On Wess–Zumino gauge

In the relation between the linear (L) supersymmetry (SUSY) representation and the nonlinear (NL) SUSY representation we discuss the role of the Wess–Zumino gauge. We show in two-dimensional spacetime that a spontaneously broken LSUSY theory with mass and Yukawa interaction terms for a minimal off-shell vector supermultiplet is obtained from a general superfield without imposing any special gauge conditions in N=2$N=2$ NL/L SUSY relation.     

AdS3×S3 弦的可积性

从Rahmfeld和Rajaraman构造的在AdS₃×S³背景中具有κ对称的GS弦的作用量出发, 推导出AdS₃×S³弦的运动方程, 然后利用连续的扭曲对偶变换构造了带有自由参数λ的平联络, 利用这些平联络可进一步得到无穷多守恒量, 说明此系统是可积的.     

On the level-dependence of Wess–Zumino–Witten three-point functions

Three-point functions of Wess–Zumino–Witten models are investigated. In particular, we study the level-dependence of three-point functions in the models based on algebras su(3) and su(4). We find a correspondence with Berenstein–Zelevinsky triangles. Using previous work connecting those triangles to the fusion multiplicities, and the Gepner–Witten depth rule, we explain how to construct the full three-point functions. We show how their level-dependence is similar to that of the related fusion multiplicity. For example, the concept of threshold level plays a prominent role, as it does for fusion.     

Wess–Zumino supersymmetric phase and superconductivity in graphene

Supersymmetry is expected to exist in nature at high energies, but must be spontaneously broken at ordinary energy scales. The required energy scale in elementary particle physics is currently inaccessible, but condensed matter could furnish low energy realizations of supersymmetry. In graphene, electrons behave as ‘relativistic’ massless fermions in 1+2$1+2$ dimensions. Here we propose phenomenologically, assuming that some microscopic parameters can be fine-tuned in graphene, the existence of a supersymmetric Wess–Zumino phase. The supersymmetry breaking leads to a superconductor phase, described by a relativistic Ginzburg–Landau phenomenology.     

Si中S0/Se0,S0/Te0和Se0/Te0对的电子结构

利用紧束缚近似下的格林函数方法,讨论了Si中硫属元素混对杂质(即S⁰/Se⁰,S⁰/Te⁰和Se⁰/Te⁰)基态的电子结构。混对杂质在Si禁带中引入两个A₁能级,其中成键性的A₁能级位置在反键性的A₁能级之上。数值计算得到的混对杂质能级与实验符合得相当好。理论分析表明,在Si中测到的那些未定的比最近邻混对杂质能级更浅的能级(S⁰/Se⁰(X₁),S⁰/Te⁰(X₁),Se⁰/Te⁰(X₁)…)不是由非最近邻位型的混对杂质引入的。本文还指出了一个极性分子放入Si晶体中,两个不同原子间s波函数的转移方向与通常极性分子相反,并讨论其物理原因。 关键词：     

Noncommutative Wess–Zumino–Witten actions and their Seiberg–Witten invariance

We analyze the noncommutative two-dimensional Wess–Zumino–Witten model and its properties under Seiberg–Witten transformations in the operator formulation. We prove that the model is invariant under such transformations even for the noncritical (non-chiral) case, in which the coefficients of the kinetic and Wess–Zumino terms are not related. The pure Wess–Zumino term represents a singular case in which this transformation fails to reach a commutative limit. We also discuss potential implications of this result for bosonization.     

Chern–Simons,Wess–Zumino and other cocycles from Kashiwara–Vergne and associators

Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern–Simons field theory and in the theory of anomalies. The second Chern class (the first Pontrjagin class) is defined as \(p= \langle F, F\rangle \) where F is the curvature 2-form and \(\langle \cdot , \cdot \rangle \) is an invariant scalar product on the corresponding Lie algebra \(\mathfrak g\). The descent for p gives rise to an element \(\omega =\omega _3+\omega _2+\omega _1+\omega _0\) of mixed degree. The 3-form part \(\omega _3\) is the Chern–Simons form. The 2-form part \(\omega _2\) is known as the Wess–Zumino action in physics. The 1-form component \(\omega _1\) is related to the canonical central extension of the loop group LG. In this paper, we give a new interpretation of the low degree components \(\omega _1\) and \(\omega _0\). Our main tool is the universal differential calculus on free Lie algebras due to Kontsevich. We establish a correspondence between solutions of the first Kashiwara–Vergne equation in Lie theory and universal solutions of the descent equation for the second Chern class p. In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara–Vergne equation F is mapped to \(\omega _1=C(F)\). Furthermore, the component \(\omega _0\) is related to the associator \(\Phi \) corresponding to F. It is surprising that while F and \(\Phi \) satisfy the highly nonlinear twist and pentagon equations, the elements \(\omega _1\) and \(\omega _0\) solve the linear descent equation.     

