Christoph Sachse, Partha Guha, Chandrashekar Devchand
This paper has been withdrawn by the authors. Because of a misunderstanding, the paper was submitted prematurely to the arXiv. A replacement will follow.
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This paper is devoted to study of integrable structures in superconformal field theory and more general coset CFT's related to the affine Yangian $\textrm{Y}\big(\widehat{\mathfrak{gl}}(2)\big)$. We derive the relation between the RLL and current realizations and prove Bethe anzatz equations for the spectrum of Integrals of Motion.
Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions using localization method. Here we discuss a connection of 4d superconformal indices and 3d partition functions using a particular example of supersymmetric theories with matter in antisymmetric representation.
Supersymmetric integrable systems from geodesic flows on superconformal groups
我们讨论了测地线流，可积性和超对称性之间的可能关系，使用费米扩展的KdV方程，以及最近推出的超对称的Camassa-Holm方程，作为说明性的例子。
Supersymmetric semi--infinite cohomology and $N = 2$ superconformal structures
本文通过 BRST 约化研究超对称半无限上同调及其 $N = 2$ 超共形结构，并利用相对超对称半无限上同调实现超陪集模型。
In this paper, we define the shifted superconformal vector of supersymmetric charged free fermion vertex algebras, which is a 1-parameter deformation of the superconformal vector of the SUSY $bc$-$βγ$ system. Moreover, we find the corresponding shifted $N=2$ superconformal symmetry of SUSY charged free fermion vertex algebras, by using the $N_{K}=1$ SUSY vertex algebra formalism. Finally, in order to describe the shifted $N=2$ superconformal symmetry of the SUSY charged free fermion vertex algebra by $N=2$ superfields, we construct an $N_{K}=2$ SUSY version of the $bc$-$βγ$ system.
Elliptic Integrable Models and Their Spectra from Superconformal Indices
本文研究 $\mathcal{N}=1$ 超共形指数与相对论性椭圆可积模型的对应，通过六维共形物质紧化得到 van Diejen 模型及其高秩推广，并提出由指数计算基态的新算法。
In the recent paper, Bruce and Duplij introduced a double-graded version of supersymmetric quantum mechanics (SQM). It is an extension of Lie superalgebraic nature of ${\cal N}=1$ SQM to a $\mathbb{Z}_2^2$-graded superalgebra. In this work, we propose an extension of Bruce-Duplij model to higher values of $\cal N.$ Furthermore, it is shown that our construction of double-graded SQM is a special case of the method which converts a given Lie superalgebra to a $\mathbb{Z}_2^2$-graded superalgebra. By employing this method one may convert a model of superconformal mechanics to its double-graded ve…
The supersymmetric Camassa-Holm equation and geodesic flow on the superconformal group
本文研究了Camassa-Holm方程的一类费米子扩展。在这个族中，我们确定了三个有趣的类：（a）方程，这是固有的汉密尔顿，描述测地流相对于一个H ^1度量的超共形变换组在二维，（b）方程是汉密尔顿的一个不同的汉密尔顿结构和（c）超对称流方程。类（a）和（b）没有交集，但类（a）和（c）的交集给出了一个新的超对称可积系统的候选。我们证明了这个系统的一些简单但非平凡的减少Painlevé属性。
We extend the differential form representation of N = (n,n) supersymmetric quantum mechanics to the superconformal case. We identify the superalgebras occurring for n = 1,2,4, give necessary and sufficient conditions for their existence, and give explicit geometric constructions of their generators and commutation relations. Quantum mechanics on the moduli space of instantons is considered as an example.
Superconformal Weight Shifting Operators
本文提出构建具有SU(m,m|2n)对称性的超共形块的框架，通过分析超空间发展出通用超多重项相关子的构造方法，提供超共形bootstrap在4D超对称设定中的新框架。
Superconformal Field Theory and SUSY N=1 KdV Hierarchy II: The Q-operator
介绍了与超共形场论（SCFT）可积结构相关的代数结构。构造了Baxter Q算子的SCFT对应算子。得到了不同表示的转移矩阵及其截断的类融合关系。
Deformations of N=2 super-conformal algebra and supersymmetric two-component Camassa-Holm equation
本文研究了N=2超共形代数的中心扩张与Camassa-Holm方程的超对称两分量推广之间的联系。超共形代数的变形产生两个相容的括号结构。其中一个括号结构是从中心扩张导出的，并允许一个动量算子，该算子与协伴轨道元的Sobolev范数一致。动量算子通过勒纳关系诱导了超对称Camassa-Holm层次的保守哈密顿链。
Two planar supersymmetric quantum mechanical systems built around the quantum integrable Kepler/Coulomb and Euler/Coulomb problems are analyzed in depth. The supersymmetric spectra of both systems are unveiled, profiting from symmetry operators not related to invariance with respect to rotations. It is shown analytically how the first problem arises at the limit of zero distance between the centers of the second problem. It appears that the supersymmetric modified Euler/Coulomb problem is a quasi-isospectral deformation of the supersymmetric Kepler/Coulomb problem.
Lax Integrable Supersymmetric Hierarchies on Extented Phase Spaces
通过贝克隆变换得到了对偶空间上的Lax型非线性动力系统族的Hamilton表示，该系统族是由一个反对易变量的超积分微分算子的李代数所构成的，通过相应的谱问题本征函数和伴随本征函数的演化所扩展，以及它们的附加对称性族的Hamilton表示.这些族与Lax（2）可积族的关系|1+1）维超对称Davey-Stewartson系统.
We introduce a new integrable supersymmetric lattice chain which violates fermion conservation and exhibits fermion-hole symmetry. The model displays exponential degeneracy in every eigenstate including the groundstate. This degeneracy is expressed in the possibility to create any number of zero modes reminiscent of Cooper pairs.
Integrable Supersymmetric Fluid Mechanics from Superstrings
在建立了平面超对称Chaubergin气体模型的基础上，从（2+1）维光锥参数化的Nambu-Goto超弦得到了（1+1）维超对称流体力学.线性模型是完全可积的，可以用黎曼坐标巧妙地表达出来。展示了守恒电荷和超荷的无限塔。它们形成了一个动力学（隐藏）SO（2，1）对称群的不可约表示。
Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mechanics such that the two-dimensional spin lattice is the quiver diagram, the partition function of the lattice model is the partition function of the gauge theory and the Yang-Baxter equation expresses the identity of partition functions for dual pairs. This correspondence is a powerful tool which enables us to generate new integrable models. The aim of the present paper is to give a short account on a progress in in…
For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of generating function for the family of commuting quantum transfer matrices. Any eigenvalue of the master T-operator is the tau-function of the classical mKP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0-th time of the hierarchy. This implies a remarkable relation between the quantum supersymmetric spin chains and classical many…
Fermionic flows and tau function of the N=(1|1) superconformal Toda lattice hierarchy
一类N=（1）的无限费米子流|1）构造了超共形Toda格族，并研究了它们的代数结构。我们完全解决了半无限N=（1| 1）Toda格和链的层次结构，并推导出它们的tau函数，这可能与建立超对称矩阵模型有关。讨论了它们的玻色极限。
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