We revisit the question whether the worldsheet theory of a string admits a global O(d,d) symmetry. We consider the truncation of the target space theory in which fields are independent of d coordinates, which is O(d,d,R) invariant. The worldsheet theory is not O(d,d,R) invariant, unless it is truncated by setting winding and center-of-mass momenta to zero. We prove consistency of this truncation and give a manifestly O(d,d,R) invariant action, generalizing a formulation due to Tseytlin by including all external and internal target space fields. It is shown that, due to chiral bosons, this symmetry is anomalous. The anomaly is cancelled by a Green-Schwarz mechanism that utilizes the external B-field.

中文翻译：

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旧的二元性和新的异常

我们重新审视弦的世界表理论是否承认全局 O(d,d) 对称性的问题。我们考虑目标空间理论的截断，其中场独立于 d 坐标，这是 O(d,d,R) 不变的。世界片理论不是 O(d,d,R) 不变的，除非通过将绕组和质心动量设置为零来截断它。我们证明了这种截断的一致性，并给出了一个明显的 O(d,d,R) 不变动作，通过包括所有外部和内部目标空间域来推广由于 Tseytlin 的公式。结果表明，由于手性玻色子，这种对称性是反常的。异常被利用外部 B 场的 Green-Schwarz 机制消除。