Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space

Abstract

We discuss multiloop MHV amplitudes in the N=4 SYM theory in terms of effective gravity in the momentum space with IR regulator branes as degrees of freedom. Kinematical invariants of external particles yield the moduli spaces of complex or Kahler structures which are the playgrounds for the Kodaira-Spencer(KS) or Kahler type gravity. We suggest fermionic representation of the loop MHV amplitudes in the N=4 SYM theory assuming the identification of the IR regulator branes with KS fermions in the B model and Lagrangian branes in A model. The two-easy mass box diagram is related to the correlator of fermionic currents on the spectral curve in B model or hyperbolic volume in the A model and it plays the role of a building block in the whole picture. The BDS-like anzatz has the interpretation as the semiclassical limit of a fermionic correlator. It is argued that fermionic representation implies a kind of integrability on the moduli spaces. We conjecture the interpretation of the reggeon degrees of freedom in terms of the open strings stretched between the IR regulator branes.

39 pages, typos corrected, journal version

References in corpus (20)

• Gluon scattering amplitudes at strong coupling
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Comments on operators with large spin
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Logarithmic scaling in gauge/string correspondence
• Lectures on Twistor Strings and Perturbative Yang-Mills Theory
• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Two Dimensional Kodaira-Spencer Theory and Three Dimensional Chern-Simons Gravity
• Exact solution of the Faddeev-Volkov model
• On the worldsheet theories of strings dual to free large N gauge theories
• Comments on worldsheet theories dual to free large N gauge theories
• D-branes as Defects in the Calabi-Yau Crystal
• Discrete Liouville equation and Teichmüller theory
• One-loop derivation of the Wilson polygon - MHV amplitude duality
• "Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle

Cited by in corpus (6)

• On form factors in N=4 sym
• Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory
• On MHV Form Factors in Superspace for $\mathcal{N}=4$ SYM Theory
• On NMHV form factors in N=4 SYM theory from generalized unitarity
• Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
• Angular Momentum and Gravimagnetization of the $\mathcal{N}=2$ SYM vacuum