可积场论的全息对偶

中文摘要 AI 辅助

我们为基于四维Chern-Simons理论构建的可积场论发展了一种全息对偶。对偶理论是广义Calabi-Yau流形上的拓扑弦，该流形完全由我们称之为平面谱曲线的几何对象编码。我们将平面可积场论的RG流描述为平面谱曲线模空间上的几何流。该描述在't Hooft耦合的所有阶都有效。我们在许多例子中显式计算了该流至两圈，并发现与已知场论结果精确匹配。在一圈阶，这涵盖了一大类模型。在两圈阶，我们重现了带WZ项的主手征模型的RG流，以及一类靶空间为U(N)×U(N)的可积σ模型的RG流。

英文摘要

We develop a holographic dual to the integrable field theories built from $4d$ Chern-Simons theory. The dual theory is a topological string on a generalized Calabi-Yau manifold, which is entirely encoded in a geometric object we call a planar spectral curve. We describe the RG flow for a planar integrable field theory as a geometric flow on the moduli of planar spectral curves. This description is valid at all orders in the 't Hooft coupling. We compute this flow explicitly up to two loops in many examples, and find an exact match with known field theory results. At one loop this includes a wide class of models. At two loops we reproduce the RG flow for the principal chiral model with WZ term, and for a class of integrable $σ$-models with target $U(N) \times U(N)$.

发表机构

• Perimeter Institute for Theoretical Physics
• School of Mathematics, University of Edinburgh（爱丁堡大学数学学院）

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