AdS5\otimes S1, AdS5\otimes S5和AdS2\otimes S2超弦模型的一种KRR参数化新方法

给出了3种典型超弦模型AdS₅\otimes S¹, AdS₅\otimes S⁵和AdS₂\otimes S²的一种简单的KRR参数化新方法, 并结合这些超弦模型所具有的κ对称性给出了它们的卡当1-form, Maurer-Cartan方程, 作用量和运动方程.     

$$\,$$ Fu–Kane–Mele invariant as Wess–Zumino action of the sewing matrix

We show that the Fu–Kane–Mele invariant of the 2d time-reversal invariant crystalline insulators is equal to the properly normalized Wess–Zumino action of the so-called sewing-matrix field defined on the Brillouin torus. Applied to 3d, the result permits a direct proof of the known relation between the strong Fu–Kane–Mele invariant and the Chern–Simons action of the non-Abelian Berry connection on the bundle of valence states.     

Ar+, He+，S+离子轰击n-InP单晶表面的机理研究

通过X射线光电子能谱和低能电子衍射实验研究了10～180 eV的Ar⁺、 He⁺、S⁺离子轰击n-InP(100)表面, 发现S⁺离子轰击可以产生In-S组分,减轻离子轰击对表面的物理损伤.对于Ar⁺离子轰击后的表面,经过S⁺离子处理和加热过程以后,表面损伤得到了修复,最终得到了2×2的InP表面,进一步验证了S⁺离子对InP表面的修复作用.     

Si中S0对、Se0对和Te0对的电子结构

利用紧束缚近似下的格林函数方法,讨论了Si中(S⁰)₂,(Se⁰)₂及(Te⁰)₂基态的能级和波函数。分析了几种不同的观点。(S⁰)₂,(Se⁰)₂及(Te⁰)₂均在禁带中引入一个对称性的A_1g能级和一个反对称性的A_2u能级,二者都是填满的。现有实验观测到的是较高的A_1g能级。从理论上指出了对称性的A_1g能级反而高于反对称性的能级的原因。而Si中(Se₂)⁺的g因子测量值和(S₂)⁺,(Se₂)⁺的ESR实验结果也支持本文的观点。 关键词：     

Gauge-theoretic invariants for topological insulators: a bridge between Berry,Wess–Zumino,and Fu–Kane–Mele

We establish a connection between two recently proposed approaches to the understanding of the geometric origin of the Fu–Kane–Mele invariant \(\mathrm {FKM}\in \mathbb {Z}_2\), arising in the context of two-dimensional time-reversal symmetric topological insulators. On the one hand, the \(\mathbb {Z}_2\) invariant can be formulated in terms of the Berry connection and the Berry curvature of the Bloch bundle of occupied states over the Brillouin torus. On the other, using techniques from the theory of bundle gerbes, it is possible to provide an expression for \(\mathrm {FKM}\) containing the square root of the Wess–Zumino amplitude for a certain U(N)-valued field over the Brillouin torus. We link the two formulas by showing directly the equality between the above-mentioned Wess–Zumino amplitude and the Berry phase, as well as between their square roots. An essential tool of independent interest is an equivariant version of the adjoint Polyakov–Wiegmann formula for fields \(\mathbb {T}^2 \rightarrow U(N)\), of which we provide a proof employing only basic homotopy theory and circumventing the language of bundle gerbes.     

Three-Body Recombination of Cold 3He–3He–T- System

The atom-atom-anion three-body recombination(TBR) and collision induced dissociation(CID) processes of the ³He–³He–T^- system at ultracold temperatures are investigated by solving the Schr¨odinger equation in the adiabatic hyperspherical representation. The variations of the TBR and CID rates with the collision energies in the ultracold temperatures are obtained. It is found that the J^Π= 1^- symmetry dominates the TBR and CID processes in most...     

AdS5○×S5背景下IIB超弦的Dressing对称性及Affine可积性

在AdS5S5背景中,IIB超弦的运动方程与Maurer-Cartan方程在世界面上存在对偶对称性.通过引入扭曲对偶(twisteddual)的概念，将有限的对偶变换推广到连续的对偶变换，并给出了AdＳ5S5中IIB超弦的Lax联络及其可积的相容条件. 关键词： 扭曲对偶 κ对称性 Lax联络