Evading the breakdown of U-duality at higher derivative order without full string-theoretic calculations

Determine whether the absence of U-duality symmetry enhancement in dimensional reductions of higher-derivative supergravity can be circumvented without performing full string-theoretic calculations, i.e., without explicitly incorporating non-perturbative effects such as wrapped-brane instanton contributions that mix with perturbative states under S-duality.

Background

The paper reviews how T-duality, a perturbative symmetry, can be used to generate higher-derivative-corrected solutions in heterotic supergravity, with the O(d+p,d; R) symmetry persisting to all orders at tree level after suitable field redefinitions.

In contrast, extending these methods to U-duality encounters an obstruction once higher-derivative terms are included: the classical scaling symmetry needed for U-duality enhancement is spoiled, and both continuous and discrete U-duality groups are broken in known examples (e.g., O(24,8; R)/(Z) for heterotic reductions and G2(2; R)/(Z) in minimal supergravity).

The authors argue that the root cause is the non-perturbative nature of S-duality, which mixes perturbative string states with solitonic branes. In type IIB, S-duality invariance at eight derivatives is restored only after including D(−1)-instanton effects. For heterotic compactifications, analogous wrapped-brane instanton contributions arise only after toroidal reduction and are not captured by the low-energy effective theory, raising the question of whether one can preserve U-duality without resorting to full string-theoretic computations.