Exact Correlation Models in Biscalar Fishnet Theory

In the study of biscalar fishnet models, various operators and spectra were explored, leading to findings on exact correlation functions, strong coupling regimes, Regge limits, and more in arbitrary dimensions. The investigation delves into Lagrangian formulations, graph-building operators, conformal blocks, and eigenvalues, shedding light on the solvability and applications of these models in different scenarios like zero-magnon and one-magnon cases. The research addresses complexities and simplifications in correlation functions, highlighting the robustness and versatility of biscalar fishnet models in theoretical physics.

• Correlation Models
• Biscalar Fishnet Theory
• Exact Functions
• Strong Coupling
• Lagrangian Formulations

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1. AYSS-2023 CORRELATORS IN 6D- FISHNET MODELS Iakhibbaev R.M. BLTP JINR

2. Outline Largrangian of biscalar fishnet model in arbitrary dimension Graph-building operator and spectrum (+6d) Exact correlation function Strong coupling Regge limit in Mellin amplitudes Conclusion

3. Kazakov,Olivucci18 Biscalar fishnet models in arbitrary dimensions Lagrangian Generalized Green s functions No mother theory No unitarity Non-local in the general case But exactly solvable (and conformal sometimes) Propagators

4. Kazakov,Olivucci18 Gromov, Korchemsky 19 Graph-building operator and spectrum Graph-building operator 2J point correlation function Geometric progression to sum up all actions of GBO: Eigenvalues of graph-building operator

5. Diagram types Have many applications (6d (1,1) SYM, or 4D N=4 SYM) 0-magnon Close to conformal zig-zag diagrams (but general) 1-magnon

6. Zero-magnon spectrum Eigenvalue of graph-building operator in 0-magnon case Examples

7. One-magnon spectrum Eigenvalue of graph-building operator in 1-magnon case Examples

8. Kazakov,Olivucci18 Exact correlation function Exact 2J function: OPE: Structure constant Conformal block

9. Strong coupling in 6d Strong coupling regime comes from large spins For general correlation function: At large spin limit conformal block reduces to: Correlation function can be obtained by steepest descent Valid also in the one-magnon case

10. Chowdhury, Haldar,Ken19 Mellin amplitudes in Regge limit 6d Correlation function Regge limit Factorization: Simplification

11. Regge limit of Mellin amplitudes (weak coupling) Leading Regge trajectory Regge Mellin amplitude LLA: Coefficients of LA s:

12. One-magnon Mellin amplitudes (weak coupling) Correlation function in Mellin represesentation Regge limit LLA Even spins Coefficients of LA s: Odd spins

13. Regge limit of Mellin amplitudes (strong coupling) Leading contribution comes from Regge Mellin amplitude One-magnon: Zero-magnon:

14. Conclusion and prospectives We computed spectrum for non-isotropic fishnets in 6d We found exact correlation function Exact Regge limits in terms of Mellin amplitudes (weak/strong coupling) Celestial Mellin amplitudes for fishchain models to test Multipoint amplitudes and correlation functions (splitting overlaps of wavefunctions?) Spectrum for two-magnon operator

15. THANKS FOR ATTENTION