arXiv 2312.140312023-12hep-th

$\n\bma\th\bfs{A}d\bms{S}_3 \ imes \bmsf{S}^3 \ imes \bmsf{T}^4$弦的椭圆形变

Elliptic deformations of the $\mathsf{AdS}_3 \times \mathsf{S}^3 \times \mathsf{T}^4$ string

Ben Hoare, Ana L. Retore, Fiona K. Seibold

备注：: 28 pages; v2: minor comments added, matches published version; v3: typos corrected, including signs in eq. (7.9); v4: corrected eq. (3.11), (3.12) and (4.16)

AI总结：

本研究探究$\bmsf{AdS}_3 \times \bmsf{S}^3 \times \bmsf{T}^4$弦的可积椭圆形变，计算对应玻色西格玛模型树级S矩阵，发现其无法嵌入已知含费米子的可积R矩阵，进而构建II型超引力中的度规嵌入，为含费米子的可积弦模型提供候选。

摘要：

为探究$\bmsf{AdS}_3 \times \bmsf{S}^3 \times \bmsf{T}^4$上弦的可积椭圆形变的存在性，我们在均匀光锥规范下计算了$\bmsf{AdS}_3 \times \bmsf{S}^3$上椭圆形变玻色西格玛模型的树级世界面S矩阵。所得树级S矩阵与模型的可积性兼容，且具备诸多有趣特性，包括拉格朗日量中未显体现的隐藏$\bmsf{U}(1)$对称性。我们发现它无法嵌入描述含费米子的未形变$\bmsf{AdS}_3 \times \bmsf{S}^3 \times \bmsf{T}^4$光锥规范S矩阵形变的已知精确可积R矩阵中。为此，我们构建了形变6维度规在具有常膨胀子和均匀通量的II型超引力中的嵌入。这些解的简洁性表明它们是有望导出含费米子的可积弦西格玛模型的候选对象。

英文摘要：

With the aim of investigating the existence of an integrable elliptic deformation of strings on $\mathsf{AdS}_3 \times \mathsf{S}^3 \times \mathsf{T}^4$, we compute the tree-level worldsheet S-matrix of the elliptically-deformed bosonic sigma model on $\mathsf{AdS}_3 \times \mathsf{S}^3$ in uniform light-cone gauge. The resulting tree-level S-matrix is compatible with the integrability of the model and has interesting features, including a hidden $\mathsf{U}(1)$ symmetry not manifest in the Lagrangian. We find that it cannot be embedded in the known exact integrable R-matrices describing deformations of the undeformed $\mathsf{AdS}_3 \times \mathsf{S}^3 \times \mathsf{T}^4$ light-cone gauge S-matrix including fermions. Therefore, we construct embeddings of the deformed 6-d metric in type II supergravity with constant dilaton and homogeneous fluxes. The simplicity of these solutions suggests they are promising candidates to lead to an integrable string sigma model including fermions.

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摘要：

英文摘要：

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