Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling

We construct an analytical solution to the integral equation which is believed to describe logarithmic growth of the anomalous dimensions of high-spin operators in planar N=4 super Yang-Mills theory and use it to determine the strong coupling expansion of the cusp anomalous dimension.     

Multi-Regge form of gluon-exchange amplitudes in supersymmetric Yang-Mills theories

Within supersymmetric Yang-Mills theories, all effective vertices for the interaction of Reggeized gluons with particles were found both in the leading-logarithm approximation and in the next-to-leading-order approximation. The contributions of scalars to the eigenfunction of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) kernel for the adjoint representation of the gauge group and to impact factors similar to those in QCD were calculated. The impact factors that arise in supersymmetric Yang-Mills theories, but which are not present in QCD, are also found. Fulfillment of all bootstrap conditions, which guarantees the multi-Regge form of multiparticle amplitudes in supersymmetric Yang-Mills theories in the next-to-leading-order approximation, was proven. A method for testing bootstrap relations without calculating explicit expressions for vertices and impact factors was developed. This method was used to prove fulfillment of bootstrap conditions in theories featuring any number of fermions and scalar particles transformed according to any representations of the color group and involved in interactions with one another via Yukawa coupling.     

The β-function in supersymmetric Yang-Mills theory

We show by means of the Adler-Bardeen theorem how to calculate the two-loop β function from a one-loop calculation of the superconformal anomaly in a supersymmetric gauge theory with arbitrary superpotential. The N = 2 and N = 4 cases are also briefly discussed.     

Charge renormalization in a supersymmetric Yang-Mills theory

The renormalization group function β(g) is found to vanish in the two-loop approximation for a recently derived SU(4) supersymmetric Yang-Mills theory.     

Yangian-invariant scattering amplitudes in supersymmetric Chern-Simons theory

We propose a generating function for scattering amplitudes of N=6 supersymmetric-Chern-Simons theory, which parallels a recent work on N=4 supersymmetric-Yang-Mills theory by Arkani-Hamed et?al. Our result suggests that the scattering amplitudes of the supersymmetric-Chern-Simons theory exhibit Yangian invariance.     

Perturbation theory and renormalization of supersymmetric Yang-Mills theories

We solve the problem of introducing, in supersymmetric Yang-Mills Lagrangians, a supersymmetric gauge breaking term and a Faddeev-Popov ghost interaction term. The resulting Lagrangian turns out to be invariant under a global symmetry transformation which is the supersymmetric extension of the Slavnov symmetry. We show that the complete analysis of all primitively divergent supergraphs ensures, in conjunction with the Slavnov identities, the renormalizability of the theory, once a supersymmetric and gauge invariant regularizing procedure has been introduced. We find that the simplest regularizing procedure is a generalization of the higher covariant derivatives method. In the case of interaction with matter fields we prove that no mass counter term is needed, in exact analogy with the model without gauge fields. Finally we show that, in the Abelian situation, a supersymmetric mass term for the vector multiplet can be introduced without spoiling the renormalizability, thus providing the supersymmetric extension of massive vector bosons theories.     

Ten-dimensional supersymmetric Yang-Mills theory in terms of four-dimensional superfields

We show that the usual formulation of the N = 4 supersymmetric Yang-Mills theory in terms of N = 1 superfields can be generalized to describe the full ten-dimensional theory.     

On quasi-self-dual fields in N=4 supersymmetric Yang-Mills theory

A general representation for a quasi-self-dual gauge field which is a generalization of the 't Hooft ansatz is obtained in the Euclidean conformally invariant Yang-Mills theory with a sextuplet of real scalar fields-the boson sector of N=4 supersymmetric Yang-Mills theory. The existence of an O(4)-symmetric quasi-self-dual solution in the region g ²>0 is proved. An explicit example of the quasi-self-dual instanton in the region g ²<0 is constructed.     

A non-perturbative contribution to the vacuum energy in supersymmetric Yang-Mills theory

It is shown that the quantum fluctuations around an interacting instanton-anti-instanton field configuration induce negative vacuum energy in supersymmetric Yang-Mills theory.     

Vanishing three-loop beta function in N = 4 supersymmetric Yang-Mills theory

We have calculated the beta function of the N = 4 supersymmetric Yang-Mills theory through three-loop order and find that it is zero. The calculation was performed using superspace techniques that also allowed the calculation of the complete three-loop chiral-multiplet propagator, which turned out to be quite simple. These results strongly support the speculations that the theory is finite order-by-order in perturbation theory.     

Conformal invariance in N = 4 supersymmetric Yang-Mills theory

It is shown, by consideration of anomaly multiplets, that the maximally extended supersymmetric Yang-Mills theory is conformally invariant, assuming that the theory is supersymmetric and O(4)-invariant and that the structure of anomalies is given by the breakdown of conformal invariance in its coupling to supergravity.     

Spontaneous quantum compactification in a d = 10 supersymmetric Yang-Mills theory

It is shown that an N = 1, d = 10 supersymmetric Yang-Mills theory admits a spontaneous quantum compactification of the form M₄ × S₆, where M₄, and S₆ are the Minkowski space and the 6-sphere, accordingly. The radius of S₆ is of the order of the Planck length L_Pl.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 77–83, January, 1990.The authors thank I. L. Bukhbinder for his help in our work.     

A generalized leading-term approximation of high-energy scattering amplitudes in Yang-Mills theory

In this paper, the high-energy vector meson-vector meson elastic scattering amplitudes of a Yang-Mills theory of an SU(2) model are calculated in a generalized leading-term approximation (s→∞ with t fixed). The resulting amplitude, through the 10th order, coincides with the expansion of an eikonal formula. The present method is generalizable to other non-Abelian gauge theories.