General Reggeon Vertex in Dual Theory

Physics Letters B, 1997

Self-dual perturbiner in the Yang-Mills theory is constructed by the twistor methods both in topologically trivial and topologically nontrivial cases. Maximally helicity violating amplitudes and their instanton induced analogies are briefly discussed.

Europhysics Letters (EPL), 2004

In this paper, we show that the propagator of the dual of a general Proca-like theory, derived from the gauging iterative Noether Dualization Method, can be written by means of a simple relation between known propagators. This result is also a demonstration that the Lagrangian obtained by dualization describes the same physical particles as the ones present in the original theory at the expense of introducing new non-physical (ghosts) excitations.

Using planar dual amplitudes as a guide, we,discuss some features of reggeon amplitudes which are relevant in the context of the topological expansion. We look into the analytic properties and, in particular, discuss the validity of finite-mass sum rules for reggeon-reggeon scattering. We investigate the form taken by planar unitarity when a multiperipheral assumption is added. The integral equations obtained are not of the standard ChewGoldberger-Low type. We find that pure pole-type solutions (i.e. without Regge cuts) to planar unitarity are possible in a way consistent with the symmetry and factorization properties of reggeon-reggeon amplitudes. The appearance of "good" FMSR in the unitarity integrals follows from a careful treatment of phase space -all possible configurations are counted uniquely -and is crucial in achieving the cut cancellation. Throughout the paper we emphasize various subtle points that have been overlooked in the literature.

2006

The duality symmetry of free electromagnetic field is analyzed within an algebraic approach. To this end, the conformal $c(1,3)$ algebra generators are expressed as operators quadratic in some abstract operators $\kappa^\alpha$ and $\pi_\beta$ which satisfy Heisenberg algebra relations. It is then shown that the duality generator can also be expressed in this manner. Standard issues regarding duality are considered in such a framework. It is shown that duality generator also generates chiral transformations, and the conflict between duality and manifest Lorentz symmetry is analyzed from the viewpoint of symmetry group greater then conformal, in which duality generator appears as a natural part of an $su(2)$ subalgebra.

Nuclear Physics B, 2008

There is growing evidence that on-shell gluon scattering amplitudes in planar N = 4 SYM theory are equivalent to Wilson loops evaluated over contours consisting of straight, light-like segments defined by the momenta of the external gluons. This equivalence was first suggested at strong coupling using the AdS/CFT correspondence and has since been verified at weak coupling to one loop in perturbation theory. Here we perform an explicit two-loop calculation of the Wilson loop dual to the four-gluon scattering amplitude and demonstrate that the relation holds beyond one loop. We also propose an anomalous conformal Ward identity which uniquely fixes the form of the finite part (up to an additive constant) of the Wilson loop dual to four-and five-gluon amplitudes, in complete agreement with the BDS conjecture for the multi-gluon MHV amplitudes.

We show how to use the Bern-Kosower master formula, originally a generating functional for on-shell gluon matrix elements, to derive well-organized form factor decompositions of the off-shell one-particle-irreducible N - gluon vertices. Two such algorithms are presented which can be used for any N, the first one optimized with respect to the nonabelian gauge invariance, the second one with respect to transversality. We give explicit results for the three- and four-gluon cases. The second algorithm in the three-point case reproduces precisely the well-known Ball-Chiu decomposition, and in the four-point case a natural generalization thereof. A particularly simple structure emerges in the N=4 SYM case.

Nuclear Physics B, 1979

The contribution of one-loop planar diagrams to the two-reggeon twoparticle amplitude is derived. Its Regge limit splits into two separate contributions which must be interpreted as renormalization effects, to order g , of the a and $ trajectories. We show that the Neveu-Scherk renormalization prescription is able to render finite both contributions. The intercept of the (J trajectory is shifted from its bare value by the renormalization procedure, whereas that of the a trajectory is not renormalized as it was required by the gauge invariance of dual theories.

2009

We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the "leading singularities" of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely determine the full amplitudes at tree level and 1-loop, and are conjectured to do so at all loop orders. The scattering amplitude for n particles in the sector with k negative helicity gluons is associated with a simple integral over the space of k planes in n dimensions, with the action of parity and cyclic symmetries manifest. The residues of the integrand compute a basis for the leading singularities. A given leading singularity is associated with a particular choice of integration contour, which we explicitly identify at tree level and 1-loop for all NMHV amplitudes as well as the 8 particle N 2 MHV amplitude. We also identify a number of 2-loop leading singularities for up to 8 particles. There are a large number of relations among residues which follow from the multi-variable generalization of Cauchy's theorem known as the "global residue theorem". These relations imply highly non-trivial identities guaranteeing the equivalence of many different representations of the same amplitude. They also enforce the cancellation of non-local poles as well as consistent infrared structure at loop level. Our conjecture connects the physics of scattering amplitudes to a particular subvariety in a Grassmannian; space-time locality is reflected in the topological properties of this space.

Nuclear Physics B, 1979

The linear triple-Regge limit of the one-loop non-planar orientable diagram is computed. It is proved that a pomeron sister trajectory does not appear in the pomeron sector, at lowest order, of the two-reggeon two-particle amplitude in the conventional dual model. As a consequence, non-planar diagrams, unlike planar ones, do not renormalize the sister Regge trajectory at lowest order. Both effects, appearance of the pomeron sister trajectory and renormalization of the sister Regge trajectory, might happen if higher-order corrections were considered, in agreement with the recent discovery of a pomeron sister in the Shapiro-Virasoro model by Barratt.

Progress of Theoretical Physics, 1971

The Veneziano model for nN~KA has been used to investigate the structure of A-particle. The imaginary parts of the form-factors (both electric and magnetic) are found to be dominated by a strong K* (nK) resonance. The ratio of the form-factors near this resonance is in accord with other theoretical estimates.