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A good analogy for the difference between the two can be given in terms of two other examples of anomalies, that are possibly more familiar. Consider a field theory with a global symmetry, take $U(1)$ for simplicity. At the classical level, the equations of motion lead to the existence of a conserved current (Noether's theorem). At the quantum level, the ...

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If the supersymetry breaking scale is close to the weak scale, the problematic renormalization parameters in the scalar sector of the Standard Model are naturally limited. In supersymemtry (when all the fields are dynamic) there are powerful non-renormalization theorems. Therefore, perturbative effects affect the scalar sector only below the supersymetry ...

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One usually considers Ricci-Flat target spaces for string propagation. If one doesn't care about the conformal anomaly, then given that one can think of an n-sheeted Riemann surface as given by the quotient of the Poincare upper half plane by some Fuchsian group. A first step to your question then is to compute the partition function for the sigma model with ...

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