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Establish a rigorous mathematical foundation for a non-Hermitian gauge theory on finite simplicial complexes.

March 16, 2026Open Access

Discrete Non-Hermitian Gauge Geometry on Simplicial Complexes: Conservation Laws, Emergent Metrics, and Topologically Protected Attractors

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Establish a rigorous mathematical foundation for a non-Hermitian gauge theory on finite simplicial complexes.
Develop the theory based on GL(k,C) non-Hermitian gauge structures.
Prove conservation of biorthogonal information charge under non-Hermitian dynamics.
Utilize log-determinant barriers to prevent gradient-flow collapses.
Derive exponential convergence to a fixed point using Weyl's Eigenvalue Inequality.
Confirmed the conservation and reality of the biorthogonal information charge.
Established conditions that prevent collapse into singular metrics.
Showed the system converges exponentially to a topologically protected fixed point.

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This manuscript demonstrates conservation and emergent metrics in gauge theory on simplicial complexes, suggesting robust geometric properties.

Chao Ma (2026) studied this question.

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This manuscript demonstrates conservation and emergent metrics in gauge theory on simplicial complexes, suggesting robust geometric properties.