We study (0,2) deformations of a (2,2) supersymmetric gauged linear sigma model for a Calabi-Yau hypersurface in a Fano toric variety. In the non-linear sigma model these correspond to some of the holomorphic deformations of the tangent bundle on the hypersurface. Combinatorial formulas are given for the number of these deformations, and we show that these numbers are exchanged by mirror symmetry in a subclass of the models.
We present homogeneous Yang-Baxter deformations of the AdS$_5\times$S$^5$ supercoset sigma model as boundary conditions of a 4D Chern-Simons theory. We first generalize the procedure for the 2D principal chiral model developed by Delduc et al [arXiv:1909.13824] so as to reproduce the 2D symmetric coset sigma model, and specify boundary conditions governing homogeneous Yang-Baxter deformations. Then the conditions are applicable for the AdS$_5\times$S$^5$ supercoset sigma model case as well. In addition, homogeneous bi-Yang-Baxter deformation is also discussed.
Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
我们提出了对称空间西格玛模型的Yang-Baxter变形等价于未变形模型关于由r-矩阵结构决定的子群的非交换对偶。我们明确地证明了这一点的情况下，AdS_5西格玛模型的许多例子。对于完整的AdS_5 x S^5超陪集模型也应该是如此，通过T对偶和非线性坐标重定义的组合，为基于非阿贝尔r矩阵的齐次杨-巴克斯特变形与未变形的AdS_5 x S^5模型之间的联系提供了一个解释，并推广了最近的几个观察结果。这也包括基于交换r-矩阵的变形的特殊情况，其对应于TsT变换：它们等价于原始模型关于交换子代数的中心扩展的非交换矩阵。
On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
考虑了AdS_n x S^n超陪集上二维西格玛模型的两个可积变形.第一种是“eta-变形”（基于Yang-Baxter西格玛模型），它是AdS_n x S^n上标准超弦作用量的单参数推广;第二种是“Edda-变形”（基于变形规范WZW模型），它是AdS_n x S^n超弦的非阿贝尔T-对偶的推广。我们表明，eta变形模型可以得到一个特殊的标度限制和解析延拓坐标结合一个特定的识别的参数的两个模型的一个变形的一个。耦合和变形参数之间的关系是一致的解释的第一个模型作为一个真正的量子变形和第二个作为根单位量子变形。对于AdS_2 × S^2的情况，我们探讨了这一极限对超重力背景的影响，这些超重力背景与AdS_2变形模型有关。我们还认为，这两个模型可能形成一个对偶泊松-李对，并在与S^2相关的陪集的可积变形的情况下提供了直接的证据。
Heterotic String Sigma Models: Discrete Light Cone Quantization and Its Current-Current Deformation
University of Groningen（格罗宁根大学）；National Institute of Physics, University of the Philippines（菲律宾大学国家物理研究所）；Universidad de Murcia（穆尔西亚大学）；KTH Royal Institute of Technology and Stockholm University（瑞典皇家理工学院和斯德哥尔摩大学）
Lie algebra valued equations translating the integrability of a general two-dimensional Wess-Zumino-Witten model are given. We found simple solutions to these equations and identified three types of new integrable non-linear sigma models. One of them is a modified Yang-Baxter sigma model supplemented with a Wess-Zumino-Witten term.
