Ilka Brunner, Ingrid Mayer, Cornelius Schmidt-Colinet
We study the effect of bulk perturbations of N=(2,2) superconformal minimal models on topological defects. In particular, symmetries and more general topological defects which survive the flow to the IR are identified. Our method is to consider the topological subsector and make use of the Landau-Ginzburg formulation to describe RG flows and topological defects in terms of matrix factorizations.
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In conformal field theories (CFTs) of dimension $d>3$, two-dimensional (2d) conformal defects are characterised in part by central charges defined via the defect's contribution to the trace anomaly. However, in general for interacting CFTs these central charges are difficult to calculate. For superconformal 2d defects in supersymmetric (SUSY) CFTs (SCFTs), we show how to compute these defect central charges from the SUSY partition function either on $S^d$ with defect along $S^2$, or on $S^1 \times S^{d-1}$ with defect along $S^1 \times S^1$. In the latter case we propose that defect central ch…
Covariant Derivation of Effective Actions for SUSY Topological Defects
我们第一步将有效作用量方法推广到超对称领域，该方法用于直接从拓扑缺陷的母场论协变推导拓扑缺陷的低能动力学。通过聚焦于二维超对称理论，我们能够推导出适当的变量变化，挑选出低能量的自由度。这些对应于超空间中受几何约束的超世界线嵌入。以标准超粒子作用量为主导项，得到了一个超对称的、$κ$ -不变的低能展开式，它可用于确定高阶修正。我们的公式很自然地符合$κ$目前的几何描述-对称性的所谓geometrodynamic约束。这也为在高维超对称理论中探索这些问题提供了基础。
Non-Perturbative Results in Global SUSY and Topological Field Theories
在这个讲座中，我们回顾了在全局超对称理论中得到的一些非微扰结果，并展示了如何在拓扑理论的框架中得到这些结果。
Nonlinear vector susy for the three-dimensional topological massive Yang-Mills theory
利用规范场的非线性但局域协变的重定义，得到了三维拓扑有质量Yang-Mills的非线性向量超对称性。
We calculate the proton lifetime and discuss topological defects in a wide class of non-supersymmetric (non-SUSY) $SO(10)$ and $E(6)$ Grand Unified Theories (GUTs), broken via left-right subgroups with one or two intermediate scales (a total of 9 different scenarios with and without D-parity), including the important effect of threshold corrections. By performing a goodness of fit test for unification using the two-loop renormalisation group evolution equations (RGEs), we find that the inclusion of threshold corrections significantly affects the proton lifetime, allowing several scenarios, whi…
Remarks on Topological SUSY in sixdimensional TQFTs
本文在Baulieu和West提出的六维拓扑场论中建立了两种形式场的拓扑向量超对称的存在性。我们调查的关系，这些对称性的扭曲操作的（2，0）超对称性和评论他们的相似之处，在拓扑杨米尔斯理论的类似对称性。
In this work we investigate some features of the fermionic sector of the supersymmetric version of the baby Skyrme model. We find that, in the background of BPS compact Skyrmions, fermionic zero modes are confined to the defect core. Further, we show that, while three SUSY generators are broken in the defect core, SUSY is completely restored outside. We study also the effect of a D-term deformation of the model. Such a deformation allows for the existence of fermionic zero modes and broken SUSY outside the compact defect.
