The cusp anomalous dimension in N=4 super Yang-Mills theory governs the divergence of Wilson loops at cusps — the ultraviolet singularity that arises when two straight Wilson lines meet at an angle. Its weak-coupling expansion is known to many loops. Its strong-coupling expansion, via AdS/CFT, begins with the classical string result and proceeds through quantum corrections.

The complete strong-coupling transseries has now been determined. Not just the perturbative series but all nonperturbative contributions — the exponentially suppressed terms that perturbation theory cannot see. The structure is unexpectedly fermionic: the nonperturbative sectors are classified by partitions of distinct odd integers.

Partitions of distinct odd integers are a combinatorial signature of fermionic degrees of freedom. In statistical mechanics, fermions obey the Pauli exclusion principle — each state is occupied at most once — and the partition function sums over states with distinct occupation numbers. The appearance of this structure in the cusp anomalous dimension means the nonperturbative physics organizes itself as though some underlying fermionic modes are being excited.

The technical tool is expressing the cusp anomalous dimension as a ratio of two determinants whose strong-coupling behavior is simple. The determinantal structure is what makes the resurgence fermionic rather than bosonic — the alternating signs from determinant expansion produce the distinct-partition combinatorics automatically.

The result is exact: the full transseries, not a truncation. For a physical quantity in an interacting four-dimensional quantum field theory, this kind of completeness is rare. The perturbative series is the ocean’s surface. The nonperturbative sectors are the currents beneath. And the currents are fermionic — they flow in channels that cannot share the same path.