Integrable deformations with twisted quantum affine symmetry

对二维qft的可积变形的研究使我们对如何利用可积性来寻找量子理论的精确、非摄动解有了深刻的认识。对Yang-Baxter变形的研究是这一显著进展的主要部分，导致了新的可积弦模型和全息对偶性的潜在发现。Yang-Baxter变形分为扭转变形和q变形两类；然而，许多q-变形模型具有难以处理的特征，如奇异目标空间几何。在这个项目中，学生将研究q-变形模型的推广，这些模型预计具有扭曲量子仿射对称。在建立变形的sigma模型后，学生将研究李泊松结构来推导和确认它们的对称性。接下来，变形将被推广到Z2和Z4集，目标是在AdS背景上构建新的，更易于处理的，可积分的弦sigma模型变形。

The study of integrable deformations of 2-d QFTs has led to significant insights into how integrability can be used to find exact, non-perturbative, solutions of quantum theories. Work on Yang-Baxter deformations has been a major part of this remarkable progress, resulting in the potential discovery of new integrable string sigma models and holographic dualities. Yang-Baxter deformations fall into two classes: twists and q-deformations; however, many of the q-deformed models have intractable features, such as a singular target space geometry. In this project the student will investigate generalisations of q-deformed models, which are expected to have twisted quantum affine symmetry. Having constructed the deformed sigma models, the student will investigate the Lie-Poisson structure to derive and confirm their symmetries. Following on from this, the deformations will be generalised to Z2 and Z4 cosets, with the goal of constructing new, more tractable, integrable deformations of string sigma models on AdS backgrounds.