Topological chiral symmetry breaking in SUSY NJL in curved space-time
在Buchbinder-Inagaki-Odintsov（BIO）模型中找到了有效势，它代表了与外部引力场非极小耦合的SUSY NJL模型，并认为空间的拓扑是非平凡的.研究了外曲率和非平凡拓扑作用下的手征对称性破缺。
Twisted N=4 SUSY Algebra in Topological Models of Schwarz Type
我们重新研究了Schwarz型拓扑场模型中存在的扭曲N=4超对称性。我们证明了三维Chern-Simons理论只有在自由情形下才能解扭为一类具有逆统计量的σ模型。通过降维，我们定义了二维BF模型。我们建立了一个关于退捻的模拟结果。由于通过降维的定义，我们发现了新的费米标量对称性，一直被忽视，迄今在文献中。
Twisting of N=1 SUSY Gauge Theories and Heterotic Topological Theories
证明了在适当的物质超多重态下，$D=4$ $N=1$ SUSY Yang-Mills理论可以在紧致Kähler流形上扭曲.给出了BRST荷反常消除的条件，扭曲理论给出了一个合适的BRST荷。我们发现一个非平凡的一组物理算子定义为类的上同调这BRST \op。我们证明了Kähler流形上的Dolbeault上同调复形的物理扩张因子在两个Ray-Singer挠率之比的幂以下都与外部Kähler度量无关。局部物理\op的分解子与Kähler流形上复结构的反全纯坐标无关。然而，仍然可以保留对全纯坐标的依赖性。对于一个超凯勒度量，物理映射与局部物理\op的插入的所有坐标无关。
In this paper and a companion one, we study the effect of integrable line defects on entanglement entropy in massive integrable field theories in 1+1 dimensions. The current paper focuses on topological defects that are purely transmissive. Using the form factor bootstrap method, we show that topological defects do not affect the the entanglement entropy in the UV limit and modify slightly the leading exponential correction in the IR. This conclusion holds for both unitary and non-unitary field theories. In contrast, non-topological defects affect the entanglement entropy more significantly bo…
A new topological aspect of the arbitrary dimensional topological defects
利用序参量场$\vec ϕ$提出了一种新的广义拓扑流来描述任意维的拓扑缺陷。利用$% ϕ$ -映射方法，证明了序参量场$\vec ϕ$的零点产生拓扑缺陷，并在Jacobian $% J(\frac ϕv)\neq 0$满足的条件下，用$ϕ$ -映射的Hopf指数和Brouwer度对拓扑缺陷的拓扑荷进行了拓扑量子化.当$J(\frac ϕv)=0$时，证明了存在分支过程的临界情况.基于隐函数定理和泰勒展开式，我们详细讨论了广义拓扑流的分支，发现了分支的不同方向。在场函数$\vec ϕ$的简并点处发现任意维拓扑缺陷分裂或合并，但拓扑缺陷的总电荷不变。
The generation of the (k-1)-dimensional defect objects and their topological quantization
利用$ϕ$ --映射方法和拓扑流理论，研究了任意维拓扑缺陷的拓扑结构和拓扑量子化。指出缺陷的拓扑量子数可用$ϕ$ -映射的缠绕数来描述，缠绕数由$ϕ$ -映射的Hopf指数和Brouwer度来确定.此外，它表明，所有的拓扑缺陷产生的地方$\vec ϕ=0$，即从零点的$ϕ$ -映射。
The topological quantization and the branch process of the (k-1)-dimensional topological defects
利用$ϕ$ -映射方法和拓扑流理论，在Jacobian $J(ϕ/v) \neq 0$满足的条件下，得到了任意维拓扑缺陷的拓扑结构和拓扑量子化.当满足$J(ϕ/v)=0$时，证明了存在分支过程的临界情形.基于隐函数定理和泰勒展开式，我们详细讨论了广义拓扑流的分支，发现了分支的不同方向。在场函数$\vec ϕ$的简并点处发现任意维拓扑缺陷分裂或合并，但拓扑缺陷的总电荷不变。
The topological quantization and bifurcation of the topological linear defects
利用$ϕ$ -映射方法和拓扑流理论，在Jacobian $J(ϕ/v) \neq 0$满足的条件下，得到了拓扑线性缺陷的拓扑结构和拓扑量子化。当满足$J(ϕ/v) = 0$时，证明了存在分支过程的临界情形.基于隐函数定理和Taylor展开式，分别在$ϕ$ -映射的极限点和分歧点附近详细讨论了线性亏损的起源和分歧.
