Supersymmetric Yang-Mills Model Research Articles

Pomeron in the N = 4 SYM at strong couplings

We show the result for the BFKL Pomeron intercept at N = 4 Supersymmetric Yang-Mills model in the form of the inverse coupling expansion j0 = 2 − 2λ−1/2 − λ−1 + 1/4 λ−3/2 + 2(1 + 3ζ3)λ−2 + O(λ−5/2), which has been calculated recently in [1] with the use of the AdS/CFT correspondence.

BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at [formula omitted] SUSY

We calculate the eigenvalues of the next-to-leading kernel for the BFKL equation in the adjoint representation of the gauge group SU(Nc) in the N=4 supersymmetric Yang–Mills model. These eigenvalues are used to obtain the high energy behavior of the remainder function for the 6-point scattering amplitude with the maximal helicity violation in the kinematical regions containing the Mandelstam cut contribution. The leading and next-to-leading singularities of the corresponding collinear anomalous dimension are calculated in all orders of perturbation theory. We compare our result with the known collinear limit and with the recently suggested ansatz for the remainder function in three loops and obtain the full agreement providing that the numerical parameters in this ansatz are chosen in an appropriate way.

Veneziano amplitudes, spin chains and Abelian reduction of QCD

Although QCD can be treated perturbatively in the high energy limit, lower energies require uses of nonperturbative methods such as ADS/CFT and/or Abelian reduction. These methods are not equivalent. While the first is restricted to supersymmetric Yang–Mills model with number of colors going to infinity, the second is not restricted by requirements of supersymmetry and is designed to work in the physically realistic limit of a finite number of colors. In this paper we provide arguments in favor of the Abelian reduction methods. This is achieved by further developing results of our recent works re-analyzing Veneziano and Veneziano-like amplitudes and the models associated with these amplitudes. It is shown, that the obtained new partition function for these amplitudes can be mapped exactly into that for the Polychronakos–Frahm (P–F) spin chain model recoverable from the Richardon–Gaudin (R–G) XXX spin chain model originally designed for treatments of the BCS-type superconductivity. Because of this, it is demonstrated that the obtained mapping is compatible with the method of Abelian reduction. The R–G model is recovered from the asymptotic (WKB-type) solutions of the rational Knizhnik–Zamolodchikov (K–Z) equation. Linear independence of these solutions is controlled by determinants whose explicit form (up to a constant) coincides with Veneziano (or Veneziano-like) amplitudes. In the simplest case, the determinantal conditions coincide with those discovered by Kummer in the 19th century. Kummer’s results admit physical interpretation by relating determinantal formula(s) to Veneziano-like amplitudes. Furthermore, these amplitudes can be interpreted as Poisson–Dirichlet distributions playing a central role in the stochastic theory of random coagulation–fragmentation processes. Such an interpretation is complementary to that known for the Lund model widely used for the description of coagulation–fragmentation processes in QCD.

${\mathcal N}=1^*$ MODEL SUPERPOTENTIAL REVISITED (IR BEHAVIOR OF ${\mathcal N}=4$ LIMIT)

The one-loop contribution to the superpotential, in particular the Veneziano–Yankielowicz potential in [Formula: see text] supersymmetric Yang–Mills model is discussed from an elementary field theory method and the matrix model point of view. Both approaches are based on the renormalization group variation of the superconformal [Formula: see text] supersymmetric Yang–Mills model.

On F-term contribution to effective action

We apply equivariant integration technique, developed in the context of instanton counting, to two dimensional = 2 supersymmetric Yang-Mills models. The expression for the twisted superpotential for U(N) model is conjectured. Connections to the four dimensional case are discussed.

Three-loop universal anomalous dimension of the Wilson operators in [formula omitted] SUSY Yang–Mills model

We present results for the three-loop universal anomalous dimension γuni(j) of Wilson twist-2 operators in the N=4 Supersymmetric Yang–Mills model. These expressions are obtained by extracting the most complicated contributions from the three loop non-singlet anomalous dimensions in QCD which were calculated recently. Their singularities at j=1 coincide with the predictions obtained from the BFKL equation for N=4 SYM in the next-to-leading order. The asymptotics of γuni(j) at large j is in an agreement with the expectations based on an interpolation between week and strong coupling regimes in the framework of the AdS/CFT correspondence.

