Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912600257724416 |
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| author | Beem, Christopher Nair, Sujay |
| author_facet | Beem, Christopher Nair, Sujay |
| contents | The correspondence between four-dimensional $\mathcal{N}=2$ superconformal field theories and vertex operator algebras, when applied to theories of class $\mathcal{S}$, leads to a rich family of VOAs that have been given the monicker chiral algebras of class $\mathcal{S}$. A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in arXiv:1811.01577. The construction of arXiv:1811.01577 takes as input a choice of simple Lie algebra $\mathfrak{g}$, and applies equally well regardless of whether $\mathfrak{g}$ is simply laced or not. In the non-simply laced case, however, the resulting VOAs do not correspond in any clear way to known four-dimensional theories. On the other hand, the standard realisation of class $\mathcal S$ theories involving non-simply laced symmetry algebras requires the inclusion of outer automorphism twist lines, and this requires a further development of the approach of arXiv:1811.01577. In this paper, we give an account of those further developments and propose definitions of most chiral algebras of class $\mathcal S$ with outer automorphism twist lines. We show that our definition passes some consistency checks and point out some important open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_13435 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing Beem, Christopher Nair, Sujay High Energy Physics - Theory Quantum Algebra Representation Theory The correspondence between four-dimensional $\mathcal{N}=2$ superconformal field theories and vertex operator algebras, when applied to theories of class $\mathcal{S}$, leads to a rich family of VOAs that have been given the monicker chiral algebras of class $\mathcal{S}$. A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in arXiv:1811.01577. The construction of arXiv:1811.01577 takes as input a choice of simple Lie algebra $\mathfrak{g}$, and applies equally well regardless of whether $\mathfrak{g}$ is simply laced or not. In the non-simply laced case, however, the resulting VOAs do not correspond in any clear way to known four-dimensional theories. On the other hand, the standard realisation of class $\mathcal S$ theories involving non-simply laced symmetry algebras requires the inclusion of outer automorphism twist lines, and this requires a further development of the approach of arXiv:1811.01577. In this paper, we give an account of those further developments and propose definitions of most chiral algebras of class $\mathcal S$ with outer automorphism twist lines. We show that our definition passes some consistency checks and point out some important open problems. |
| title | Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing |
| topic | High Energy Physics - Theory Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2201.13435 |