Creating an outdoor plant box inspired by 11-dimensional string theory is a fascinating intersection of theoretical physics and botany. While traditional gardening focuses on three-dimensional space, this concept invites us to imagine flora that thrives in higher dimensions. Here are some ideal "plants" for such a unique setup:

1. Quantum Ferns: These fractal-like plants could represent the curled-up dimensions of string theory, with fronds that appear to vibrate in higher-dimensional space.

2. Cosmic Vines: Hypothetical vines that "entangle" across dimensions, symbolizing the interconnectedness of the universe as described by string theory.

3. M-Brane Moss: A low-growing ground cover that visually represents the membranous surfaces (branes) central to M-theory, the framework unifying string theories.

4. Superstring Shrubs: Compact bushes with helical growth patterns mimicking superstrings, the fundamental objects in string theory.

5. Calabi-Yau Blooms: Flowers shaped like the complex 6-dimensional Calabi-Yau manifolds that may determine our universe's particle physics in string theory.

For care tips:

- Use geometric planting patterns to suggest higher dimensions.

- Incorporate metallic or iridescent foliage to represent quantum effects.

- Arrange plants to create optical illusions of extra dimensions.

Remember, this is a thought experiment blending science and imagination. While we can't truly grow 11-dimensional plants, this approach makes abstract physics concepts visually engaging. The garden becomes a living metaphor for the hidden complexities of our universe.