The SM as the quantum low-energy effective theory of the MSSM

In the framework of the minimal supersymmetric standard model we compute the one-loop effective action for the electroweak bosons obtained after integrating out the different sleptons, squarks, neutralinos and charginos, and present the result in terms of the physical sparticle masses. In addition we study the asymptotic behavior of the two-, three- and four-point Green's functions with external electroweak bosons in the limit where the physical sparticle masses are very large in comparison with the electroweak scale. We find that in this limit all the effects produced by the supersymmetric particles can either be absorbed in the standard model parameters and gauge bosons wave functions, or else they are suppressed by inverse powers of the supersymmetric particle masses. This work, therefore, completes the proof of decoupling of the heavy supersymmetric particles from the standard ones in the electroweak bosons effective action and in the sense of the Appelquist–Carazzone theorem; we started this proof in a previous work. From the point of view of effective field theories this work can be seen as a (partial) proof that the SM can indeed be obtained from the MSSM as the quantum low-energy effective theory of the latter when the SUSY spectra are much heavier than the electroweak scale. Received: 27 March 1999 / Revised version: 7 September 1999 / Published online: 27 January 2000     

Anomaly matching conditions and the moduli space of supersymmetric gauge theories

The structure of the moduli space of N = 1 supersymmetric gauge theories is analyzed from an algebraic geometric viewpoint. The connection between the fundamental fields of the ultraviolet theory, and the gauge-invariant composite fields of the infrared theory is explained in detail. The results are then used to prove an anomaly matching theorem. The theorem is used to study anomaly matching for supersymmetric QCD, and can explain all the known anomaly matching results for this case.     

Generalized recursion relations for correlators in the gauge-gravity correspondence

We show that a generalization of the Britto-Cachazo-Feng-Witten recursion relations gives a new and efficient method of computing correlation functions of the stress tensor or conserved currents in conformal field theories with an (d+1)-dimensional anti-de Sitter space dual, for d≥4, in the limit where the bulk theory is approximated by tree-level Yang-Mills theory or gravity. In supersymmetric theories, additional correlators of operators that live in the same multiplet as a conserved current or stress tensor can be computed by these means.     

闭路格林函数和非线性响应理论(Ⅰ)

本文是关于非线性响应理论的文章的前半部分。由闭路格林函数的生成泛函的展开式及闭路格林函数的变换关系导出非线性响应的一般表示式。从代数关系、KMS条件、时间反演不变性和谱表示等四个方面,提出寻求多点函数间关系的一般考虑。 关键词：     

Renormalization and symmetry conditions in supersymmetric QED

For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic renormalization. For practical calculations, a non-invariant regularization scheme may be used together with counterterms from all power-counting renormalizable interactions. From the Slavnov–Taylor identity, expressing gauge invariance, supersymmetry and translational invariance, simple symmetry conditions are derived that are important in a twofold respect: they establish exact relations between physical quantities that are valid to all orders, and they provide a powerful tool for the practical determination of the counterterms. We perform concrete one-loop calculations in dimensional regularization, where supersymmetry is spoiled at the regularized level, and show how the counterterms necessary to restore supersymmetry can be read off easily. In addition, a specific example is given how the supersymmetry transformations in one-loop order are modified by non-local terms. Received: 23 July 1999 / Published online: 14 October 1999     

The supersymmetric transfer matrix for linear chains with nondiagonal disorder

A study is made of the supersymmetric transfer matrix of then-orbital linear chain with Gaussian nondiagonal and diagonal disorder in the matrix (Hubbard-Stratonovich) variables. This formalism is applied to the one-point Green's function. Invariant functions of supersymmetric matrices are discussed in Section 3.Work supported by the Deutsche Forschungsgemeinschaft.     

A new derivation of the Picard-Fuchs equations for effective N = 2 super Yang-Mills theories

A new method to obtain the Picard-Fuchs equations of effective, N = 2 supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. It applies to all classical gauge groups, and directly produces a decoupled set of second-order, partial differential equations satisfied by the period integrals of the Seiberg-Witten differential along the 1-cycles of the algebraic curves describing the vacuum structure of the corresponding N = 2 theory.     

A systematization for one-loop 4D Feynman integrals

We present a strategy for the systematization of manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one-loop perturbative solutions of QFT, where the use of an explicit regularization is avoided. Two types of systematization are adopted. The divergent parts are put in terms of a small number of standard objects, and a set of structure functions for the finite parts is also defined. Some important properties of the finite structures, specially useful in the verification of relations among Green's functions, are identified. We show that, in fundamental (renormalizable) theories, all the finite parts of two-, three- and four-point functions can be written in terms of only three basic functions while the divergent parts require (only) five objects. The final results obtained within the proposed strategy can be easily converted into those corresponding to any specific regularization technique providing an unified point of view for the treatment of divergent Feynman integrals. Examples of physical amplitudes evaluation and their corresponding symmetry relations verification are presented as well as generalizations of our results for the treatment of Green's functions having an arbitrary number of points are considered.     

