Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model
We revisit the critical two-dimensional Ashkin-Teller model, i.e. the $\mathbb{Z}_2$ orbifold of the compactified free boson CFT at $c=1$. We solve the model on the plane by computing its three-point structure constants and proving crossing symmetry of four-point correlation functions. We do this...
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oai:doaj.org-article:e057ab3c9b20439188cb2b3962476d932021-11-09T16:53:02ZAnalytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model2542-465310.21468/SciPostPhys.11.5.089https://doaj.org/article/e057ab3c9b20439188cb2b3962476d932021-11-01T00:00:00Zhttps://scipost.org/SciPostPhys.11.5.089https://doaj.org/toc/2542-4653We revisit the critical two-dimensional Ashkin-Teller model, i.e. the $\mathbb{Z}_2$ orbifold of the compactified free boson CFT at $c=1$. We solve the model on the plane by computing its three-point structure constants and proving crossing symmetry of four-point correlation functions. We do this not only for affine primary fields, but also for Virasoro primary fields, i.e. higher twist fields and degenerate fields. This leads us to clarify the analytic properties of Virasoro conformal blocks and fusion kernels at $c=1$. We show that blocks with a degenerate channel field should be computed by taking limits in the central charge, rather than in the conformal dimension. In particular, Al. Zamolodchikov's simple explicit expression for the blocks that appear in four-twist correlation functions is only valid in the non-degenerate case: degenerate blocks, starting with the identity block, are more complicated generalized theta functions.Nikita Nemkov, Sylvain RibaultSciPostarticlePhysicsQC1-999ENSciPost Physics, Vol 11, Iss 5, p 089 (2021) |
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DOAJ |
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DOAJ |
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EN |
| topic |
Physics QC1-999 |
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Physics QC1-999 Nikita Nemkov, Sylvain Ribault Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model |
| description |
We revisit the critical two-dimensional Ashkin-Teller model, i.e. the
$\mathbb{Z}_2$ orbifold of the compactified free boson CFT at $c=1$. We solve
the model on the plane by computing its three-point structure constants and
proving crossing symmetry of four-point correlation functions. We do this not
only for affine primary fields, but also for Virasoro primary fields, i.e.
higher twist fields and degenerate fields.
This leads us to clarify the analytic properties of Virasoro conformal blocks
and fusion kernels at $c=1$. We show that blocks with a degenerate channel
field should be computed by taking limits in the central charge, rather than in
the conformal dimension. In particular, Al. Zamolodchikov's simple explicit
expression for the blocks that appear in four-twist correlation functions is
only valid in the non-degenerate case: degenerate blocks, starting with the
identity block, are more complicated generalized theta functions. |
| format |
article |
| author |
Nikita Nemkov, Sylvain Ribault |
| author_facet |
Nikita Nemkov, Sylvain Ribault |
| author_sort |
Nikita Nemkov, Sylvain Ribault |
| title |
Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model |
| title_short |
Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model |
| title_full |
Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model |
| title_fullStr |
Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model |
| title_full_unstemmed |
Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model |
| title_sort |
analytic conformal bootstrap and virasoro primary fields in the ashkin-teller model |
| publisher |
SciPost |
| publishDate |
2021 |
| url |
https://doaj.org/article/e057ab3c9b20439188cb2b3962476d93 |
| work_keys_str_mv |
AT nikitanemkovsylvainribault analyticconformalbootstrapandvirasoroprimaryfieldsintheashkintellermodel |
| _version_ |
1718440974995161088 |