Topological current of point defects and its bifurcation
从三维矢量序参量的拓扑性质出发，得到了点缺陷的拓扑流。一种是点缺陷的电荷由Hopf指数和Brouwer度决定。点缺陷的演变也进行了研究。当Jacobian矩阵$D(\frac ϕx)=0$满足一定的条件时，点缺陷的演化过程中存在分支过程。
Solving topological defects via fusion
二维可积模型中的可积亏损是纯传递的，因此是拓扑的。通过融合它们的可积边界新的可积边界条件可以产生，并从两个解决边界理论的比较，可以提取明确的解决方案的缺陷模型。利用这一思想确定了sinh-Gordon和Lee-Yang模型中拓扑缺陷的透射因子和缺陷能量。在sinh-Gordon情形下，用拉格朗日微扰理论计算了透射因子，而用缺陷热力学Bethe方程计算了缺陷能量，该方程用于描述圆柱体上对角缺陷系统的基态能量.通过确定Lee-Yang模型中缺陷束缚态的谱，分析并封闭了缺陷自举方程。
Higgsed antisymmetric tensors and topological defects
我们找到了具有反对称张量场的广义Higgs模型的运动方程的拓扑亏损解。这些解是四维规范场的Nielsen-Olesen涡旋解的直接高维类似物。
Fusion of Integrable Defects and the Defect $g$-Function
本文研究了二维可积量子场论中可积线缺陷的精确缺陷g函数，并利用它们探测缺陷融合。研究了三种情况：纯传输拓扑缺陷的融合、非拓扑缺陷与反射和传输的融合，以及缺陷与可积边界之间的融合。对于拓扑缺陷，分离的对数g函数是加法的，融合极限由传输因子的乘法组合控制。对于非拓扑缺陷，分离依赖的相位在Bethe-Yang方程中产生振荡的有限尺寸效应，而融合的缺陷由有效的反射和传输振幅描述。在本文研究的Ising例子中，涉及非拓扑缺陷的融合降低了有限局部贡献到熵的值，而拓扑缺陷-边界融合则保持不变。
I explain how conventional topological defects -- the Abrikosov-Nielsen-Olesen (ANO) string and domain walls -- can acquire non-Abelian moduli localized on their world sheets. The set-up is conceptually similar and generalizes that used by Witten for cosmic strings.
We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on boundary condition changing fields. Special care is devoted to the general case when nontrivial multiplicities arise upon defect action. Surprisingly the fusion algebra of defects is realized on open string fields only up to a (star algebra) isomorphism.
This is the second part of two papers where we study the effect of integrable line defects on bipartite entanglement entropy in integrable field theories. In this paper, we consider non-topological line defects in Ising field theory. We derive an infinite series expression for the entanglement entropy and show that both the UV and IR limits of the bulk entanglement entropy are modified by the line defect. In the UV limit, we give an infinite series expression for the coefficient in front of the logarithmic divergence and the exact defect $g$-function. By tuning the defect to be purely transmis…
Topological defects for the free boson CFT
两种不同的共形场论可以沿着一条缺陷线结合在一起。我们研究这样的缺陷的情况下，共形场论的任何一方是单一的自由玻色子紧化在一个圆。我们专注于拓扑缺陷的左，右移动维拉索罗代数分别保存，但不一定有任何额外的对称性。对于两个半径都是自对偶半径的有理倍数的情况，我们对这些拓扑缺陷进行了分类。我们还证明了两个T-对偶自由玻色子共形场论之间的同构可以用拓扑亏损的作用来描述，从而T-对偶可以理解为一种特殊类型的有序-无序对偶.
