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Operator Product Expansion for Form Factors.

Amit Sever1, Alexander G Tumanov2, Matthias Wilhelm3

  • 1School of Physics and Astronomy, Tel Aviv University, Ramat Aviv 69978, Israel.

Physical Review Letters
|February 5, 2021
PubMed
Summary

We introduce a new operator product expansion for N=4 Super Yang-Mills (SYM) theory. This method decomposes form factors into known transitions and a universal "form factor transition" object, enabling predictions at any loop order.

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Area of Science:

  • High-energy physics
  • Quantum field theory
  • Theoretical physics

Background:

  • Operator product expansions (OPE) are crucial for analyzing quantum field theories.
  • Planar form factors in N=4 Super Yang-Mills (SYM) theory exhibit dual conformal symmetry.
  • Periodic Wilson loops provide a dual description related to conformal symmetry.

Purpose of the Study:

  • To develop a novel operator product expansion for planar form factors in N=4 SYM theory.
  • To leverage dual conformal symmetry for a new decomposition of form factors.
  • To introduce and characterize a universal 'form factor transition' object.

Main Methods:

  • Decomposition of form factors into known pentagon transitions and a new 'form factor transition'.
  • Application of bootstrap constraints to determine the form factor transition.
  • Evaluation of the form factor transition for specific operators at leading order.

Main Results:

  • A new operator product expansion for planar form factors in N=4 SYM theory is proposed.
  • The 'form factor transition' is identified as a universal object subject to bootstrap constraints.
  • Leading-order evaluation of the form factor transition enables predictions at any loop order.

Conclusions:

  • The proposed operator product expansion provides a powerful tool for studying form factors in N=4 SYM theory.
  • The results are consistent with existing one-loop and two-loop data.
  • This framework offers a path to systematically compute form factors at higher loop orders.