Abstract
Ambiguity and BRST anomaly which appear in the string higher-loop calculation are studied in 4-dimensional heterotic string theory. In particular, we intensively investigate the models with an anomalous U(1) gauge group, and show that the possible ambiguities (A-B mixing, U(1) D-term tadpole etc.) are made to vanish by suitable field redefinition within a class of gauge slices satisfying the factorization hypothesis. Subtlety of massless three point amplitudes is clarified. We also extend the factorization hypothesis to the case of fermion amplitudes and study the ambiguities in them. We illustrate that the vertex operator correction which is consistent to the loop corrected Dirac equation indeed guarantees the absence of the ambiguity.
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