On the superfield effective potential in three dimensions

We develop the superfield approach to the effective potential in three dimensions and calculate the one-loop and two-loop Kählerian effective potential in commutative and noncommutative cases.     

One-loop renormalisation of superfield Yang-Mills theories

We calculate the one-loop ultraviolet and infrared divergences in superfield Yang-Mills theories to fourth order in the gauge field. The ultraviolet divergences require a non-linear field renormalisation, and graphs with external ghost fields show that a non-linear renormalisation of the gauge-fixing function is also needed. These observations are confirmed by calculations incorporating matter fields, which are used to extend the result to all orders for the special case of SU(2). On the other hand the infrared divergences, which occur in general gauges, are apparently impossible to remove in any acceptable way.     

Gauge invariance of effective potential in Kaluza-Klein theories

The vacuum energy in Kaluza-Klein theories, as calculated at the extremals of the generating functional of vertices, is gauge independent. The general assertion is illustrated by vacuum-energy calculations in a one-parameter gauge in vector-field theory and of Einstein gravity in the space M₄×T_D–4, where M₄ is Minkowski space and T_D is a D-dimensional torus.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 20–25, December, 1988.     

A superfield formulation of extended supersymmetric gauge theories

We present a superfield framework in which to discuss extended supersymmetric Yang-Mills theories in an unconstrained manner. Superfields and lagrangians are constructed for the SO(2) and SO(4) cases for both the abelian and linearised non-abelian versions and the auxiliary component fields are obtained in those cases. Extension to the interacting or non-abelian case presents severe difficulties which are discussed briefly.     

Cohomological aspects of gauge theories: superfield formalism

Some of the key cohomological features of the two (1 + 1)-dimensional (2D) free Abelian- and self-interacting non-Abelian gauge theories (having no interaction with matter fields) are briefly discussed first in the language of symmetry properties of the Lagrangian densities and the same issues are subsequently addressed in the framework of superfield formulation on the four (2 + 2)-dimensional supermanifold. Special emphasis is laid on the on-shell- and off-shell nilpotent (co-)BRST symmetries that emerge after the application of (dual) horizontality conditions on the supermanifold. The (anti-)chiral superfields play a very decisive role in the derivation of the on-shell nilpotent symmetries. The study of the present superfield formulation leads to the derivation of some new symmetries for the Lagrangian density and the symmetric energy-momentum tensor. The topological nature of the above theories is captured in the framework of superfield formulation and the geometrical interpretations are provided for some of the topologically interesting quantities.     

On the short-distance potential in confining theories

The structure of leading nonperturbative corrections to the static Coulomb potential at small distances in Abelian and non-Abelian theories is analyzed. Related problems of validity of the Dirac quantization condition for running charges in Abelian theory and significance of the quantity 〈A²〉 are briefly discussed.     

One-loop effective action in three-dimensional general chiral superfield model

Using the heat kernel approach we calculate one-loop Kähler effective potential for the general chiral superfield model in three dimensions.     

Superfield effective action within the general chiral superfield model

The chiral superfield model associated with the low-energy limit of superstring theory and characterized by the Kähler and the chiral potential [K(Φ, $\overline \Phi$ ) and W(Φ), respectively] is analyzed. An approach to solving a general problem is developed, and quantum loop corrections at arbitrary K(Φ, $\overline \Phi$ ) and W(Φ) are found. Various aspects of a supergraph technique that are associated with calculating perturbative contributions to the superfield effective action are analyzed. Explicit expressions for the one-and two-loop corrections to the Kähler potential are calculated. The leading two-loop correction to the chiral potential is obtained, and it is shown that, irrespective of the form of K(Φ, $\overline \Phi$ ) and W(Φ), counterterms are not needed for deducing this correction.     

On the effective quark potential in baryons

We analyse the splitting of the non-strange memebers of the first excited level [70,1^?]₁ of baryon resonances. The spin-dependent forces (spin-spin, spin-orbit, tensor) are supposed to arise from the Coulomb term due to one-gluon exchange, from the long-range linearly rising part of the potential, and from additional “hard-core” spin-spin terms which may be generated by higher-order graphs contributing to the qq kernel. For the long range part we either assume that it comes from a superposition of a vector and a scalar kernel of the form ?(γ^μ ? γ_μ ? 1 + (1 ? ?)(1 ? 1 ? 1) (+ permutations), or, alternatively, that it arises from a vector exchange with an anomalous moment κ in the quark-gluon vertex. Values of ? ≈ 0 orκ ≈ ?1 turn out to be favoured. The strong coupling constant and the slope of the linear potential come out in the correct order of magnitude. Very large hard-core spin-spin terms are needed. This fact makes the determination of the effective potential from the underlying theory of quantum chromodynamics as well as the phenomenological analysis of the observed spectra rather problematic.     

The effective action for superfield Lagrangian quantization in reducible hypergauges

The rules of local superfield Lagrangian quantization in reducible non-Abelian hypergauge functions are formulated for an arbitrary gauge theory. The generating functionals of standard and vertex Greens functions which depend on the Grassmann variable via super(anti)fields and sources are constructed. The difference between the local quantum and the gauge fixing action determines an almost Hamiltonian system such that translations with respect to along the solutions of this system define the superfield BRST transformations. The Ward identities are derived and the gauge independence of the S-matrix is proved.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 5966, October, 2004.     

Structural properties of effective potential model by liquid state theories

This paper investigates the structural properties of a model fluid dictated by an effective inter-particle oscillatory potential by grand canonical ensemble Monte Carlo (GCEMC) simulation and classical liquid state theories.The chosen oscillatory potential incorporates basic interaction terms used in modeling of various complex fluids which is composed of mesoscopic particles dispersed in a solvent bath,the studied structural properties include radial distribution function in bulk and inhomogeneous density distribution profile due to influence of several external fields.The GCEMC results are employed to test the validity of two recently proposed theoretical approaches in the field of atomic fluids.One is an Ornstein-Zernike integral equation theory approach;the other is a third order + second order perturbation density functional theory.Satisfactory agreement between the GCEMC simulation and the pure theories fully indicates the ready adaptability of the atomic fluid theories to effective model potentials in complex fluids,and classifies the proposed theoretical approaches as convenient tools for the investigation of complex fluids under the single component macro-fluid approximation.     

On superfield covariant quantization in general coordinates

We propose a natural extension of the BRST-antiBRST superfield covariant scheme in general coordinates. Thus, the coordinate dependence of the basic tensor fields and scalar density of the formalism is extended from the base supermanifold to the complete set of superfield variables. Received: 23 June 2005, Revised: 18 July 2005, Published online: 6 October 2005     

On the effective potential minimum versus the tree level potential minimum

We analyze the effective potential minimum (true vacuum of the theory) versus the tree level potential minimum in order to decide under which conditions they coincide. A criterion is found. Applications are made to monomial potentials (Coleman-Weinberg type models) and to theN=1 Supergravity Minimal Model.     

On the colour contribution to effective weak vertex in broken colour gauge theories

Treating the breaking of colour symmetry via the mixing between the colour gluons and weak bosons (a la Rajasekaran and Roy) it is observed that the colour contribution to the effective weak vertex of a quark at zero momentum transfer is zero uptoO(α). An erratum to this article is available at .