Constraining conformal theories in large dimensions
Abstract In this paper, we analyze the constraints imposed by unitarity and crossing symmetry on conformal theories in large dimensions. In particular, we show that in a unitary conformal theory in large dimension D, the four-point function of identical scalar operators ϕ with scaling dimension ∆ ϕ...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2022)035 |
| _version_ | 1828135889401806848 |
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| author | Abhijit Gadde Trakshu Sharma |
| author_facet | Abhijit Gadde Trakshu Sharma |
| author_sort | Abhijit Gadde |
| collection | DOAJ |
| description | Abstract In this paper, we analyze the constraints imposed by unitarity and crossing symmetry on conformal theories in large dimensions. In particular, we show that in a unitary conformal theory in large dimension D, the four-point function of identical scalar operators ϕ with scaling dimension ∆ ϕ such that ∆ ϕ /D < 3/4, is necessarily that of the generalized free field theory. This result follows only from crossing symmetry and unitarity. In particular, we do not impose the existence of a conserved spin two operator (stress tensor). We also present an argument to extend the applicability of this result to a larger range of conformal dimensions, namely to ∆ ϕ /D < 1. This extension requires some reasonable assumptions about the spectrum of light operators. Together, these results suggest that if there is a non-trivial conformal theory in large dimensions, not necessarily having a stress tensor, then its relevant operators must be exponentially weakly coupled with the rest. |
| first_indexed | 2024-04-11T17:55:00Z |
| format | Article |
| id | doaj.art-fdec1f6e57d949fbaa6ae567eaa23544 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-11T17:55:00Z |
| publishDate | 2022-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-fdec1f6e57d949fbaa6ae567eaa235442022-12-22T04:10:56ZengSpringerOpenJournal of High Energy Physics1029-84792022-02-012022212810.1007/JHEP02(2022)035Constraining conformal theories in large dimensionsAbhijit Gadde0Trakshu Sharma1Department of Theoretical Physics, Tata Institute for Fundamental ResearchDepartment of Theoretical Physics, Tata Institute for Fundamental ResearchAbstract In this paper, we analyze the constraints imposed by unitarity and crossing symmetry on conformal theories in large dimensions. In particular, we show that in a unitary conformal theory in large dimension D, the four-point function of identical scalar operators ϕ with scaling dimension ∆ ϕ such that ∆ ϕ /D < 3/4, is necessarily that of the generalized free field theory. This result follows only from crossing symmetry and unitarity. In particular, we do not impose the existence of a conserved spin two operator (stress tensor). We also present an argument to extend the applicability of this result to a larger range of conformal dimensions, namely to ∆ ϕ /D < 1. This extension requires some reasonable assumptions about the spectrum of light operators. Together, these results suggest that if there is a non-trivial conformal theory in large dimensions, not necessarily having a stress tensor, then its relevant operators must be exponentially weakly coupled with the rest.https://doi.org/10.1007/JHEP02(2022)035Conformal Field TheoryField Theories in Higher DimensionsNonperturbative Effects |
| spellingShingle | Abhijit Gadde Trakshu Sharma Constraining conformal theories in large dimensions Journal of High Energy Physics Conformal Field Theory Field Theories in Higher Dimensions Nonperturbative Effects |
| title | Constraining conformal theories in large dimensions |
| title_full | Constraining conformal theories in large dimensions |
| title_fullStr | Constraining conformal theories in large dimensions |
| title_full_unstemmed | Constraining conformal theories in large dimensions |
| title_short | Constraining conformal theories in large dimensions |
| title_sort | constraining conformal theories in large dimensions |
| topic | Conformal Field Theory Field Theories in Higher Dimensions Nonperturbative Effects |
| url | https://doi.org/10.1007/JHEP02(2022)035 |
| work_keys_str_mv | AT abhijitgadde constrainingconformaltheoriesinlargedimensions AT trakshusharma constrainingconformaltheoriesinlargedimensions |