Hidden Topological Angles in Path Integrals

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• Quantum Mechanics

Background:

• Topological angles are crucial in quantum field theories and mechanical systems.
• Understanding their origin and effects is key to advancing quantum physics.
• Existing models do not fully account for certain quantum phenomena.

Purpose of the Study:

• To demonstrate the existence of hidden topological angles (HTAs) in quantum field theories and quantum mechanical systems.
• To elucidate the distinct nature of HTAs compared to Lagrangian theta parameters.
• To explain the microscopic mechanism behind the vanishing of the gluon condensate.

Main Methods:

• Analyzing saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles).
• Employing analytic continuation in the number of flavors (n_f) to reveal HTA effects.
• Investigating N=1 super Yang-Mills theory and QCD-like SU(N) gauge theories.

Main Results:

• Existence of hidden topological angles (HTAs) demonstrated across various quantum systems.
• HTAs arise from saddle points and Lefschetz thimbles, distinct from theta parameters.
• Microscopic mechanism for gluon condensate vanishing in N=1 super Yang-Mills theory identified.
• Anomalously small condensates observed in QCD-like theories.
• HTAs explain differences in semiclassical expansions for integer and half-integer spin particles in quantum mechanics.

Conclusions:

• Hidden topological angles are a fundamental feature of quantum theories.
• HTAs provide a new framework for understanding quantum phenomena, including condensates and spin-dependent expansions.
• This work opens new avenues for research in theoretical and quantum physics.