A note on the Virasoro blocks at order 1 / c
Abstract We derive an explicit expression for the 1 / c contribution to the Virasoro blocks in 2D CFT in the limit of large c with fixed values of the operators’ dimensions. We follow the direct approach of orthonormalising, at order 1 / c, the space of the Virasoro descendants to obtain the blocks...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-01-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-018-6522-5 |
| _version_ | 1811221732433854464 |
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| author | Alessandro Bombini Stefano Giusto Rodolfo Russo |
| author_facet | Alessandro Bombini Stefano Giusto Rodolfo Russo |
| author_sort | Alessandro Bombini |
| collection | DOAJ |
| description | Abstract We derive an explicit expression for the 1 / c contribution to the Virasoro blocks in 2D CFT in the limit of large c with fixed values of the operators’ dimensions. We follow the direct approach of orthonormalising, at order 1 / c, the space of the Virasoro descendants to obtain the blocks as a series expansion around $$z=0$$ z=0 . For generic conformal weights this expansion can be summed in terms of hypergeometric functions and their first derivatives with respect to one parameter. For integer conformal weights we provide an equivalent expression written in terms of a finite sum of undifferentiated hypergeometric functions. These results make the monodromies of the blocks around $$z=1$$ z=1 manifest. |
| first_indexed | 2024-04-12T08:05:46Z |
| format | Article |
| id | doaj.art-78a2f6e80fa84ca48f501b00024fb5e2 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-04-12T08:05:46Z |
| publishDate | 2019-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-78a2f6e80fa84ca48f501b00024fb5e22022-12-22T03:41:11ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522019-01-017911710.1140/epjc/s10052-018-6522-5A note on the Virasoro blocks at order 1 / cAlessandro Bombini0Stefano Giusto1Rodolfo Russo2Dipartimento di Fisica ed Astronomia “Galileo Galilei”, Università di PadovaDipartimento di Fisica ed Astronomia “Galileo Galilei”, Università di PadovaCentre for Research in String Theory, School of Physics and Astronomy Queen Mary University of LondonAbstract We derive an explicit expression for the 1 / c contribution to the Virasoro blocks in 2D CFT in the limit of large c with fixed values of the operators’ dimensions. We follow the direct approach of orthonormalising, at order 1 / c, the space of the Virasoro descendants to obtain the blocks as a series expansion around $$z=0$$ z=0 . For generic conformal weights this expansion can be summed in terms of hypergeometric functions and their first derivatives with respect to one parameter. For integer conformal weights we provide an equivalent expression written in terms of a finite sum of undifferentiated hypergeometric functions. These results make the monodromies of the blocks around $$z=1$$ z=1 manifest.http://link.springer.com/article/10.1140/epjc/s10052-018-6522-5 |
| spellingShingle | Alessandro Bombini Stefano Giusto Rodolfo Russo A note on the Virasoro blocks at order 1 / c European Physical Journal C: Particles and Fields |
| title | A note on the Virasoro blocks at order 1 / c |
| title_full | A note on the Virasoro blocks at order 1 / c |
| title_fullStr | A note on the Virasoro blocks at order 1 / c |
| title_full_unstemmed | A note on the Virasoro blocks at order 1 / c |
| title_short | A note on the Virasoro blocks at order 1 / c |
| title_sort | note on the virasoro blocks at order 1 c |
| url | http://link.springer.com/article/10.1140/epjc/s10052-018-6522-5 |
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