Yang-Mills theory is parameterized by the number of colors, N_c — the dimension of the gauge group. In the real world, N_c = 3. In the large-N_c limit, the theory simplifies. Between these two values, the theory is Hermitian and well-behaved.
This paper continues N_c into the complex plane. At complex values of N_c, the theory becomes non-Hermitian, and something new appears: exceptional points — degeneracies where eigenvalues and eigenvectors of an operator simultaneously coalesce. These are not ordinary level crossings. At an exceptional point, the operator's Jordan form is non-diagonal, producing logarithmic rather than power-law behavior.
The exceptional points act as topological defects in the complex-N_c plane. Encircling one generates a non-Abelian geometric phase — the eigenstates permute in a way that depends on the path, not just the endpoint. The topological structure organizes the analytic continuation: it determines which branches of the theory connect to which as N_c varies.
At the exceptional points themselves, the theory exhibits logarithmic scaling characteristic of logarithmic conformal field theories — a class of CFTs where correlation functions contain log terms rather than pure power laws. These log-CFTs appear here not as exotic constructions but as the natural boundary behavior of ordinary Yang-Mills theory at its non-Hermitian degeneracies.
The result reframes what the number of colors means. It is not merely a parameter to be set to 3 or sent to infinity. It is a complex variable whose analytic structure — its singularities, branch cuts, and topological defects — encodes physical information about the theory at its real, physical value.