On the random vector potential model in two dimensions

The random vector potential model describes massless fermions coupled to a quenched random gauge field. We study its abelian and non-abelian versions. The abelian version can be completely solved using bosonization. We analyse the non-abelian model using its supersymmetric formulation and show, by a perturbative renormalization group computation, that it is asymptotically free at large distances. We also show that all the quenched chiral current correlation functions can be computed exactly, without using the replica trick or the supersymmetric formulation, but using an exact expression for the effective action for any sample of the random gauge field. These chiral correlation functions are purely algebraic.     

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.     

Localized vibrations of point defects in body-centred cubic lattices

The paper gives an exact calculation of the localized frequencies of substitutional defects in a body-centred cubic lattice by the method of Green's functions and compares it with the approximate calculation carried out after [14]. The exact calculation is based on newly computed Green's functions of a b.c.c. lattice [18]. It is shown how by means of group theory the symmetry of the system can be used both in an approximate and in the exact calculation. Some symmetry relations between Green's functions, which limit the number of functions necessary for numerical calculations, are derived.     

Renormalization of the 1/N expansion and critical behaviour of (2+1)-dimensional supersymmetric non-linear sigma-models

Renormalized 1/N expansion in both high-and low-temperature phases as well as of the critical theory of three-dimensional supersymmetric generalized non-linear sigma-models is constructed and scaling laws for the Green's functions near the critical point with only two independent critical exponents are established.     

Supersymmetric Noether Currents and Seiberg–Witten Theory

The purpose of this paper is twofold. The first purpose is to review a systematic construction of Noether currents for supersymmetric theories, especially effective supersymmetric theories. The second purpose is to use these currents to derive the mass-formula for the quantized Seiberg–Witten model from the supersymmetric algebra. We check that the mass-formula of the low-energy theory agrees with that of the full theory (in the broken phase).     

Properties of the covariant formulation of superstring theories

The covariant two-dimensional action principle that describes the dynamics of free superstrings in a Minkowski background is reviewed. Covariant gauge conditions are formulated, which simplify the equations of motion of the superspace coordinates to free equations. In this gauge there are bosonic and fermionic constraints whose generators give a supersymmetric generalization of the Virasoro algebra. As in certain supersymmetric field theories, closure of the algebra requires using the equations of motion. Covariant constrained bracket relations are obtained for the classical theory, but it is very difficult to extend them to quantum mechanical commutation relations. Interaction vertices satisfying supersymmetry and the necessary gauge conditions are constructed. They reduce in a special frame to ones found in earlier work in the light-cone gauge, and then can be interpreted quantum mechanically.     

The extended Hubbard model in the ionic limit

In this paper, we study the Hubbard model with intersite Coulomb interaction in the ionic limit (i.e. no kinetic energy). It is shown that this model is isomorphic to the spin-1 Ising model in presence of a crystal field and an external magnetic field. We show that for such models it is possible to find, for any dimension, a finite complete set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of motion closes and analytical expressions for the relevant Green's functions and correlation functions can be obtained. These expressions are formal because these functions depend on a finite set of unknown parameters, and only a set of exact relations among the correlation functions can be derived. In the one-dimensional case we show that by means of algebraic constraints it is possible to obtain extra equations which close the set and allow us to obtain a complete exact solution of the model. The behavior of the relevant physical properties for the 1D system is reported.     

Correlations of RMT characteristic polynomials and integrability: Hermitean matrices

Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general theory of τ functions, we (i) identify a zoo of hierarchical relations satisfied by τ functions in an abstract infinite-dimensional space and (ii) present a technology to translate these relations into hierarchically structured nonlinear differential equations describing the correlation functions of characteristic polynomials in the physical, spectral space. Implications of this formalism for fermionic, bosonic, and supersymmetric variations of zero-dimensional replica field theories are discussed at length. A particular emphasis is placed on the phenomenon of fermionic-bosonic factorisation of random-matrix-theory correlation functions.     

Ultraviolet divergences in non-renormalizable supersymmetric theories

We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang–Mills theory and of N = 8 4D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higherdimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.     

Two-dimensional fractional supersymmetric conformal and logarithmic conformal field theories and two point functions

A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Applying the generators of the closed subalgebra generated by and , the two point functions of the component fields of supermultiplets are calculated. Then the logarithmic superconformal field theories are investigated and the chiral and full two point functions are obtained. Received: 15 December 2000 / Revised version: 19 March 2001 / Published online: 18 May 2001     

Regularization by higher derivatives and quantum correction for <Emphasis Type="Italic">N</Emphasis> = 1 supersymmetric theories

Some results of regularization by higher covariant derivatives used for investigation of the structure of quantum corrections in N = 1 supersymmetric theories are summarized in the present work. In particular, it is demonstrated that all integrals determining the Hell-Mann-Low functions in supersymmetric theories are integrals of total derivatives. As a consequence, in the N = 1 supersymmetric theories there exists an identity for the Green’s functions which follows from none of the symmetry theories known thus far. The problem of obtaining the exact β-function by the methods of perturbation theory is discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 5–35, May, 2008.     

Instanton effects in supersymmetric theories

We calculate some simplest n-point functions in supersymmetric Yang-Mills theories contributed by instantons. The result is not vanishing and we discuss some implications of this. In particular, the dynamics of the supersymmetric theories must exhibit some unusual features.