Expansion of Einstein’s Field Equations through Fractal Holographic Emergent String Theory (FHEST) and Holographic Duality Theory (AdS/CFT)

This paper explores how the holographic duality theory (AdS/CFT) providesa unique perspective for deriving Einstein’s field equations through the dual re?lationship between gravitational theory in high-dimensional anti-de Sitter (AdS)space and conformal field theory (CFT) on a low-dimensional boundary. On thisbasis, we further introduce Fractal Holographic Emergent String Theory (FHEST),which extends and modifies the AdS/CFT framework by incorporating the con?cepts of fractal geometry and fractal dimensions. FHEST is not only mathemati?cally more self-consistent but also offers new perspectives for addressing core issuesin high-energy physics, such as non-renormalization of quantum gravity, black holeinformation paradox, and the origin of dark energy. We elaborate on the extensionsand modifications of FHEST to AdS/CFT and propose experimentally verifiablepredictions to provide new directions for future research.