How do deformed string backgrounds reshape the physics on branes?

When spacetime gets geometrically deformed in string theory, the physics experienced by objects living on branes changes in predictable ways. The authors prove these changes follow the same mathematical rules as T-bar-T flows—a well-studied class of deformations in quantum field theory. This connection holds for both simple (abelian) and complex (non-abelian) deformations, suggesting a deeper unified structure.