We study vacua, walls and three-pronged junctions of mass-deformed nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ for generic $N$. We review and discuss the on-shell component Lagrangians of the ${\mathcal{N}}=2$ nonlinear sigma model on the Grassmann manifold, which are obtained in the ${\mathcal{N}}=1$ superspace formalism and in the harmonic superspace formalism. We also show that the Kähler potential of the ${\mathcal{N}}=2$ nonlinear sigma model on the complex projective space, which is obtained in the projective superspace formalism, is equivalent to the Kähler potential of the ${\mathcal{N}}=2$ nonlinear sigma model with the Fayet-Iliopoulos parameters $c^a=(0,0,c=1)$ on the complex projective space, which is obtained in the ${\mathcal{N}}=1$ superspace formalism.
We construct on-shell ${\mathcal{N}}=2$ nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ by holomorphically embedding the models in the hyper-Kähler nonlinear sigma model on the cotangent bundle of the Grassmann manifold $T^\ast G_{2N,N}$ in the ${\mathcal{N}}=1$ superspace formalism. We apply the moduli matrix formalism to the mass-deformed nonlinear sigma models on the quadrics to study three-pronged junctions by using a recently proposed diagram method.
Recently, a variety of deformed $T^{1,1}$ manifolds, with which 2D non-linear sigma models (NLSMs) are classically integrable, have been presented by Arutyunov, Bassi and Lacroix (ABL) [arXiv:2010.05573]. We refer to the NLSMs with the integrable deformed $T^{1,1}$ as the ABL model for brevity. Motivated by this progress, we consider deriving the ABL model from a 4D Chern-Simons (CS) theory with a meromorphic one-form with four double poles and six simple zeros. We specify boundary conditions in the CS theory that give rise to the ABL model and derive the sigma-model background with target-spa…
Beta Function of k Deformed AdS_5 x S^5 String Theory
我们计算了与q=exp（i pi/k）的量子群相关联的k个变形西格玛模型的世界片上可能的边缘耦合的单圈β函数.这包括玻色子主手征模型和对称空间西格玛模型，也包括k变形半对称空间西格玛模型，它描述了AdS_5 x S^5变形的弦。世界片西格玛模型是规范WZW模型对PSU（2，2）超群的电流-电流变形|4）k级。在弦论中，由于PSU（2，2）的Killing形式为零，β函数为零|4）这是另一个证明k变形理论定义了相容的弦论的证据。
We study the dual description of the $η$-deformed $OSP(N|2m)$ sigma model in the asymptotically free regime ($N>2m+2$). Compared to the case of classical Lie groups, for supergroups there are inequivalent $η$-deformations corresponding to different choices of simple roots. For a class of such deformations we propose the system of screening charges depending on a continuous parameter $b$, which defines the $η$-deformed $OSP(N|2m)$ sigma model in the limit $b\rightarrow\infty$ and a certain Toda QFT as $b\rightarrow0$. In the sigma model regime we show that the leading UV asymptotic of the $η$-d…
Recently, Arutyunov, Bassi and Lacroix have shown that 2D non-linear sigma model with a deformed $T^{1,1}$ background is classically integrable [arXiv:2010.05573 [hep-th]]. This background includes a Kalb-Ramond two-form with a critical value. Then the sigma model has been conjectured to be non-integrable when the two-form is off critical. We confirm this conjecure by explicitly presenting classical chaos. With a winding string ansatz, the system is reduced to a dynamical system described by a set of ordinary differential equations. Then we find classical chaos, which indicates non-integrabili…
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。
Yang-Baxter deformed sigma models on $\mathrm{SU}(N)/\mathrm{SO}(N)$
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；HSE University（高等经济学院）；Institute for Theoretical and Mathematical Physics MSU（莫斯科大学理论与数学物理研究所）
Supergravity background of lambda-deformed model for AdS2 x S2 supercoset
从对应于AdS_n x S^n超弦的F/G超陪集模型开始，我们可以将arXiv：1409.1538的σ-模型定义为F/F规范WZW模型的变形，或者定义为AdS_n x S^n超弦西格玛模型关于整个超群F的非阿贝尔T-对偶的可积单参数推广。在这里，我们考虑n=2的情况，并找到PSU（1，1）的四维目标空间背景的显式形式|2）/[SO（1，1）× SO（2）]超陪集。我们表明，这个背景下表示的解决方案IIB型10 d超引力紧致的6-torus与唯一的度量，π和RR 5-形式（表示为2-形式F在4d）是非平凡的。这意味着，在量子水平上，希达模型是外尔不变的，因此定义了一个相容的超弦西格玛模型。我们发现的超引力解与arXiv：1410.1886中的解不同，后者应该对应于一个只规范F的玻色子子群的版本。尽管如此，这两个解决方案具有等效的缩放极限arXiv：1504.07213，导致度量和e^Phi F的等距背景，其与arXiv：1309.5850的η变形的AdS_2 x S^2西格玛模型相关。在AdS_3 x S^3和AdS_5 x S^5的情况下，预期得到类似的结果。
