Fixed point resolution in extensions of permutation orbifolds

We determine the simple currents and fixed points of the orbifold theory CFT⊗CFT/Z₂$\mathit{CFT}\otimes \mathit{CFT}/{\mathbb{Z}}_2$, given the simple currents and fixed point of the original CFT  . We see in detail how this works for the SUk₍₂₎$\mathit{SU}{(2)}_k$ WZW model, focusing on the field content (i.e. h  -spectrum of the primary fields) of the theory. We also look at the fixed point resolution of the simple current extended orbifold theory and determine the SJ$S^J$ matrices associated to each simple current for SU₂₍₂₎$\mathit{SU}{(2)}_2$ and for the B_1(n)$B{(n)}_1$ and D_1(n)$D{(n)}_1$ series.     

parafermionic current algebras of torus/orbifold models

We study the quantum field theory of bosons on the torus and the orbifold. When the torus is in special moduli, the representations of the theory are equivalent to those of some rational conformal field theories. We show that there are parafermonic current algebras in Z_N orbifold models.     

Simple currents and extensions of vertex operator algebras

We consider how a vertex operator algebra can be extended to an abelian interwining algebra by a family of weak twisted modules which aresimple currents associated with semisimple weight one primary vectors. In the case that the extension is again a vertex operator algebra, the rationality of the extended algebra is discussed. These results are applied to affine Kac-Moody algebras in order to construct all the simple currents explicitly (except forE ₈) and to get various extensions of the vertex operator algebras associated with integrable representations.Supported by NSF grant DMS-9303374 and a research grant from the Committee on Research, UC Santa Cruz.Supported by NSF grant DMS-9401272 and a research grant from the Committee on Research, UC Santa Cruz.     

Central extensions of quantum current groups

We describe Hopf algebras which are central extensions of quantum current groups. For a special value of the central charge, we describe Casimir elements in these algebras. New types of generators for quantum current algebra and its central extension for quantum simple Lie groups, are obtained. The application of our construction to the elliptic case is also discussed.     

Metastable kinks in the orbifold

We consider static configurations of bulk scalar fields in extra-dimensional models in which the fifth dimension is an S1/Z2 orbifold. There may exist a finite number of such configurations, with the total number depending on the size of the orbifold interval. We perform a detailed Sturm-Liouville stability analysis that demonstrates that all but the lowest-lying configurations--those with no nodes in the interval--are unstable. We also present a powerful general criterion with which to determine which of these nodeless solutions are stable. The detailed analysis underlying the results presented in this Letter, and applications to specific models, are presented in a comprehensive companion paper [M. Toharia and M. Trodden, arXiv:hep-ph/0708.4008].     

Characterizing invariants for local extensions of current algebras

ParisA of local quantum field theories are studied, whereA is a chiral conformal quantum field theory and is a local extension, either chiral or two-dimensional. The local correlation functions of fields from have an expansion with respect toA into conformal blocks, which are non-local in general. Two methods of computing characteristic invariant ratios of structure constants in these expansions are compared: (a) by constructing the monodromy representation of the braid group in the space of solutions of the Knizhnik-Zamolodchikov differential equation, and (b) by an analysis of the local subfactors associated with the extension with methods from operator algebra (Jones theory) and algebraic quantum field theory. Both approaches apply also to the reverse problem: the characterization and (in principle) classification of local extensions of a given theory.     

Central extensions of current groups in two dimensions

The paper is devoted to generalization of the theory of loop groups to the two-dimensional case. To every complex Riemann surface we assign a central extension of the group of smooth maps from this surface to a simple complex Lie group G by the Jacobian of this surface. This extension is topologically nontrivial, as in the loop group case. Orbits of coadjoint representation of this extension correspond to equivalence classes of holomorphic principalG-bundles over the surface. When the surface is the torus (elliptic curve), classification of coadjoint orbits is related to linear difference equations in one variable, and to classification of conjugacy classes in the loop group. We study integral orbits, for which the Kirillov-Kostant form is a curvature form for some principal torus bundle. The number of such orbits for a given level is finite, as in the loop group case; conjecturedly, they correspond to analogues of integrable modules occurring in conformal field theory.     

