# Main Mathematical Equations in AdS/CFT Gauge Quantum Gravity ### Holographic Principle, AdS/CFT Correspondence, and Gauge/Gravity Duality 1. **AdS Space formula** ``` ds^2 = R^2 * (dz^2/(1 - z^2) + (1 - z^2) * (dt^2 - dx^2)) ``` 2. **Conformal group formula** ``` SO(2, 4) ~ SU(2, 2) ``` 3. **Schwarzschild-AdS metric** ``` ds^2 = -f(r) * dt^2 + dr^2/f(r) + r^2 * dΩ^2 ``` 4. **Function f( r )** ``` f(r) = 1 - (2 * M * G_N)/r + (r^2 * Λ)/3 ``` 5. **Area of the minimal surface formula** ``` A(Γ) = ∫ d^2x * √(det(h_ij)) ``` 6. **Ryu-Takayanagi formula** ``` S_A = (A(Γ_A))/(4 * G_N) ``` 7. **Holographic entanglement entropy formula** ``` S_A = (Area(Γ))/(4 * G_N) ``` These formulas are crucial in understanding AdS/CFT Gauge Quantum Gravity and provide a solid foundation for further investigation into the topic.