Dual conformal symmetry on the light cone
We study the properties of conformal operators in the SL(2) sector of planar N=4 SYM and its supersymmetric SL(2|2) extension. The correlation functions of these operators and their form factors with respect to asymptotic on-shell states are determined by two different polynomials which can be ident...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2014-09-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321314002338 |
| _version_ | 1818214154678304768 |
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| author | S.É. Derkachov G.P. Korchemsky A.N. Manashov |
| author_facet | S.É. Derkachov G.P. Korchemsky A.N. Manashov |
| author_sort | S.É. Derkachov |
| collection | DOAJ |
| description | We study the properties of conformal operators in the SL(2) sector of planar N=4 SYM and its supersymmetric SL(2|2) extension. The correlation functions of these operators and their form factors with respect to asymptotic on-shell states are determined by two different polynomials which can be identified as eigenstates of the dilatation operator in the coordinate and momentum representations, respectively. We argue that, in virtue of integrability of the dilatation operator, the two polynomials satisfy a duality relation – they are proportional to each other upon an appropriate identification of momenta and coordinates. Combined with the conventional N=4 superconformal symmetry, this leads to the dual superconformal symmetry of the dilatation operator. We demonstrate that this symmetry is powerful enough to fix the eigenspectrum of the dilatation operator to the lowest order in the coupling. We use the relation between the one-loop dilatation operator and Heisenberg spin chain to show that, to lowest order in the coupling, the dual symmetry is generated by the Baxter Q-operator in the limit of large spectral parameter. |
| first_indexed | 2024-12-12T06:15:41Z |
| format | Article |
| id | doaj.art-6036d4f366f54fc4957840ee5f84a05e |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-12-12T06:15:41Z |
| publishDate | 2014-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-6036d4f366f54fc4957840ee5f84a05e2022-12-22T00:35:02ZengElsevierNuclear Physics B0550-32131873-15622014-09-01886C1102112710.1016/j.nuclphysb.2014.07.014Dual conformal symmetry on the light coneS.É. Derkachov0G.P. Korchemsky1A.N. Manashov2St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, RussiaInstitut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex, FranceDepartment of Theoretical Physics, St.-Petersburg State University, 199034 St.-Petersburg, RussiaWe study the properties of conformal operators in the SL(2) sector of planar N=4 SYM and its supersymmetric SL(2|2) extension. The correlation functions of these operators and their form factors with respect to asymptotic on-shell states are determined by two different polynomials which can be identified as eigenstates of the dilatation operator in the coordinate and momentum representations, respectively. We argue that, in virtue of integrability of the dilatation operator, the two polynomials satisfy a duality relation – they are proportional to each other upon an appropriate identification of momenta and coordinates. Combined with the conventional N=4 superconformal symmetry, this leads to the dual superconformal symmetry of the dilatation operator. We demonstrate that this symmetry is powerful enough to fix the eigenspectrum of the dilatation operator to the lowest order in the coupling. We use the relation between the one-loop dilatation operator and Heisenberg spin chain to show that, to lowest order in the coupling, the dual symmetry is generated by the Baxter Q-operator in the limit of large spectral parameter.http://www.sciencedirect.com/science/article/pii/S0550321314002338 |
| spellingShingle | S.É. Derkachov G.P. Korchemsky A.N. Manashov Dual conformal symmetry on the light cone Nuclear Physics B |
| title | Dual conformal symmetry on the light cone |
| title_full | Dual conformal symmetry on the light cone |
| title_fullStr | Dual conformal symmetry on the light cone |
| title_full_unstemmed | Dual conformal symmetry on the light cone |
| title_short | Dual conformal symmetry on the light cone |
| title_sort | dual conformal symmetry on the light cone |
| url | http://www.sciencedirect.com/science/article/pii/S0550321314002338 |
| work_keys_str_mv | AT sederkachov dualconformalsymmetryonthelightcone AT gpkorchemsky dualconformalsymmetryonthelightcone AT anmanashov dualconformalsymmetryonthelightcone |