What are the limitations of CFT?

Answer 1

Conformal Field Theory (CFT) has several limitations, including its reliance on the conformal symmetry, which restricts its applicability to systems where such symmetry is present. Additionally, CFT typically deals with two-dimensional systems, making it challenging to extend the insights gained to higher dimensions or more complex physical scenarios. The mathematical framework can also be complex, sometimes leading to difficulties in practical calculations or interpretations in real-world applications. Lastly, CFT may not adequately capture the dynamics of certain critical phenomena or interactions that break conformal invariance.