Regge amplitudes in generalized fishnet and chiral fishnet theories
Abstract We extend the analysis of [1] to study the Regge trajectories of the Mellin amplitudes of the 0- and 1-magnon correlators of the generalized Fishnet theory in d dimensions and one type of correlators of chiral fishnet theory in 4 dimensions. We develop a systematic procedure to perturbative...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2020)117 |
| _version_ | 1818380722549817344 |
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| author | Subham Dutta Chowdhury Parthiv Haldar Kallol Sen |
| author_facet | Subham Dutta Chowdhury Parthiv Haldar Kallol Sen |
| author_sort | Subham Dutta Chowdhury |
| collection | DOAJ |
| description | Abstract We extend the analysis of [1] to study the Regge trajectories of the Mellin amplitudes of the 0- and 1-magnon correlators of the generalized Fishnet theory in d dimensions and one type of correlators of chiral fishnet theory in 4 dimensions. We develop a systematic procedure to perturbatively study the Regge trajectories and subsequently perform the spectral integral. Our perturbative method is very generic and in principle can be applied to correlators whose perturbative Regge trajectories obey some structural conditions which we list down. Our d dimensional results reduce to previously known results in d = 4 for 0-magnon and 1-magnon. As a non-trivial check, we show that the results for 1-magnon correlator in d = 8, when evaluated using the exact techniques in [1, 2] are in perfect agreement with our d dimensional perturbative results. We also perturbatively compute the Regge trajectories and Regge-Mellin amplitudes of the chiral fishnet correlator Tr ϕ 1 x 1 ϕ 1 x 2 Tr ϕ 1 † x 3 ϕ 1 † x 4 $$ \left\langle \mathrm{Tr}\left[{\phi}_1\left({x}_1\right){\phi}_1\left({x}_2\right)\right]\mathrm{Tr}\left[{\phi}_1^{\dagger}\left({x}_3\right){\phi}_1^{\dagger}\left({x}_4\right)\right]\right\rangle $$ using the techniques developed in this paper. Since this correlator has two couplings κ and ω, we have obtained closed-form results in the limit κ → 0, ω → 0 with κ/ω held constant. We verify this computation with an independent method of computing the same and obtain perfect agreement. |
| first_indexed | 2024-12-14T02:23:12Z |
| format | Article |
| id | doaj.art-09be2d2044fb452bb95570ee42da56b7 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T02:23:12Z |
| publishDate | 2020-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-09be2d2044fb452bb95570ee42da56b72022-12-21T23:20:27ZengSpringerOpenJournal of High Energy Physics1029-84792020-12-0120201215210.1007/JHEP12(2020)117Regge amplitudes in generalized fishnet and chiral fishnet theoriesSubham Dutta Chowdhury0Parthiv Haldar1Kallol Sen2Department of Theoretical Physics, Tata Institute for Fundamental ResearchCenter for High Energy Physics, Indian Institute of ScienceTrinity College Dublin, The University of DublinAbstract We extend the analysis of [1] to study the Regge trajectories of the Mellin amplitudes of the 0- and 1-magnon correlators of the generalized Fishnet theory in d dimensions and one type of correlators of chiral fishnet theory in 4 dimensions. We develop a systematic procedure to perturbatively study the Regge trajectories and subsequently perform the spectral integral. Our perturbative method is very generic and in principle can be applied to correlators whose perturbative Regge trajectories obey some structural conditions which we list down. Our d dimensional results reduce to previously known results in d = 4 for 0-magnon and 1-magnon. As a non-trivial check, we show that the results for 1-magnon correlator in d = 8, when evaluated using the exact techniques in [1, 2] are in perfect agreement with our d dimensional perturbative results. We also perturbatively compute the Regge trajectories and Regge-Mellin amplitudes of the chiral fishnet correlator Tr ϕ 1 x 1 ϕ 1 x 2 Tr ϕ 1 † x 3 ϕ 1 † x 4 $$ \left\langle \mathrm{Tr}\left[{\phi}_1\left({x}_1\right){\phi}_1\left({x}_2\right)\right]\mathrm{Tr}\left[{\phi}_1^{\dagger}\left({x}_3\right){\phi}_1^{\dagger}\left({x}_4\right)\right]\right\rangle $$ using the techniques developed in this paper. Since this correlator has two couplings κ and ω, we have obtained closed-form results in the limit κ → 0, ω → 0 with κ/ω held constant. We verify this computation with an independent method of computing the same and obtain perfect agreement.https://doi.org/10.1007/JHEP12(2020)117AdS-CFT CorrespondenceConformal Field TheoryIntegrable Field Theories |
| spellingShingle | Subham Dutta Chowdhury Parthiv Haldar Kallol Sen Regge amplitudes in generalized fishnet and chiral fishnet theories Journal of High Energy Physics AdS-CFT Correspondence Conformal Field Theory Integrable Field Theories |
| title | Regge amplitudes in generalized fishnet and chiral fishnet theories |
| title_full | Regge amplitudes in generalized fishnet and chiral fishnet theories |
| title_fullStr | Regge amplitudes in generalized fishnet and chiral fishnet theories |
| title_full_unstemmed | Regge amplitudes in generalized fishnet and chiral fishnet theories |
| title_short | Regge amplitudes in generalized fishnet and chiral fishnet theories |
| title_sort | regge amplitudes in generalized fishnet and chiral fishnet theories |
| topic | AdS-CFT Correspondence Conformal Field Theory Integrable Field Theories |
| url | https://doi.org/10.1007/JHEP12(2020)117 |
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