Exact Operator Map from Strong Coupling to Free Fields: Beyond Seiberg-Witten Theory

Area of Science:

• Quantum Field Theory
• High Energy Physics
• Supersymmetry

Background:

• Exact operator maps in quantum field theory (QFT) typically apply only to symmetry-protected observables.
• Renormalization group (RG) flows in strongly coupled theories are challenging to analyze nonperturbatively.
• Previous work focused on specific cases like chiral rings in 4D N=2 supersymmetry.

Purpose of the Study:

• To construct the first nonperturbative UV-IR map for less protected operators in QFT.
• To establish an exact, bijective mapping between UV and infrared (IR) dynamics of a specific non-Lagrangian theory.
• To utilize this map for calculating the exact UV Macdonald index in the IR.

Main Methods:

• Development of a novel nonperturbative UV-IR map.
• Utilizing a "simple" UV strongly coupled non-Lagrangian 4D N=2 quantum field theory as a starting point.
• Application of the arc space concept to establish the bijection.

Main Results:

• Construction of the first nonperturbative UV-IR map for less protected operators.
• Demonstration of a universal nonchiral quarter-Bogomol'nyi-Prasad-Sommerfield ring mapping from UV to IR.
• Identification of strongly coupled UV dynamics manifesting as Fermi statistics of free gauginos in the IR.

Conclusions:

• The established UV-IR map provides a powerful tool for studying strongly coupled QFTs.
• The bijection enables exact computation of the UV Macdonald index from IR properties.
• This work opens new avenues for analyzing less protected observables in QFT.