Planar amplitudes in maximally supersymmetric Yang-Mills theory

The collinear factorization properties of two-loop scattering amplitudes in dimensionally regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the anti-de Sitter/conformal field theory correspondence that the form of the large-N(c) L-loop amplitudes should be simple enough to allow a resummation to all orders.     

The ultra-violet question in maximally supersymmetric field theories

We discuss various approaches to the problem of determining which supersymmetric invariants are permitted as counterterms in maximally supersymmetric super Yang–Mills and supergravity theories in various dimensions. We review the superspace non-renormalisation theorems based on conventional, light-cone, harmonic and certain non-Lorentz covariant superspaces, and we write down explicitly the relevant invariants. While the first two types of superspace admit the possibility of one-half BPS counterterms, of the form F ⁴ and R ⁴ respectively, the last two do not. This suggests that UV divergences begin with one-quarter BPS counterterms, i.e. d ² F ⁴ and d ⁴ R ⁴, and this is supported by an entirely different approach based on algebraic renormalisation. The algebraic formalism is discussed for non-renormalisable theories and it is shown how the allowable supersymmetric counterterms can be determined via cohomological methods. These results are in agreement with all the explicit computations that have been carried out to date. In particular, they suggest that maximal supergravity is likely to diverge at four loops in D = 5 and at five loops in D = 4, unless other infinity suppression mechanisms not involving supersymmetry or gauge invariance are at work.     

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.     

Some properties of scattering amplitudes in supersymmetric theories

Properties of S-matrix amplitudes are investigated in theories invariant under global supersymmetry transformations. Many amplitudes are related to each other by supersymmetry and many others have to vanish. In particular a general helicity conservation law holds.     

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.     

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.     

Local rings of singularities andN=2 supersymmetric quantum mechanics

We investigate the Kähler structure arising inn-component,N=2 supersymmetric quantum mechanics. We defineL ²-cohomology groups of a modified and relate them to the corresponding spaces of harmonic forms. We prove that the cohomology is concentrated in the middle dimension, and is isomorphic to the direct sum of the local rings of the singularities of the superpotential. In the physics language, this means that the number of ground states is equal to the absolute value of the index of the supercharge, and each ground state contains exactlyn fermions.Supported in part by the Department of Energy under Grant DE-F602-88ER25065     

Singularities and accumulation of singularities of πN scattering amplitudes

It is demonstrated that for the isospin I = 1/2 πN scattering amplitude, T^I=1/2(s, t), $s={\left({m}_{N}^{2}-{m}_{\pi }^{2}\right)}^{2}/{m}_{N}^{2}$ and $s={m}_{N}^{2}+2{m}_{\pi }^{2}$ are two accumulation points of poles on the second sheet of complex s plane, and are hence accumulation of singularities of T^I=1/2(s, t). For T^I=3/2(s, t), $s={\left({m}_{N}^{2}-{m}_{\pi }^{2}\right)}^{2}/{m}_{N}^{2}$ is the accumulation point of poles on the second sheet of the complex s plane. The proof is valid up to all orders of chiral expansions.     

Structure of infrared singularities of gauge-theory amplitudes at three and four loops

Journal of High Energy Physics - Working to lowest non-trivial order in fermions, we consider the four-derivative order corrected Lagrangian and supersymmetry transformations of the Euclidean...     

Double logarithmic asymptotics and regge singularities of quark amplitudes with flavour exchange

We derive simple equations in terms of definite signature partial waves for the quark scattering and annihilation amplitudes in the double logarithmic approximation of QCD. We apply the method of isolating the softest virtual particle in the graphs which is based on gauge invariance and unitarity. Besides the particle Regge trajectories and corresponding cuts, there are further singularities in the angular momentum plane generated by perturbative double logarithmic contributions and which may be of phenomenological relevance. We also consider amplitudes with external currents and discuss how to include ultraviolet single logarithms and non-perturbative contributions.     

The gauge invariance,kinematical singularities and the electro- and photopion production amplitudes

The kinematical singularities connected with the gauge invariance are considered and the conventional sets of invariant amplitudes discussed. A new set of invariant amplitudes for electro-production of pions on nucleons is proposed, which contains the transversal subset of photo-production amplitudes, is free of kinematical singularities and more convenient for practical calculations.I would like to thank Dr. M. Petrá for a valuable discussion on some points, Dr. P. Lichard and Dr. J. Piút for useful remarks and Dr. F. A. Berends for a valuable correspondence. I am also indebted to Prof. Moorhouse for drawing my attention to some important papers and sending me a preprint of one of them.     

Clockwork SUSY: supersymmetric Ward and Slavnov-Taylor identities at workin Green's functions and scattering amplitudes

We study the cancellations among Feynman diagrams that implement the Ward and Slavnov-Taylor identities corresponding to the conserved supersymmetry current in supersymmetric quantum field theories. In particular, we show that the Faddeev-Popov ghosts of gauge and supersymmetries never decouple from the physical fields, even for abelian gauge groups. The supersymmetric Slavnov-Taylor identities provide efficient consistency checks for automatized calculations and can verify the supersymmetry of Feynman rules and the numerical stability of phenomenological predictions simultaneously.Received: 2 June 2003, Revised: 1 July 2003, Published online: 5 September 2003     

Logarithmic two dimensional spin-1/3 fractional supersymmetric conformal field theories and the two-point functions

Logarithmic spin-1/3 superconformal field theories are investigated. The chiral and full two-point functions of two- (or higher-) dimensional Jordanian blocks of arbitrary weights are obtained. Received: 30 September 2000 / Published online: 5 February 2001