Singular Dimensions of the¶N= 2 Superconformal Algebras. I

Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras. We prove several general results on the ordering kernels associated to the adapted orderings and show that the size of an ordering kernel implies an upper limit for the dimension of a singular vector space. We apply this method to the topological N= 2 algebra and obtain the maximal dimensions of the singular vector spaces in the topological Verma modules: 0, 1, 2 or 3 depending on the type of Verma module and the type of singular vector. As a consequence we prove the conjecture of Gato-Rivera and Rosado on the possible existing types of topological singular vectors (4 in chiral Verma modules and 29 in complete Verma modules). Interestingly, we have found two-dimensional spaces of singular vectors at level 1. Finally, by using the topological twists and the spectral flows, we also obtain the maximal dimensions of the singular vector spaces for the Neveu–Schwarz N= 2 algebra (0, 1 or 2) and for the Ramond N= 2 algebra (0, 1, 2 or 3). Received: 19 August 1998 / Accepted: 15 March 1999     

Computations of ¶in the 2-d O(N) Non-Linear σ-Model

We review the various computations of the ratio of the mass gap M to the Λ-parameter entering the perturbative computations of amplitudes at high energies in the O(n) non-linear σ-model. In particular we reproduce from original notes of H. Lehmann his computation of this ratio in the (next–to) leading order of the 1/n expansion. Received: 23 March 2000 / Accepted: 10 April 2000     

c=3, N=2 超共形场论的Z2 Orbifold-Prime模型

讨论了二维环面上中心荷c=3, N=2 的超共形场论. 特别给出该理论的配分函数. 进一步,为了产生新的模型,回顾了一般的orbifold方法. 然后构造了模不变的Z2 Orbifold-Prime模型.     

TheΔN=2 interaction and one-nucleon transfer reactions

Influence of theN=2 interaction on the one-nucleon transfer reactions is considered. The expressions for the (d, p) and (d, t) differential cross sections are derived in terms of the DWBA theory. Some modifications of obtained expressions convenient for numerical calculations are discussed.     

N=2 superstrings in more than two dimensions?

For a string propagating in a Parisi-Sourlas superspace the critical dimension equals the difference in the number of positive-and negative-dimensional coordinates. In this way the dimension of the Minkowski subspace can be increased. Here we apply this to the N=2 superstring, with D_c=2 and find anomaly-free N=2 superstrings in all positive even dimensions. Nontrivial theories can be constructed from these N=2 theories by truncation: In a Parisi-Sourlas superspace with a ten-dimensional Minkowski subspace we find the N=1 NSR superstring, and with a four-dimensional Minkowski subspace we find an N=1 superstring, classically related to the D=10 NSR superstring by a canonical transformation.     

A heterotic N=2 string with space–time supersymmetry

We reconsider the issue of embedding space–time fermions into the four-dimensional N=2 worldsheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N=4 topological extension of the conventional N=2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U(1,1), just as in the usual N=2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1,0) supersymmetry.     

N=4超对称量子力学

利用Clifford代数构造了N=4超对称量子力学的一般形式,并讨论了它的实现.     

Birkhoff’s Polytope and Unistochastic Matrices,N = 3 and N = 4

The set of bistochastic or doubly stochastic N×N matrices is a convex set called Birkhoff’s polytope, which we describe in some detail. Our problem is to characterize the set of unistochastic matrices as a subset of Birkhoff’s polytope. For N=3 we present fairly complete results. For N=4 partial results are obtained. An interesting difference between the two cases is that there is a ball of unistochastic matrices around the van der Waerden matrix for N=3, while this is not the case for N=4.     

On Twisted N = 2 5D Super Yang–Mills Theory

On a five-dimensional simply connected Sasaki–Einstein manifold, one can construct Yang–Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however, the contact instanton equations are not elliptic. It turns out that these equations can be embedded into the Haydys–Witten equations (which are elliptic) in the same way the 4D anti-self-dual instanton equations are embedded in the Vafa–Witten equations. We show that under some favourable circumstances, the latter equations will reduce to the former by proving some vanishing theorems. It was also known that the Haydys–Witten equations on product manifolds \({M_5 = M_4 \times \mathbb{R}}\) arise in the context of twisting the 5D maximally supersymmetric Yang–Mills theory. In this paper, we present the construction of twisted N = 2 Yang–Mills theory on Sasaki–Einstein manifolds, and more generally on K-contact manifolds. The localisation locus of this new theory thus provides a covariant version of the Haydys–Witten equation.     

N=2超对称量子力学的新实现和形状不变性

构造新的超荷和定义权重函数,并研究了N=2一维超对称量子力学.在新的实现中讨论了若干实例.     

BPS States of D=4 ␣N=1 Supersymmetry

We find the combinations of momentum and domain-wall charges corresponding to BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how the supersymmetry algebra implies their stability. These states form the boundary of the convex cone associated with the Jordan algebra of 4× 4 real symmetric matrices, and we explore some implications of the associated geometry. For the Wess–Zumino model we derive the conditions for preservation of 1/4 supersymmetry when one of two parallel domain-walls is rotated and in addition show that this model does not admit any classical configurations with 3/4 supersymmetry. Our analysis also provides information about BPS states of N=1 D=4 anti-de Sitter supersymmetry. Received: 6 April 2000/ Accepted: 10 September 2000     

N=2超对称大统一理论中规范破缺注记

本文讨论了用N=2超对称有限理论建立现实大统一模型的可能性. 发现规范对称自发破缺和超对称破缺是可以实现的, 但在夸克轻子质量问题上遇到困难.     

Complete N=4 structure of low-energy effective action in N=4 super-Yang–Mills theories

Using the $\text{N}\text{=2}$ superfield approach, we construct full $\text{N}\text{=4}$ supersymmetric low-energy effective actions for $\text{N}\text{=4}$ SYM models, with both $\text{N}\text{=2}$ gauge superfield strengths and hypermultiplet superfields included. The basic idea is to complete the known non-holomorphic effective potentials which depend only on $\text{N}\text{=2}$ superfield strengths W and W̄ to the full on-shell $\text{N}\text{=4}$ invariants by adding the appropriate superfield hypermultiplet terms. We prove that the effective potentials of the form $\text{ln}\text{W}\text{ln}\text{W}\text{̄}$ can be $\text{N}\text{=4}$ completed in this way and present the precise structure of the corresponding completions. However, the effective potentials of the non-logarithmic form suggested in hep-th/9811017 and hep-th/9909020 do not admit the $\text{N}\text{=4}$ completion. Therefore, such potentials cannot come out as (perturbative or non-perturbative) quantum corrections in $\text{N}\text{=4}$ SYM models.     

N=Z原子核性质的研究

论述了N=Z核实验和理论研究的历史和现状在,N=Z,是研究T=0对关联最好的核区,实验表明T=0和n-p对关联起着重要的作用,理论研究知心朋友同时包括T=0和T=1的对关联,是研究它们之间竞争及相变。 The history and current status of the study of N=Z nuclei are reviewed. T=0 n p pairing correlation is expected to play an important role in the structure of the nuclei along N=Z line. Both T=0 and T=1 pairing modes should be included in the theoretical models. Phenomena like possible competition and phase transition between different pairing modes are becoming important issues in nuclear structure.