Instanton-Induced Supersymmetry Breaking in Topological Semimetals
本研究将超对称量子力学引入拓扑半金属体系，发现瞬子诱导的动力学超对称破缺是半金属相打开能隙的机制，给出能隙打开的简单判据，且极小磁场即可在拓扑半金属中打开能隙，为拓扑半金属研究提供新方向。
The U(1) Topological Gauge Field Theory for Topological Defects in Liquid Crystals
考虑指向矢反演下U（1）规范场不变性，构造了一种新的液晶拓扑缺陷的U（1）拓扑规范场理论.利用U（1）规范势分解理论和$ϕ$ -映射拓扑流理论，得到了液晶中U（1）规范场的分解表达式和单极子与弦的统一拓扑流.结果表明，磁单极子与弦处于不同的空间维，它们的拓扑荷就是$ϕ$ -映射的缠绕数。
We examine codimension--1 topological defects whose associated worldline is geodesically embedded in $\AdS_{2}$. This discussion extends a previous study of exact analytical solutions to the equations of motion of topological defects in $\AdS_{n}$ in a particular limit where the masses of the scalar and gauge field vanish. We study the linear perturbations about the zeroth order kink-like solution and verify that they are stable. We also discuss general features of the perturbation expansion to all orders.
I discuss the possibility of topological defect solutions in field theories containing a tensor field which spontaneously breaks Lorentz symmetry. I find that for theories of a tensor with rank r <= 5 and for which the vacuum manifold consists of the tensors whose "square" is some constant value, only three types of tensor (vectors, antisymmetric two-tensors, and symmetric two-tensors) have the appropriate vacuum manifold topology to support topological defects. Of these, topological defect solutions can be easily constructed for two: vector domain wall solutions and antisymmetric tensor monop…
WDVV-like equations in N=2 SUSY Yang-Mills Theory
预势$F(a_i)$定义了$SU(N)$ ${\cal N}=2$ SUSY Yang-Mills理论的低能有效作用量，对于任何三重$i,j,k = 1,\ldots,N-1$，满足一组扩大的WDVV类方程$F_iF_k^{-1}F_j = F_jF_k^{-1}F_i$，其中矩阵$F_i$等于$(F_i)_{mn} = \partial^3 F/\partial a_i\partial a_m\partial a_n$。同样的方程实际上也适用于一般拓扑理论。与传统的公式相反，当$k$被限制为$k=0$时，在所提出的系统中没有明显的“第一”时间变量，并且指数可以在任何"度量“$η_{mn}^{(k)} = (F_k)_{mn}$的帮助下提高，而不是强制性的平坦。所有方程（对于所有$i,j,k$）同时为真。这一结果提供了一个新的平行之间的Seiberg-Witten理论的低能规范模型在$4d$和拓扑理论。
Towards a covariant canonical formulation for closed topological defects without boundaries
在量子化正则形式的协变描述的基础上，我们给出了在弯曲背景时空上传播的一类受限拓扑缺陷的辛几何的基本元素。我们讨论了目前的结果的未来扩展。
We study conformal defects in two important examples of string theory orbifolds. First, we show that topological defects in the language of Landau-Ginzburg models carry information about the RG flow between the non-compact orbifolds $\mathbb{C}/\mathbb{Z}_d$. Such defects are shown to correctly implement the bulk-induced RG flow on the boundary. Secondly, we study what the possible conformal defects are between the $c=1$ bosonic 2D conformal field theories with target space $S^1/\mathbb{Z}_2$. The defects cataloged here are obtained from boundary states corresponding to D-branes in the $c=2$ f…
Non BPS topological defect associated with two coupled real field
研究了一个由两个耦合实标量场表示的势模型所对应的包含两分量本征函数的稳定性方程，该方程具有非BPS拓扑缺陷。
We explore perturbations to a kink-like (codimension 1) topological defect whose world brane is $AdS_{q}$ embedded into $AdS_{q+1}$. Previously, we found solutions in the limit the mass of the scalar field vanishes. In this article we extend a calculation previously done in $AdS_{2}$ to higher-dimensional embedding spaces and find that all perturbations to the mass of the field are stable to first order as expected in a theory with topological defects. We find that the equation of motion to the correction strongly resembles a problem well-known in quantum mechanics.
