Quantum reduction in the twisted case
Victor G. Kac, Minoru Wakimoto
研究了仿射超代数在扭曲情形下的量子哈密顿约化。这导致了所有超共形代数的一般表示理论，包括扭曲代数（如Ramond代数）。特别是，我们发现一般的自由场实现和行列式公式。
We study the quantum Hamiltonian reduction for affine superalgebras in the twisted case. This leads to a general representation theory of all superconformal algebras, including the twisted ones (like the Ramond algebra). In particular, we find general free field realizations and determinant formulae.
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Reduction of twisted generalized Kähler structure
我们证明了我们以前在\cite{LT05}中的工作扩展到了扭曲的情形，即我们定义了扭曲广义复几何和扭曲广义Kähler几何中的矩映射和约化的概念.
Twisted spin Sutherland models from quantum Hamiltonian reduction
最近的一般结果哈密尔顿约化下的极群作用，研究了一些约化的自由粒子所支配的Laplace-Beltrami算子的紧凑，连接，简单的李群。利用扭共轭诱导的对称性，详细描述了与群的任意有限维不可约表示相联系的约化系统。这些系统一般产生可积的Sutherland型多体模型的自旋，这被称为扭曲的自旋Sutherland模型，如果潜在的扭曲共轭是建立在非平凡的Dynkin图自同构。这些模型的谱可以计算，在原则上，通过解决某些Clebsch-Gordan问题，并提出了与SU（N）的定义表示的对称张量幂的模型的结果。
We consider the $k$-twisted Nekrasov-Shatashvili limit (NS$_k$ limit) of 5d (K-theoretic) and 6d (elliptic) quiver gauge theory, where one of the multiplicative equivariant parameters is taken to be the $k$-th root of unity. We obtain the extended center of the associated $q$-deformed quiver W-algebras constructed by our formalism [arXiv:1512.08533; arXiv:1608.04651; arXiv:1705.04410], which provides gauge theoretic proof of Bouwknegt-Pilch's statement on the relation to the representation ring of quantum affine algebra.
Resonances in twisted quantum waveguides
本文研究了波导中薛定谔哈密顿量在对称微扰作用下的嵌入本征值。结果表明，这些特征值变得不稳定，并在扭转波导后变成共振。本文计算了弱扭转波导谐振宽度的微扰展开式，并在具体模型中详细讨论了扭转对谐振宽度的影响。
Twisted Hochschild Homology of Quantum Hyperplanes
利用扭曲的霍赫希尔德同调计算了量子超平面的Hochschild维数。
After the introduction of $λ$-symmetries by Muriel and Romero, several other types of so called "twisted symmetries" have been considered in the literature (their name refers to the fact they are defined through a deformation of the familiar prolongation operation); they are as useful as standard symmetries for what concerns symmetry reduction of ODEs or determination of special (invariant) solutions for PDEs and have thus attracted attention. The geometrical relation of twisted symmetries to standard ones has already been noted: for some type of twisted symmetries (in particular, $λ$ and $μ$-…
Ramond sector of superconformal algebras via quantum reduction
在扭曲情形下研究仿射超代数的量子哈密尔顿约化。对“极小”超共形W-代数的Ramond扇区进行了详细的刻画，得到了其行列式公式。广泛的例子列表包括所有秩为2的单李超代数。本文将Kac和Wakimoto（math-ph/0304011）的结果推广到扭转情况。
Twisted Dirac Operators over Quantum Spheres
我们在量子球上构造了新的谱三元组族，特别关注标准Podles量子球和扭曲Dirac算子。
We extend the noncommutative geometry model of the fractional quantum Hall effect, previously developed by Mathai and the first author, to orbifold symmetric products. It retains the same properties of quantization of the Hall conductance at integer multiples of the fractional Satake orbifold Euler characteristics. We show that it also allows for interesting composite fermions and anyon representations, and possibly for Laughlin type wave functions.
We study the Kaluza-Klein reduction of various $6d$ holomorphic theories. The KK reduction is analyzed in the BV formalism, resulting in theories that come from the holomorphic topological twist of $3d$ $\mathcal{N} = 2$ supersymmetric field theories. Effective interactions of the KK theories at the classical level can be obtained at all orders using homotopy transfer theorem. We also analyze a deformation of the theories that comes from deforming the spacetime geometry to $SL_2(\mathbb{C})$ due to the brane back-reaction. We study the boundary chiral algebras for the various KK theories. Usin…
We prove how the Yangian of $\mathfrak{gl}_N$ in its RTT presentation and Olshanski's twisted Yangians for the orthogonal and symplectic Lie algebras can be obtained by a degeneration process from the corresponding quantum loop algebra and some of its twisted analogues.
