbb{Z}_r$-parafermions and a free boson appear and the value of the central charge that we obtain agrees with that of the 2d coset CFT with para-Virasoro symmetry, which corresponds to the 4d $\mathcal{N}=2$ $SU(2)$ gauge theory on $\mathbb{R}^4/\mathbb{Z}_r$. 22 pages; v2: references added |
| Databáze: | OpenAIRE |
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