No abstract

A proof is given of the formula, recently proposed by Cachazo, He and Yuan (CHY) for gluon tree amplitudes in pure Yang-Mills theory in arbitrary dimension. The approach is to first establish the corresponding result for massless φ 3 theory using the BCFW recurrence relation and then to extend this to the gauge theory case. Additionally, it is shown that the scattering equations introduced by CHY can be generalized to massive particles, enabling the description of tree amplitudes for massive φ 3 theory.

Given a simple self-dual quantum Hamiltonian H =KB +rB, where K and are coupling constants, and the condition that [B,[B,[B,B]]]=~~ [B,B], then we construct an infinite set of conserved charges Q2n; [H,Qzn] =O. In simple models, like the twodimensional Ising or Baxter eight-vertex, these charges appear in the associated quantum theories and are equivalent to those which result from the transfer-matrix formulation and exact quantum integrability of the system. The power of our result is that it is an operator statement and does not refer to the number of dimensions or the nature of the space-time manifold: lattice, continuum, or loop space, It is suggested how the establishment of this link between duality and integrability could be used to exploit the Kramers-Wannier-type self-duality of the four-dimensional SU(N) gauge theory to find hidden symmetry.

We make contact between the infinite-dimensional non-local symmetry of the type IIB superstring on AdS 5 × S 5 and a non-abelian infinite-dimensional symmetry algebra for the weakly coupled superconformal gauge theory. We explain why the planar limit of the one-loop dilatation operator is the Hamiltonian of a spin chain, and show that it commutes with the g 2 N = 0 limit of the non-abelian charges.

Mechanics (McGraw-Hill , New York, 1964), Part I. %. Matsson, Nucl. Phys. e, 647 (1969); M. Roos and A. Sirlin, ibid. E , 296 (1971); D. A. Ross, Nuovo Cimento 10, 475 (1972).The effective potential is computed to order ti in an Abelian gauge theory-scalar electrodynamics. The calculation is performed first in the ghost-requiring R gauges. The corresponding expression is also derived from the unitary Lagrangian. W e discuss the gauge dependence of the effective potential and its minima in connection with spontaneous symmetry breakdown; and we interpret the unitary computation tot be the physically relevant one.