String theory’s background independence explained through the theory’s moduli space
Tiziana Vistarini · 2019
One may say that string theory moduli space represents the totality of possibilities for stringy worlds to be in a way or another. Somehow this totality is &s;fundamental&s; in two senses. First, it shows unambiguously what in the theory is not fundamental: geometry. T-duality and the anti-de Sitter (AdS)/conformal field theory (CFT) duality show that both ordinary spacetime and compact extra dimensions are emergent in the theory. Second, it shows what might be more fundamental than geometry and in some cases than topology: their deformations. The AdS/CFT duality corresponds to some “path” of physical invariance over the moduli space. A complex manifold is a topological structure that can be entirely covered by an atlas of charts, each patch representing a unit disk in the ordinary numerical space Cn. The Kodaira-Spencer map has a crucial role in the context of infinitesimal deformations of compact geometrical structures.