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Large-N reduction in the continuum three-dimensional Yang-Mills theory.
1Department of Physics, Florida International University, Miami, Florida 33199, USA.
Physical Review Letters
|October 4, 2003
Summary
Three-dimensional Euclidean Yang-Mills theory exhibits a phase transition at a critical torus size. Above this size, the theory behaves like a noninteracting string theory, independent of size.
Area of Science:
- Theoretical physics
- Quantum field theory
- String theory
Background:
- Understanding phase transitions in quantum field theories is crucial for fundamental physics.
- The behavior of three-dimensional Euclidean Yang-Mills theory is of significant interest.
Purpose of the Study:
- To investigate the phase transition of three-dimensional Euclidean Yang-Mills theory in the planar limit.
- To determine the conditions under which the theory behaves as a noninteracting string theory.
Main Methods:
- Numerical simulations
- Theoretical analysis
- Planar limit calculations
Main Results:
- Evidence suggests a phase transition occurs at a critical torus side length, l(c).
- For torus sizes l > l(c), the planar limit becomes independent of l.
- This behavior aligns with expectations for a noninteracting string theory.
Conclusions:
- The study proposes a phase transition in 3D Euclidean Yang-Mills theory.
- The theory's behavior for l > l(c) supports a connection to noninteracting string theory.
- Similar phenomena are anticipated in four-dimensional theories.
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