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Bootstrapping a Two-Loop Four-Point Form Factor.

Yuanhong Guo1,2, Lei Wang1,2, Gang Yang1,2,3,4

  • 1CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.

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|October 22, 2021
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Summary
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Researchers computed a key scattering amplitude in N=4 Super Yang-Mills (SYM) theory using a novel bootstrapping strategy. This method leverages physical constraints to determine complex mathematical expressions, advancing understanding of quantum field theory.

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Area of Science:

  • Theoretical Physics
  • High-Energy Physics
  • Quantum Field Theory

Background:

  • Planar N=4 Super Yang-Mills (SYM) theory is a crucial model in theoretical physics, offering insights into quantum chromodynamics and string theory.
  • Scattering amplitudes and form factors are fundamental observables for probing the dynamics of quantum field theories.

Purpose of the Study:

  • To compute the two-loop four-point form factor of a specific operator in planar N=4 SYM theory.
  • To develop and apply a new bootstrapping strategy for determining complex scattering observables.

Main Methods:

  • An ansatz was constructed using master integrals for the form factor.
  • Physical constraints, including infrared divergences, collinear limits, and unitarity cuts, were employed to determine the coefficients of the ansatz.
  • The result was expressed using symbols and Goncharov polylogarithms.

Main Results:

  • The two-loop four-point form factor of the length-3 half-BPS operator was successfully computed.
  • A novel bootstrapping strategy combining physical constraints and unitarity cuts proved effective.
  • Full analytic results were obtained in terms of standard mathematical functions.

Conclusions:

  • The developed bootstrapping strategy provides a powerful tool for calculating scattering observables in quantum field theories.
  • The computed form factor offers a precise prediction within planar N=4 SYM theory.
  • The results contribute to the ongoing effort to understand the structure of scattering amplitudes in strongly coupled field theories.