What does the Noether theorem in CFT state?

The Noether theorem in Two-Dimensional Conformal Field Theory (CFT) states that symmetries correspond to conserved currents. This theorem establishes a fundamental connection between symmetries and conservation laws in quantum field theory, showing that every continuous symmetry of the action leads to a conserved current via Noether's theorem. These conserved currents encode important physical information about the theory and play a crucial role in understanding its symmetries and dynamics. By studying the Noether theorem, researchers can uncover deep insights into the underlying structure of CFT and its physical implications.