Duality Symmetry Breaking and Predictivity in Circle-Compactified String Vacua

This technical note examines the relationship between duality symmetry and predictivity in the simplest string-theoretic setting: a closed bosonic string compactified on a circle. Using only standard worldsheet methods, we show that exact T-duality at the self-dual radius corresponds to a structurally non-predictive regime in which all duality-invariant observables are stationary and spectral degeneracy is maximal. At this fixed point, infinitesimal variations of the compactification radius produce no first-order change in physical quantities, implying minimal Fisher information and limited parametric distinguishability. We demonstrate that controlled departure from the self-dual point lifts momentum–winding degeneracies and restores monotonic, distinguishable behavior in multiple observables, including the lowest mass gap, the thermal free energy, and the density of low-lying states. These results are independent of any vacuum-selection mechanism and do not modify string dynamics. Physical consistency, perturbative control, and decompactification constraints together define a bounded stability corridor, symmetric in logarithmic moduli space, within which duality symmetry and predictivity coexist. The analysis generalizes to superstring compactifications, S-duality, and higher-dimensional duality groups. The central conclusion is structural: exact involutive duality fixed points suppress predictive content by enforcing indistinguishability, and predictivity is recovered only when duality symmetry is not saturated. This reframes aspects of the string predictivity problem as a consequence of symmetry structure rather than vacuum multiplicity.