论文标题
可集成的Sigma模型的通用1循环差异
Universal 1-loop divergences for integrable sigma models
论文作者
论文摘要
我们提出了一种简单的新方法，用于集成$σ$ - 模型的1循环重新归一化。通过在平等的基础上处理运动方程和比安奇身份，我们为1循环的壳差异得出了“通用”公式，从而在文献中逐渐计算概括了案例计算。考虑到对经典的LAX连接的选择，差异是根据零曲面方程上的“完整性”条件，根据宽松电流（杆子的残基）采用与理论无关的形式。我们计算了这些差异的大类理论，并在松弛连接中具有简单的极点。我们还表明，$ z_t $ coset型号的“纯旋转”类型及其最近构造的$η$ - $λ$ - 定性是1循环的可重新分配的，当杀戮形式消失时1-循环规模不变。
We present a simple, new method for the 1-loop renormalization of integrable $σ$-models. By treating equations of motion and Bianchi identities on an equal footing, we derive 'universal' formulae for the 1-loop on-shell divergences, generalizing case-by-case computations in the literature. Given a choice of poles for the classical Lax connection, the divergences take a theory-independent form in terms of the Lax currents (the residues of the poles), assuming a 'completeness' condition on the zero-curvature equations. We compute these divergences for a large class of theories with simple poles in the Lax connection. We also show that $Z_T$ coset models of 'pure-spinor' type and their recently constructed $η$- and $λ$-deformations are 1-loop renormalizable, and 1-loop scale-invariant when the Killing form vanishes.