We define integrability preserving Yang-Baxter deformations of symmetric space sigma models with non-semi-simple symmetry group, in particular the flat space string, using only the essential structures of a symmetric space sigma model. For homogeneous deformations, the Lax connection is of the same form as the semi-simple case, although the R operator no longer satisfies a freestanding operator equation. For inhomogeneous deformations, the form of the Lax connection needs to be relaxed, by modifying the underlying algebra. We illustrate the construction by discussing nonabelian deformations of…
Integrable Sigma Models and Universal Root $T\bar{T}$ Deformation via Courant-Hilbert Approach
Ningbo University（宁波大学）；Peking University（北京大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（阿尔伯特·爱因斯坦研究所））
An Integrable Deformation of the AdS5 x S5 Superstring
在AdS 5 x S5中，弦的世界片理论的S-矩阵先前已经被证明允许变形，其中对称代数被相关的量子群取代。q为实数的情况被认为是格林-施瓦茨西格玛模型的一种特殊变形。到目前为止，对于q是单位根的情况还缺乏解释。我们证明了Green-Schwarz西格玛模型允许一个离散变形，这个离散变形可以看作是F/F_V规范WZW模型的一个相当简单的变形，其中F=PSU（2，2| 4）。变形参数q则是单位的k次根，其中k是水平。变形理论具有与格林-施瓦茨西格玛模型相同的运动方程，但具有不同的辛结构。我们表明，由此产生的理论是可积的，并有恰到好处的数量的卡帕对称性，出现作为一个残余的原始规范对称性的费米部分。这表明存在一个完全一致的变形弦背景。
We search for integrable boundary conditions and their geometric interpretation as $D$-branes, in models constructed as generalized $λ$-deformations of products of group- and coset-spaces. Using the sigma-model approach, we find that all the conformal brane geometries known in the literature for a product of WZW models solve the corresponding boundary conditions, thus persisting as integrable branes along the RG flows of our sigma-models. They consist of the well known $G$-conjugacy classes, twisted $G$-conjugacy classes by a permutation automorphism (permutation branes) and generalized permut…
In this pedagogical review we introduce systematic approaches to deforming integrable 2-dimensional sigma models. We use the integrable principal chiral model and the conformal Wess-Zumino-Witten model as our starting points and explore their Yang-Baxter and current-current deformations. There is an intricate web of relations between these models based on underlying algebraic structures and worldsheet dualities, which is highlighted throughout. We finish with a discussion of the generalisation to other symmetric integrable models, including some original results related to Z T cosets and their…
We probe warped BTZ $ \times S^3 $ geometry with various string solitons and explore the classical integrability criteria of the associated phase space configurations using Kovacic's algorithm. We consider consistent truncation of the parent sigma model into one dimension and obtain the corresponding normal variational equations (NVE). Two specific examples have been considered where the sigma model is reduced over the subspace of the full target space geometry. In both examples, NVEs are found to possess the Liouvillian form of solutions which ensures the classical integrability of the associ…
Nonrelativistic string theory is a self-contained corner of string theory, with its string spectrum enjoying a Galilean-invariant dispersion relation. This theory is unitary and ultraviolet complete, and can be studied from first principles. In these notes, we focus on the bosonic closed string sector. In curved spacetime, nonrelativistic string theory is defined by a renormalizable quantum nonlinear sigma model in background fields, following certain symmetry principles that disallow any deformation towards relativistic string theory. We review previous proposals of such symmetry principles a…
Deformations of $T^{1,1}$ as Yang-Baxter sigma models
我们考虑一族变形T^{1，1}在杨巴克斯特西格玛模型的方法。我们首先讨论T^{1，1}的超陪集描述，它表明了空间的完全对称性，并导出了标准的Sasaki-Einstein度规。其次，我们考虑T^{1，1}的三参数变形，通过使用经典的r-矩阵满足经典的Yang-Baxter方程（CYBE）。由此得到的度量和NS-NS两种形式与TsT变换得到的度量和NS-NS两种形式完全一致，并包含Lunin-Maldacena背景作为特例。值得注意的是，对于AdS_5 x T^{1，1}，整个扇区的经典可积性被认为是丢失的。因此，我们的结果表明，杨巴克斯特西格玛模型的方法是适用的，即使是不可积陪集。这一观察表明，重力/CYBE对应可以扩展到可积的情况之外。
The classical Yangian symmetry of Auxiliary Field Sigma Models
Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；High Energy Physics Research Unit, Faculty of Science Chulalongkorn University（朱拉隆功大学理学院高能物理研究单元）；Department of Physics, Northeastern University（东北大学物理系）；The NSF Institute for Artificial Intelligence and Fundamental Interactions（美国国家科学基金会人工智能与基本相互作用研究所）；School of Mathematics and Physics, University of Queensland（昆士兰大学数学与物理学院）
Based on work done by Bonechi, Cattaneo, Felder and Zabzine on Poisson sigma models, we formally show that Kontsevich's star product can be obtained from the twisted convolution algebra of the geometric quantization of a Lie 2-groupoid, one which integrates the Poisson structure. We show that there is an analogue of the Poisson sigma model which is valued in Lie 1-groupoids and which can often be defined non-perturbatively; it can be obtained by symplectic reduction using the quantization of the Lie 2-groupoid. We call these groupoid-valued sigma models and we argue that, when they exist, they…