Spectrum of a duality-twisted Ising quantum chain
研究了具有特殊扭曲边界条件的伊辛量子链。这个边界条件首先在自旋为1/2 XXZ的海森堡量子链的框架中引入，与对偶变换有关，对偶变换在临界点处成为模型的对称性。因此，在临界点处，具有对偶扭曲边界的伊辛量子链是几何不变的，类似于通常的周期或反周期边界条件的情况。对有限系统的伊辛量子链的完全能谱进行了解析计算，并研究了标度极限的共形性质。这提供了一个明确的例子，共形扭曲边界条件和相应的广义扭曲配分函数。
Intertwiners of representations of twisted quantum affine algebras
本文利用q-特征标方法，给出了所有类型扭量子仿射代数第一基本表示R-矩阵的显式计算公式。
SCFT/VOA correspondence and R-twisted reductions of $(A_2,D_{3n-2})$ Argyres--Douglas theories
本文研究n≥2时(A₂,D_{3n−2}) Argyres–Douglas理论的SCFT/VOA对应，提出相关VOA为对数二重态代数𝒜(4n−2)，推广n=2的结果并构造对应3d理论，验证其超对称与分支结构。
On the configuration space of projections in a noncommutative algebra, and for an automorphism of the algebra, we use a twisted Hochschild cocycle for an action functional, and a twisted cyclic cocycle for a topological term. The latter is Hochschild-cohomologous to the former and positivity in twisted Hochschild cohomology results into a lower bound for the action functional. While the equations for the critical points are rather complicate, the use of the positivity and the bound by the topological term leads to self-duality equations (thus yielding twisted noncommutative sigma-model soliton…
Twisted Araki-Woods Algebras, the Yang-Baxter Equation, and quantum field theory
本文回顾了twisted Araki-Woods代数的研究，介绍了twisted Fock空间，并探讨了源自集合论Yang-Baxter方程的新示例族及其在构建量子场论模型中的相关性。
In the preceding paper of this series of articles we constructed the twisted geometry coherent states in all dimensional loop quantum gravity and established their peakedness properties. In this paper we establish the "Ehrenfest property" of these coherent states which are labelled by the twisted geometry parameters. By this we mean that the expectation values of the polynomials of the elementary operators as well as the operators which are not polynomial functions of the elementary operators, reproduce, to zeroth order in $\hbar$, the values of the corresponding classical functions at the twi…
Twisted Poincaré Invariant Quantum Field Theories
众所周知，庞加莱群作用在Moyal平面上，有一个扭曲的余积。庞加莱不变的经典场论可以为这个扭曲的余积制定。本文系统地研究了Moyal平面上量子理论中的这种扭曲庞加莱作用量。我们从庞加莱群的表象出发，发展了在扭曲作用下不变性的量子场论，同时也保证了S-矩阵在群的扭曲作用下的不变性。一个重要的新贡献是使用量子场的庞加莱生成器的建设。
Twisted cyclic cohomology of the quantum SU(2)
撤回通过数学进行概括和归纳。QA/0405249
The Drinfled realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization for the twisted quantum affine algebras using Lusztig's twisted braid group action.
Twisted Superalgebras and Cohomologies of the N=2 Superconformal Quantum Mechanics
证明了N=2超共形量子力学的不变性是由6个费米子（幂零）生成元和6个玻色生成元（含一个中心荷）构成的扭曲超代数的子代数控制的.超共形量子力学作用量在这个相当大的扭曲超代数下是不变的。另一方面，它们完全由只有2个费米子和2个玻色子（中心荷和鬼数）生成元的子代数决定。不变动作是Q_i-精确的（i= 1，2，.，6），所有6个费米子生成元都有一个Q_{i'} -精确（i' \neq i）前件.因此，即使在其玻色子扇区中，扭曲超代数不包含一维共形代数sl（2），而只包含其Borel子代数，具有Calogero势的超共形量子力学作用量也是唯一确定的.弯曲靶空间中N=2超对称量子力学的非线性σ模型的广义坐标协方差仅由其在6种扭曲超对称中的一对下的世界线不变性来充分暗示。给出了N=2超共形量子力学的普通公式和扭曲公式之间的变换。
This thesis studies the algebro-geometric aspects of supersymmetric abelian gauge theories in three dimensions. The supersymmetric vacua are demonstrated to exhibit a window phenomenon in Chern-Simons levels, which is analogous to the window phenomenon in quantum K-theory with level structures. This correspondence between three-dimensional gauge theories and quantum K-theory is investigated from the perspectives of semi-classical vacua, twisted chiral rings, and twisted indices. In particular, the twisted index admits an algebro-geometric interpretation as the supersymmetric index of an effect…
Twisted partition functions for ADE boundary conformal field theories and Ocneanu algebras of quantum symmetries