Dirichlet Topological Defects
我们提出了一类场论，其特点是当拓扑缺陷与其他相等或更高维的缺陷相交时，可以终止拓扑缺陷的孤子解。这样的结构可以称为"狄利克雷拓扑缺陷“，类似于弦论的D膜。我们的讨论集中在（3+1）维中具有规范对称性或整体对称性的标量场中的缺陷;考虑的缺陷类型包括墙对墙、弦对墙、弦对弦。
Topological Defects and the Trial Orbit Method
本文讨论了两个实标量场模型中拓扑缺陷的存在。我们评论的缺陷托管拓扑缺陷，我们寻找明确的缺陷的解决方案，使用试轨法。我们知道，在某些情况下，二阶运动方程可以用一阶微分方程求解。在这种情况下，我们表明，试验轨道方法可以非常有效地获得明确的解决方案。
Unification of Laughlin and Moore-Read States in SUSY Quantum Hall Effect
基于最近提出的超对称量子霍尔效应，我们证明了Laughlin态和Moore-Read态之间存在一个隐含的超对称变换。以超对称Laughlin波函数作为主波函数，Laughlin态和Moore-Read态作为分量波函数的两个极限。本文还讨论了在超对称性理论中实现Laughlin态和Moore-Read态的拓扑激发。我们发展了超对称量子霍尔效应的一个投影公式。通过对Grassmann奇坐标的解释，我们发现超对称量子霍尔效应与超流性有着惊人的相似性。
Textures and Semi-Local Strings in SUSY Hybrid Inflation
全球拓扑缺陷可能解释了在宇宙微波背景中观测到的大冷点。我们探讨了构建超对称F项混合暴胀模型的可能性，其中瀑布场是全局SU（2）对称的。与SU（2）规范化的情况相反，出现了戈德斯通玻色子和附加模量，它们只被软超对称破缺标度的质量提升。该模型预测了全局纹理的存在，如果瀑布场在U（1）_X下规范，则全局纹理可以变成半局部字符串。如果通过轻SU（2）模或右手中微子进行再加热，可以避免引力子的过度产生。当暴胀子-瀑布耦合的值大于等于10^-4时，暴胀产生的功率谱的归一化所施加的对称性破缺尺度与解释最显著的冷点所需的能量尺度相吻合。在这种情况下，密度波动的频谱接近尺度不变，这可以通过包含由于拓扑缺陷而导致的次主导分量来与功率谱的测量值相协调。
The structure of extrinsic defects in topologically ordered states of matter is host to a rich set of universal physics. Extrinsic defects in 2+1 dimensional topological states include line-like defects, such as boundaries between topologically distinct states, and point-like defects, such as junctions between different line defects. Gapped boundaries in particular can themselves be \it topologically \rm distinct, and the junctions between them can localize topologically protected zero modes, giving rise to topological ground state degeneracies and projective non-Abelian statistics. In this pa…
I generalize the theory of phonon topological band structures of isostatic lattices to frustrated antiferromagnets. I achieve this with a discovery of a many-body supersymmetry (SUSY) in the phonon problem of balls and springs and its connection to local constraints satisfied by ground states. The Witten index of the SUSY model demands the Maxwell-Calladine index of mechanical structures. "Spontaneous supersymmetry breaking" is identified as the need to gap all modes in the bulk to create the topological isostatic lattice state. Since ground states of magnetic systems also satisfy local constr…
We consider the broken phase of the n-vector model in n+1 dimensions with boundary conditions enforcing the presence of topological defect lines (Ising domain walls, XY vortex lines, and so on), and use field theory to argue an exact expression for the order parameter.
SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry
本文综述了超对称量子霍尔效应的最新研究进展[hep-th/0409230，hep-th/0411137，hep-th/0503162，hep-th/0606007，arXiv：0705.4527]。我们引入了超流形上量子霍尔效应的超对称表述。在超球和超平面上，我们分别研究了超对称朗道问题，明确地构造了Laughlin波函数的超对称延拓和拓扑激发。非反对易几何在最低朗道能级自然出现，并为超对称量子霍尔效应带来特殊的物理性质。结果表明，超对称性提供了一个统一的图片的原始劳克林和摩尔-里德状态。基于电荷-通量对偶性，我们还发展了超对称量子霍尔效应的陈-西蒙斯有效场论。
A topological defect separating a pair of two-dimensional CFTs is a codimension one interface along which all components of the stress-energy tensor glue continuously. We study topological defects of the bosonic, (0,1)- and (0,2)-supersymmetric sigma models in two dimensions. We find a geometric classification of such defects closely analogous to that of A-branes of symplectic manifolds, with the role of symplectic form played instead by a neutral signature metric. Alternatively, we find a compact description in terms of a generalized metric on the product of the targets. In the (0,1) case, we…
Lectures on Cosmic Topological Defects
这些讲座回顾某些拓扑缺陷和他们的宇宙学方面。非常规材料包括对电弱缺陷的简要描述，非阿贝尔理论中的畴壁结构，以及SU（5）大统一理论中的磁单极子谱。
We explore topological defects in the 4-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. This theory has 1-form $\mathbb{Z}_{2}$ center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW duality topological defects in the similar way to that constructed by Aasen, Mong, Fendley arXiv:1601.07185 for the 2-dimensional Ising model. These duality defects turn out to be non-invertible. We also construct the 1-form $\mathbb{Z}_{2}$ symmetry defects as well as the junctions among KWW duality defects and 1-form $\mathbb{Z}_{2}$ center symmetry defects. The crossing …
Topological defects attract much recent interest in high-energy and condensed matter physics because they encode (non-invertible) symmetries and dualities. We study codimension-1 topological defects from a hamiltonian point of view, with the defect location playing the role of `time'. We show that the Weinstein symplectic category governs topological defects and their fusion: each defect is a lagrangian correspondence, and defect fusion is their geometric composition. We illustrate the utility of these ideas by constructing S- and T-duality defects in string theory, including a novel topology-…
Periodically driven (Floquet) systems have been under active theoretical and experimental investigations. This paper aims at a systematic study in the following aspects of Floquet systems: (i) A systematic formulation of topological invariants of Floquet systems based on the cooperation of topology and symmetries. Topological invariants are constructed for the ten symmetry classes in all spatial dimensions, for both homogeneous Floquet systems (Floquet topological insulators and superconductors) and Floquet topological defects. Meanwhile, useful representative Dirac Hamiltonians for all the sy…
Topological Incarnations of Electroweak Defects
我们提出了一个标准分类的混合缺陷发生在场论模型，如标准电弱模型。这个判据使我们考虑电弱模型的最小扩展，其中电弱磁单极子和$Z$ -弦是拓扑的。我们简要地讨论这种缺陷的宇宙学。
Formation of Topological Defects
在这些讲座中，我回顾宇宙相变和自发对称性破缺的拓扑方面。然后，我讨论了形成的墙壁，字符串和单极相变，包括晶格为基础的研究缺陷的形成和最近的尝试超越晶格。阐述了缺陷形成与渗流的密切联系。开放的问题和可能的未来方向。
Boundary conditions and defects of any codimension are natural parts of any quantum field theory. Surface defects in three-dimensional topological field theories of Turaev-Reshetikhin type have applications to two-dimensional conformal field theories, in solid state physics and in quantum computing. We explain an obstruction to the existence of surface defects that takes values in a Witt group. We then turn to surface defects in Dijkgraaf-Witten theories and their construction in terms of relative bundles; this allows one to exhibit Brauer-Picard groups as symmetry groups of three-dimensional …
Translation invariant defects as an extension of topological symmetries
本文指出2d QFT中的拓扑缺陷可扩展为平移不变缺陷，后者构成包含前者的张量范畴，并通过手征三维TFT给出微扰描述，证明在Ising和Lee-Yang CFT变形中仍有平移不变缺陷存留。
