Superconformal invariants and extended supersymmetry

The superconformal invariants in analytic superspace are found. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant holomorphic sections of a line bundle on a product of certain harmonic superspaces. It is argued that the correlation functions for a class of sufficiently low dimension gauge invariant operators in N = 2 and N = 4 supersymmetric Yang-Mills theory can be evaluated up to constants.     

Heterotic modular invariants and level-rank duality

New heterotic modular invariants are found using the level-rank duality of affine Kac-Moody algebras. They provide strong evidence for the consistency of an infinite list of heterotic Wess-Zumino-Witten (WZW) conformal field theories. We call the basic construction the dual-flip, since it flips chirality (exchanges left and right movers) and takes the level-rank dual. We compare the dual-flip to the method of conformal subalgebras, another way of constructing heterotic invariants. To do so, new level-one heterotic invariants are first bound; the complete list of a specified subclass of these is obtained. We also prove (under a mild hypothesis) an old conjecture concerning exceptional A_r,k invariants and level-rank duality.     

Galois modular invariants of WZW models

The set of modular invariants that can be obtained from Galois transformations is investigated systematically for WZW models. It is shown that a large subset of Galois modular invariants coincides with simple current invariants. For algebras of type B and D infinite series of previously unknown exceptional automorphism invariants are found.     

Automorphism modular invariants of current algebras

We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some untwisted affine Lie algebra at fixed level. In this case the partition function is specified by an automorphism of the fusion ring and corresponding symmetry of the Kac-Peterson modular matrices. We classify all such partition functions when the underlying finite-dimensional Lie algebra is simple. This gives all possible spectra for this class of RCFTs. While accomplishing this, we also find the primary fields with second smallest quantum dimension.Supported in part by NSERC.     

On the classification of diagonal coset modular invariants

We relate in a novel way the modular matrices of GKO diagonal cosets without fixed points to those of WZNW tensor products. Using this we classify all modular invariant partition functions ofsu(3) _k su(3)₁/su(3) _k+1 for all positive integer levelk, andsu(2) _k su(2) _l /su(2) _k+1 for allk and infinitely manyl (in fact, for eachk a positive density ofl). Of all these classifications, only that forsu(2) _k su(2)₁/su(2) _k+1 had been known. Our lists include many new invariants.Supported in part by NSERC.     

Conformal embeddings,rank-level duality and exceptional modular invariants

We compute the branching rules of the conformal embeddingsSO(4nk)₁Sp(2n) _k Sp(2k) _n andSO(rq) ₁SO(r) _q SO(q) _r forrq even. Using this we prove that the affine algebrasSp(2n) _k andSp(2k) _n have the sameS matrix and modular invariants. As a second application, we show how the triality ofSO(8) leads to an exceptional modular invariant forSU(2) at level 16 and for allSO(q4) at level 8.chargé de recherches du FNRS     

The axial gauge and supersymmetry

We examine the supersymmetry Ward identity for supersymmetric Yang-Mills theories in the axial gauge. In the pure N = 1 (no matter) case the Ward identity leads to supersymmetric counterterms to all orders. This result does not survive the introduction of matter fields, however, and we therefore conclude that the gauge is not useful in the context of supersymmetry.     

Half-sided modular inclusion and the construction of the Poincaré group

In this note we will give a construction of the Poincaré group out of the modular groups of the wedge algebras provided the groups act on the algebra of every double cone like the associated Lorentz boosts. This construction will use the concept of half-sided modular inclusions instead of the first and second cohomology of the Poincaré group as used by Brunetti, Guido and Longo. By our method we obtain directly the Poincaré group and not its covering group.     

The status of supersymmetry phenomenology

In this brief review the following topics are discussed: Direct searches for SUSY in mSUGRA: a brief review of the relevant mass limits, the clean trilepton signal, the hunt for the third generation of sfermions, Direct searches beyond mSUGRA: search prospects in models with nonuniversal gaugino masses, search prospects in models with nonuniversal scalar masses, Indirect searches for SUSY: precision electroweak observables and SUSY, ε′/ε and SUSY.     

The spinorial charges of supersymmetry and twisters

We investigate the precise connection between the spinorial charges of the original supersymmetry algebra of Wess and Zumino and the twisters of Penrose.     

转动相对论Birkhoff约束系统积分不变量的构造

研究转动相对论Birkhoff约束系统积分不变量的构造首先,建立转动相对论系统的约束Birkhoff方程;其次,利用等时变分与非等时变分之间的关系建立系统的非等时变分方程;然后,研究转动相对论Birkhoff约束系统的第一积分与积分不变量之间的关系,证明由系统的一个第一积分可以构造一个积分不变量,并给出自由Birkhoff系统的相应结果;最后,讨论转动相对论Hamilton系统、相对论Birkhoff系统和Hamilton系统、经典转动系统和等时变分情形下的积分不变量的构造,结果表明相关的结论均为该定理的特款给出一个例子说明结果的应用 关键词： 转动相对论 Birkhoff系统 约束 第一积分 积分不变量     

超对称准经典近似和本征值问题

运用超对称准经典近似方法给出三维谐振子、氢原子的能谱,进而将该方法用于含角坐标的二阶微分方程,得到角动量平方L2的本征值和非中心势的角向本征值.     

The generalized zero-mode supersymmetry scheme and the confluent algorithm

We show the relationship between the mathematical framework used in recent papers by Rosu et al. (2014) [1–3] and the second-order confluent supersymmetric quantum mechanics. In addition, we point out several immediate generalizations of the approach taken in the latter references. Furthermore, it is shown how to apply the generalized scheme to the Dirac and to the Fokker–Planck equation.     

Temperature and supersymmetry

We study equal-time correlation functions at finite temperature in field theories with global supersymmetry. Global supersymmetry is found to be broken at finite temperature; the ground state is not supersymmetric but no Goldstone fermion appears. The temperature dependence of the mass spectrum in the one-loop approximation and leading order in temperature is investigated in several models. In the models that we consider with spontaneous supersymmetry breaking we find that the Goldstone fermion remains massless at the one-loop level. Ward identities describing the supersymmetry of the underlying theory are checked at the one-loop level. We also discuss the situation in supergravity.     

Fractional supersymmetry as a superposition of ordinary supersymmetry

It is shown how to derive fractional supersymmetric quantum mechanics of order k as a superposition of k-1 copies of ordinary supersymmetric quantum mechanics.