Derive improved cusp bounds from non-planar wireframe geometries

Derive improved bounds on the pair consisting of the universal defect Casimir energy \(\varepsilon^{a\bar a}\) and the right-angle cusp anomalous dimension \(\Gamma^{a\bar a}(\pi/2)\) by applying cutting-and-gluing or positivity methods to non-planar wireframe configurations in which defects decorate some or all edges of a cuboid.

Background

The paper establishes a universal right-angle cusp bound using planar rectangular defect geometries. Because the planar rectangle is insensitive to the dimension of the ambient spacetime, the authors consider non-planar wireframes, including cuboids, as a possible route to stronger constraints that probe higher-dimensional geometry.

Although the cuboid analysis yields a new bound for three-way defect junctions, the authors explicitly state that they were unable to use these non-planar shapes to improve the existing bound involving εaaˉ\varepsilon^{a\bar a} and Γaaˉ(π/2)\Gamma^{a\bar a}(\pi/2). Thus, constructing a successful wireframe-based improvement remains unresolved.

References

Promising non-planar shapes are ``wireframes'' where some or all edges of a cuboid are decorated with defects. Such shapes preserve much of the structure of the planar rectangles, since many can be built entirely out of right angle cusps, but we could not leverage them to find improved bounds on (\varepsilon{a \bar a},\Gamma{a \bar a}(\tfrac{\pi}{2})).

— Cutting corners: exciting and magical bounds from the cusp bootstrap  (2609.04041 - Lanzetta et al., 3 Sep 2026) in End Matter, section “Cuboids”