Supersymmetry (SUSY) is a symmetry transforming bosons to fermions and vice versa. Indications of its existence have been extensively sought after in high-energy experiments. However, signatures of SUSY have yet to be detected. In this manuscript we propose a condensed matter realization of SUSY on the edge of a Read-Rezayi quantum Hall state, given by filling factors of the form $ν=\frac{k}{k+2}$, where $k$ is an integer. As we show, this strongly interacting state exhibits an $\mathcal{N}=2$ SUSY. This allows us to use a topological invariant - the Witten index - defined specifically for sup…
Motivated by the three-dimensional topological field theory / two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, that can give rise to an enormously rich (and largely unexplored) space of two-dimensional critical theories in the thermodynamic limit. One remarkable feature of these systems is the appearance of non-local microscopic "topological symmetries" that descend to topological defects of the resulting CFTs. We derive various model-independent properties of these theories and of this to…
Non-Topological Inflation from Embedded Defects
我们在弦论的背景下讨论了一种获得宇宙膨胀周期的新机制。这种机制是基于嵌入的缺陷，动态地形成在高维D膜。这些缺陷产生拓扑膨胀，但与稳定缺陷的拓扑膨胀不同，这里有一个自然的优雅的膨胀出口：嵌入缺陷的衰变。我们证明了一个膜的背景下，反膜湮灭过程的想法。这里提出的优美退出机制一般适用于D-膜上暴胀的所有实现。
We propose an experimentally feasible scheme for topological interface engineering and show how it can be used for studies of dynamics of topologically nontrivial interfaces and perforation of defects and textures across such interfaces. The method makes use of the internal spin structure of the atoms together with locally applied control of interaction strengths to create many-particle states with highly complex topological properties. In particular, we consider a constructed coherent interface between topologically distinct phases of spinor Bose-Einstein condensates.
We present a mathematical derivation of some of the most important physical quantities arising in topological bilayer systems with permutation twist defects as introduced by Barkeshli et al. in cond-mat/1208.4834. A crucial tool is the theory of permutation equivariant modular functors developed by Barmeier et al. in math.CT/0812.0986 and math.QA/1004.1825.
We study the diffusion processes of a real scalar field in the presence of the distorsion field induced by a chiral topological defect. The defect modifies the usual Euclidean background geometry into a non-diagonal Riemann-Cartan geometry characterized by a singular torsion field. The new form of the diffusion equation is established and the scalar field distribution in the vicinity of the defect is investigated numerically. Results show a high sensitivity to the boundary conditions. In the transient regime, we find that the defect vorticity generates an angular momentum associated to the dif…
Entanglement Through Topological Defects: Reconciling Theory with Numerics
本文通过引入新的减少密度矩阵制备方法，解决了拓扑缺陷与纠缠熵理论预测之间的矛盾，并展示了其在Ising模型中对群状和对偶缺陷的有效性。
In this paper we study Weyl fermions in a family of Gödel-type geometries in Einstein general relativity. We also consider that these solutions are embedded in a topological defect background. We solve the Weyl equation and find the energy eigenvalues and eigenspinors for all three cases of Gödel-type geometries where a topological defect is passing through them. We show that the presence of a topological in these geometries contributes to modification of the spectrum of energy. The energy zero modes for all three cases of the Gödel geometries are discussed.
Topological Defects in 3-d Euclidean Gravity
利用SO（3）自旋联络的完全分解，详细研究了三维欧氏引力的拓扑亏损。给出了向错的拓扑结构，它是一个涡结构和一个旋结构的组合。在三维Chern-Simons理论中，讨论了由涡旋和涡生成的卡茨-穆迪代数.
Phase separation seeded by Z2 and U(1) topological defects from holography
利用全息双淬火协议，研究自发对称破缺与相分离动力学的相互作用，发现拓扑缺陷作为相分离的动力学种子，且不同对称性下表现出普适动力学行为。
Lattice Topological Defects in Non-Unitary Conformal Field Theories
研究非单位ary共形场理论中拓扑缺陷的构造与特性，利用受限固体-固体模型变种进行数值和解析计算，分析能量谱、缺陷算子本征值及热力学特性，并探讨不同固定点间的重整化群流。
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