The problem of maintaining scale and conformal invariance in Maxwell and general N form gauge theories away from their critical dimension d_c = 2(N + 1) is analyzed. We first exhibit the underlying group-theoretical clash between locality, gauge, Lorentz and conformal invariance requirements. “Improved"-traceless-stress tensors are then constructed; each violates one of the above criteria. However, when d = N + 2, there is a duality equivalence between N-form models and massless scalars in d = N + 2. Here we show that N-form conformal invariance is not lost, by constructing a quasilocal gauge invariant improved stress tensor. The correlators of the scalar theory are then reproduced, including the latter’s trace anomaly. This resolves the old conformal invariance “paradox” between the dual partners.
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机译：分析了麦克斯韦和一般的N型规范理论中远离其临界尺寸d_c = 2（N + 1）保持尺度和共形不变性的问题。我们首先展示局部性，量规，洛伦兹和共形不变性要求之间潜在的群体理论冲突。然后构造“改进的”无痕应力张量；每个都违反上述标准之一；但是，当d = N + 2时，在d = N + 2中，N形式模型与无质量标量之间存在对偶等价关系。通过构造拟局部量规不变的改进应力张量，我们表明N型共形不变性不会丢失，然后重现了标量理论的相关因子，包括后者的迹线异常，从而解决了对偶之间旧的共形不变性“悖论”。伙伴。
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