论文标题
杨巴克斯特变形字符串的放松单二型性
Relaxing unimodularity for Yang-Baxter deformed strings
论文作者
论文摘要
我们基于$ r $ -Matrix求解（修改的）经典Yang-baxter方程的玻色弦Sigma-Models的所谓Yang-baxter变形。众所周知，$ r $的单二型条件至少足以使Weyl不变性至至少两个循环（$α'$）。在这里，我们问什么是必要的条件。我们发现，如果矩阵$（g+b）_ {mn} $，由未经构造的背景的公制和$ b $构建的构建，则是退化的，在一个循环下产生的单对象条件可以用较弱的条件代替。我们进一步表明，对于满足一环条件的非符号变形，Weyl不变性至少扩展到两个环（$α'$）。通过在$ O（d，d）$ - 协方差配方中工作来简化计算。
We consider so-called Yang-Baxter deformations of bosonic string sigma-models, based on an $R$-matrix solving the (modified) classical Yang-Baxter equation. It is known that a unimodularity condition on $R$ is sufficient for Weyl invariance at least to two loops (first order in $α'$). Here we ask what the necessary condition is. We find that in cases where the matrix $(G+B)_{mn}$, constructed from the metric and $B$-field of the undeformed background, is degenerate the unimodularity condition arising at one loop can be replaced by weaker conditions. We further show that for non-unimodular deformations satisfying the one-loop conditions the Weyl invariance extends at least to two loops (first order in $α'$). The calculations are simplified by working in an $O(D,D)$-covariant doubled formulation.
