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A Survey in ABJM: Scattering Amplitudes and Wilson loops Silvia Penati

A Survey in ABJM: Scattering Amplitudes and Wilson loops Silvia Penati Universi ty of Milano-Bicocca and INFN. In collaboration with Marco Bianchi, Gaston Giribet, Matias Leoni, Andrea Mauri, Alberto Santambrogio. The N=6 SCFT (ABJM). Aharony, Bergman, Jafferis, Maldacena 0806.1218

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A Survey in ABJM: Scattering Amplitudes and Wilson loops Silvia Penati

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  1. A Survey in ABJM: Scattering Amplitudes and Wilson loops Silvia Penati University of Milano-Bicocca and INFN In collaboration with Marco Bianchi, Gaston Giribet, Matias Leoni, Andrea Mauri, Alberto Santambrogio S. Penati

  2. The N=6 SCFT (ABJM) Aharony, Bergman, Jafferis, Maldacena 0806.1218 Aharony, Bergman, Jafferis 0807.4924 SU(2) x SU(2) global symmetry A B The theory is at its superconformal point S. Penati

  3. AdS4/CFT3 CORRESPONDENCE (Bagger, Lambert; Gustavsson; Aharony, Bergman, Jafferis, Maldacena) N >> k 5 For N << k type IIA on AdS x CP 4 3 S. Penati

  4. Why AdS4/CFT3 correspondence? The ultimate goal is to go deeper inside the nature of the AdS/CFT correspondence by disclosing model independent features. (Not simple replication of the 4d case) Why scattering amplitudes ? The main focus is on conceivable integrability structures at both sides of the correspondence. Tracks in the on-shell sector of the theories Why Wilson loops? Light-like Wilson loops are strictly connected to the amplitudes, via AdS/CFT correspondence. BPS WL computed using localization. S. Penati

  5. Plan of the talk • Amplitudes in N=6 Chern-Simons-matter models (ABJM/ABJ models): Duality with light-like 4pt polygon WL, Dual superconformal invariance, BDS-like ansatz for 4pt 2) ½ BPS Wilson loops for ABJM and comparison with results from localization S. Penati

  6. In N=4 SYM the planar on-shell sector exhibits powerful symmetries and dualities that rely on an integrable structure at both sides of AdS/CFT correspondence AdS/CFT perturbative investigation Integrability Dualities Symmetries of the planar on-shell sector of the theory S. Penati

  7. DUALITIES CFT contains other non-trivial objects like Wilson loops and correlation functions 2 • Amplitudes are functions of p , p = 0 • - Polygon WL and correlators are functions of x i i ij Dual variables S. Penati

  8. What happens in three dimensions ? • String side: Integrability is still an open question, although classically there are strong evidences. • CFT side: All loop Bethe Ansatz for the dilatation operator. But effects on the on-shell sector still to be deeply investigated at both sides of the correspondence. S. Penati

  9. 1) Planar scattering amplitudes • Only matter particles are dynamical. Therefore only scattering of scalars and fermions in the bifundamental repr. • Gauge invariance, Lorentz and SU(2)xSU(2) invariances force the number of particles to be evenand configurations with equal number ofbifundamental and anti-bifundamental fields n/2-2 N MHV S. Penati

  10. Tree level results • General constraints from superconformal invariance, once solved, allow to determine tree level amplitudes in terms of a restrict number of functions (Bargheer, Loebbert, Meneghelli). • The dual superconformal symmetry has been proved at tree level (Huang, Lipstein). • TheYangiansymmetry is realized at tree level. Proposed generating functional for tree amplitudes is manifestly Yangian invariant (Lee). S. Penati

  11. We move at loop level… Two loops JHEP1201 (2012) 056, JHEP 1112 (2011) 073 S. Penati

  12. (1) Amplitude/WL duality Duality with a light-like 4-polygon Wilson loop It is zero at one-loop, but…. x x 4 1 x x 2 3 (Henn, Plefka, Wiegandt; Bianchi, Leoni, Mauri, SP, Santambrogio; Bianchi, Giribet, Leoni, SP, 1304.6085) S. Penati

  13. (2) Dual conformal invariance Chen-Huang (JHEP 11(2011) 057) have computed the 2 loop correction by assuming dual conformal invariance + generalized unitarity cuts They find exactly the same result !! S. Penati

  14. (3) Another duality ?? Identification: At all orders in epsilon : Bianchi, Leoni, SP, arXiv:1112.3649 S. Penati

  15. (4) An all loop 4pt amplitude N=4 SYM case the BDS ansatz Analogy between the integrable structures (Gromov, Vieira) Identification of 4D 4pt at 1 loop and 3D 4pt at 2 loops Therefore….. S. Penati

  16. Confirmed by our two-loop result Confirmed at strong coupling 4pt amplitude at four loops needs be computed !! S. Penati

  17. 2) 1/2 BPS vs 1/6 Wilson loops We consider U(N) x U(M) ABJ(M) theory C = circle Superconnection (Drukker-Trancanelli 0912.3006) S. Penati

  18. Prediction from localization Pestun 0712.2824; Kapustin-Willett-Yaakov 0909.4559; Drukker-Marino-Putrov 1007.3837 Drukker-Trancanelli S. Penati

  19. Change of framing Guadagnini-Martellini-Mintchev NPB330 (1990) 575 Framing gives an overall phase which affects the one-loop result. In ordinary perturbation theory <WL> = 0 which corresponds to framing zero 1loop S. Penati

  20. The two-loop calculation (DRED scheme) Bianchi, Giribet, Leoni, SP, 1303.6939; in preparation S. Penati

  21. Conclusions and outlook Amplitudes:already remarkable results but still…..many open problems • 4pt amplitude at four loops to confirm the BDS-like ansatz and amplitude/WL duality. • Are scattering amplitudes with n>4 dual to some Wilson loop? Which one? • Better comprehension of the holomorphic anomaly arising for n>4. • Correlators? • We have generalized the calculation to the case of ABJ theory. At the order we have worked things do not seem to change much. What about higher orders? • Fermionic T-duality not completely understood at strong coupling Wilson Loops: • We have found perfect agreement with the two-loop result from localization • The calculation has required a consistent effort in evaluating loop integrals • We could exploit the techniques developed for evaluating more general BPS Wilson loops (Cardinali, Griguolo, Martelloni, Seminara, 1209.4032) S. Penati

  22. New COST Action “The String Theory Universe” 17 european Countries, 130 people and more… http://www.cost.eu/domains_actions/mpns/Actions/MP1210 S. Penati

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