Completing the Square to Find the Supersymmetric Matter Effective Action Induced by Coupling to Linearized N=1 Supergravity

We consider generic N=1 supersymmetric matter coupled to linearized N=1 supergravity through the multiplet of currents. By completing the square, we find the effective action giving the leading supergravity induced correction to the matter dynamics, expressed explicitly as a quadratic form in the components of the current multiplet. The effective action is supersymmetry invariant through an interplay of the local terms arising from the auxiliary field couplings, and the nonlocal terms arising from graviton and gravitino exchange, neither of which is separately invariant. Having an explicit form for the supergravity induced effective action is a first step in studying effects of supergravity corrections on dynamical supersymmetry breaking and condensate formation in supersymmetric matter dynamics. In the Appendixes we give explicit expressions for the currents, in our notational conventions, in the Wess–Zumino and supersymmetric Yang–Mills models.

GAUGINO DETERMINANT IN SUPERSYMMETRIC YANG–MILLS THEORY

We resolve an ambiguity in the sign of the determinant of a single Weyl fermion, such as the gaugino in supersymmetric models. Positivity of this determinant is necessary for the application of QCD inequalities and lattice Monte–Carlo methods to supersymmetric Yang–Mills models.

OCTONIONS AND SUPER-LIE ALGEBRA

We discuss how to represent the nonassociative octonionic structure in terms of the associative matrix algebra using the left and right octonionic operators. As an example we construct explicitly some Lie and super-Lie algebra. Then we discuss the notion of octonionic Grassmann numbers and explain its possible application for giving a superspace formulation of the minimal supersymmetric Yang–Mills models.

Poincaré supersymmetry representations over trace class non-commutative graded operator algebras

We show that rigid supersymmetry theories in four dimensions can be extended to give supersymmetric trace (or generalized quantum) dynamics theories, in which the supersymmetry algebra is represented by the generalized Poisson bracket of trace supercharges, constructed from fields that form a trace class non-commutative graded operator algebra. In particular, supersymmetry theories can be turned into supersymmetric matrix models this way. We demonstrate our results by detailed component field calculations for the Wess-Zumino and the supersymmetric Yang-Mills models (the latter with axial gauge fixing), and then show that they are also implied by a simple and general superspace argument.

The one-loop Green’s functions of dimensionally reduced gauge theories

We apply the dimensional regularization technique as well as that by dimensional reduction to the calculation of the regularized one-loop Green’s functions ind0-dimensional Yang-Mills theory with real massless scalars and spinors in arbitrary (real) representations of a gauge groupG. As a particular example, the super-symmetrically regularized one-loop Green’s functions of theN=4 supersymmetric Yang-Mills model are derived.

Simulating simple supersymmetric field theories

Using hybrid differential equations and fermion fields represented by stochastic noise, we simulate SU(2) lattice gauge theory with a variable number N f of Majorana fermions in the adjoint representation of the gauge group. For N f = 1, the continuum limit of the lattice theory is the supersymmetric Yang-Mills model. For N f = 0, 1 and 4 we find chiral symmetry breaking and hierarchal mass scales.

The 2-dimensionalN=2 supersymmetric Yang-Mills model on the discrete space-time lattice

We use the Dirac-Kahler formalism in order to put a two-dimensional Yang-Mills theory with a complex supersymmetry on the Euclidean space-time lattice. The theory presents two supersymmetric invariant actions related to each other by a kind of “time reflection” transformation.

On the Dynamical Symmetry Breaking for the N=1 Pure Supersymmetric Yang-Mills Model

An approximate effective Lagrangian of composite operators in superfield formalism for the N=1 pure supersymmetric Yang-Mills model is obtained with the help of renormalization group equations for the generating functional. While the supersymmetry is always kept unbroken by this effective Lagrangian we find that the chiral symmetry may and may not be unbroken.

Ten-dimensional supersymmetric Yang-Mills theory is not ultraviolet finite on-shell

We find that the one-loop on-shell transition amplitude with four external fermions is not ultraviolet finite in the ten-dimensional supersymmetric Yang-Mills model.

Six-dimensional supersymmetric Yang-Mills theory is not finite

We find that the transition amplitudes with three external gauge fields and four external fermions are not finite in the six-dimensional supersymmetric Yang-Mills model.