对于每一个ADE Dynkin图，我们给出了一个实现，在通常的融合代数（图代数），由相关的Ocneanu图描述的量子对称性的代数。在每种情况下，我们都明确地给出了相应的扭曲配分函数的列表
Twisted Conformal Symmetry in Noncommutative Two-Dimensional Quantum Field Theory
通过扭曲产生算符和湮灭算符之间的对易关系，我们证明了量子共形不变性可以在二维Moyal平面上实现。这是无限维对称性作为量子代数的明确实现。
Affine $\imath$quantum groups and twisted Yangians in Drinfeld presentations
本文通过仿射 ı 量子群 Drinfeld 呈现的退化构造了分裂型扭 Yangian，证明其具有 PBW 型基且为扭流代数的形变，并猜想其与 RTT 呈现中的对应代数同构。
Poincaré Invariant Quantum Field Theories With Twisted Internal Symmetries
在[1]关于形变代数的工作的基础上，我们提出了一类粒子具有形变内部对称性的Poincaré不变量量子场论.本文讨论的扭曲量子场满足不同于通常玻色子/费米子对易关系的对易关系。这种构造的扭曲场本质上是非定域的。尽管存在这种非定域性，但我们表明可以构造满足簇分解原理且洛伦兹不变量的局部相互作用汉密尔顿。我们进一步说明这些想法，考虑全球SU（N）对称性。特别地，我们表明扭曲的内部对称性可以显着简化讨论的边缘变形（β变形）的N=4超对称理论。
(Quantum) twisted Yangians: symmetry, Baxterisation and centralizers
基于（量子）扭曲杨氏，可以构造具有特殊边界条件的可积系统，称为孤子非保持（SNP）。在这篇文章中，我们专注于研究（量子）扭曲的杨氏子代数，我们表明，这样的子代数提供了一个确切的对称性的合理的转移矩阵。我们讨论了如何通过只关注两种类型的特殊边界来获得通用传递矩阵的谱。它还表明，子代数，出现的（量子）扭曲的杨代数的张量积表示的渐近性，原来是对偶的（量子）Brauer代数。为了处理一般边界的三角函数的情况下，我们提出了一个新的代数，这也提供了适当的框架，在SNP的情况下的deleterisation程序。
Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras
We propose factorized difference operators L(u) associated with the twisted quantum affine algebras U_{q} (A^{(2)}_{2n}), U_{q} (A^{(2)}_{2n-1}), U_{q} (D^{(2)}_{n+1}), U_{q} (D^{(3)}_{4}). These operators are shown to be annihilated by a screening operator. Based on a basis of the solutions of the difference equation L(u)w(u)=0, we also construct a Casorati determinant solution to the T-system for U_{q} (A^{(2)}_{2n}), U_{q} (A^{(2)}_{2n-1}).
We consider the Dirichlet Laplacian $H_γ$ on a 3D twisted waveguide with random Anderson-type twisting $γ$. We introduce the integrated density of states $N_γ$ for the operator $H_γ$, and investigate the Lifshits tails of $N_γ$, i.e. the asymptotic behavior of $N_γ(E)$ as $E \downarrow \inf {\rm supp}\, dN_γ$. In particular, we study the dependence of the Lifshits exponent on the decay rate of the single-site twisting at infinity.
Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI
本研究利用高斯分解，建立了AI型对称对对应的扭曲$q$-Yangian与仿射$\imath$量子群的显式同构，并由此得到该类仿射$\imath$量子群的PBW型基。
Twisted Quantum Double Model of Topological Phases in Two--Dimension
基于有限群$G$和$G$上的3-上循环$α$，提出了一种新的二维拓扑相位离散模型--扭曲量子双模型.研究了基态的详细性质，发现基态子空间可以用$G$的扭曲量子偶$D^α(G)$来刻画。当$α$是平凡的3-上循环时，该模型成为基于有限群$G$的Kitaev量子双模型，其中已知元激发被分类为$G$的量子双$D(G)$。我们的模型可以看作是Dijkgraaf-Witten拓扑规范理论到离散图情形的Hamilton推广，其中规范群是有限群。通过将弦网6 j符号映射到相应的3-上循环，我们还证明了一大类Levin-Wen弦网模型和某些扭曲量子双模型之间的对偶性。这篇论文以一种广泛的物理学家都能接触到的方式提出。
Twisted Quantum Deformations of Lorentz and Poincaré algebras
讨论了D=4 Lorentz代数和Poincare代数的扭曲量子形变.在Poincare代数的情况下，它表明，几乎所有的经典的R-矩阵的S.Zakrzewski分类可以表示为从属的阿贝尔和约旦型的R-矩阵的和。相应的扭曲描述量子形变得到明确的形式。这项工作是一个扩展版本的文件\url{arXiv:0704.0081v1 [math.QA]}。
Statistics and UV-IR Mixing with Twisted Poincare Invariance
我们详细阐述了量子统计在扭曲庞加莱不变量理论中的作用。证明了要使扭曲庞加莱群成为量子理论的对称性，统计量必须是扭曲的。它也证实，在这种理论中的紫外-红外混合（在规范场的情况下）的去除是一个自然的结果。
We investigate a quantum geometric space in the context of what could be considered an emerging effective theory from Quantum Gravity. Specifically we consider a two-parameter class of twisted Poincaré algebras, from which Lie-algebraic noncommutativities of the translations are derived as well as associative star-products, deformed Riemannian geometries, Lie-algebraic twisted Minkowski spaces and quantum effects that arise as noncommutativities. Starting from a universal differential algebra of forms based on the above mentioned Lie-algebraic noncommutativities of the translations, we constru…
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