Simple millimeter wave notch filters based on rectangular waveguide extensions

A new efficient notch filter is proposed. Some details of notch filter operation at millimeter waves are discussed. A 110 GHz notch filter is numerically and experimentally tested.     

Comment on the generation number in orbifold compactifications

There has been some confusion concerning the number of (1, 1)-forms in orbifold compactifications of the heterotic string in numerous publications. In this note we point out the relevance of the underlying torus lattice on this number. We answer the question when different lattices mimic the same physics and when this is not the case. As a byproduct we classify all symmetricZ _N -orbifolds with (2, 2) world sheet supersymmetry obtaining also some new ones.Supported by Deutsche Forschungsgemeinschaft     

Topological orbifold models and quantum cohomology rings

We discuss the topological sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold ofCP ¹ by the dihedral groupD ₄, how to compute the complete ring of observables. Through this procedure, we compute all the rings of dihedralCP ¹ orbifolds. We then considerCP ²/D ₄, and show how the techniques of topologicalanti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds.Supported in part by Fannie and John Hertz Foundation     

同心球之间空间电荷限制电流的简单理论

在高功率微波二极管的设计中,空间电荷限制电流因其与二极管的特性及虚阴极形成关系密切而显得十分重要,虽然Langmuir和Blodgett给出的数值解十分有用,但是在实际的应用中一个简单的函数表达式还是更为方便,同时也可以避免当R_c/R_a很大时带来的级数发散问题.第一性原理已经应用在平行板和共轴圆柱之间二维空间电荷限制电流的推导,它的可靠性也已经得到了大量的验证.本文利用第一性原理推导出了同心球二极管空间电荷限制电流的解析表达式,其中的 关键词： 第一性原理 同心球二极管 空间电荷限制电流     

A hyper-chaos-based image encryption algorithm using pixel-level permutation and bit-level permutation

Recently, a number of chaos-based image encryption algorithms that use low-dimensional chaotic map and permutation-diffusion architecture have been proposed. However, low-dimensional chaotic map is less safe than high-dimensional chaotic system. And permutation process is independent of plaintext and diffusion process. Therefore, they cannot resist efficiently the chosen-plaintext attack and chosen-ciphertext attack. In this paper, we propose a hyper-chaos-based image encryption algorithm. The algorithm adopts a 5-D multi-wing hyper-chaotic system, and the key stream generated by hyper-chaotic system is related to the original image. Then, pixel-level permutation and bit-level permutation are employed to strengthen security of the cryptosystem. Finally, a diffusion operation is employed to change pixels. Theoretical analysis and numerical simulations demonstrate that the proposed algorithm is secure and reliable for image encryption.     

Classification of symmetry breaking by Wilson lines on the Z orbifold

We give a complete classification of gauge symmetry breaking by Wilson lines on the standard Z orbifold by deriving the general formula of the conditions of modular invariance and group invariance in the presence of background gauge fields. All possible E₆×SU(3) breaking in terms of one Wilson line is given. The symmetries of the electroweak and grand unification are obtained by combining two Wilson lines.     

Simple approach to the mesoscopic open electron resonator: quantum current oscillations

The open electron resonator, described by Duncan et al. [D.S. Duncan, M.A. Topinka, R.M. Westervelt, K.D. Maranowski, A.C. Gossard, Phys. Rev. B 64 (2001) 033310. [1]], is a mesoscopic device that has attracted considerable attention due to its remarkable behaviour (conductance oscillations), which has been explained by detailed theories based on the behaviour of electrons at the top of the Fermi sea. In this work, we study the resonator using the simple quantum quantum electrical circuit approach, developed recently by Li and Chen [Y.Q. Li, B. Chen, Phys. Rev. B 53 (1996) 4027. [2]]. With this approach, and considering a very simple capacitor-like model of the system, we are able to theoretically reproduce the observed conductance oscillations. A very remarkable feature of the simple theory developed here is the fact that the predictions depend mostly on very general facts, namely, the discrete nature of electric charge and quantum mechanics; other detailed features of the systems described enter as parameters of the system, such as capacities and inductances.