A Format for Instantons and Their Characterizations.pdf

a r X i v : p h y s i c s / 0 5 0 7 1 7 1 v 1 [ p h y s i c s .g e n - p h ] 2 3 J u l 2 0 0 5 hep-th/0507171 A Format for Instantons and Their Characterizations Gordon Chalmers e-mail: gordon@ Abstract A characterization of instanton contributions to gauge field theory is given. The dynamics of instantons with the gluon field is given in terms of ’classical’ instanton contributions, i.e. on the same footing as tree amplitudes in field theory. This para- materization depends on the kinematics of the local instanton operators and their coupling dependence. A primary advantage of this ’classical’ formulation is that the weak-strong duality and its relations with the perturbative sector are possibly made more manifest. 1 Introduction The classical dynamics of gauge theory has been investigated for many years. Obsta- cles associated with the computation of these tree amplitudes have been circumvented for a variety of reasons, including spinor helicity, color ordering, analyticity, KLT re- lations with gravity, the string-inspired derivation, and the recent twistor formulation of classical gauge theory. The derivative expansion is useful for finding results in the quantum regime [1]-[16]. Potential simplifications based on a well-ordered formulation of the instanton contributions to an n-point scattering amplitude can be useful in finding the total correction to the quantum amplitudes. These terms to the amplitude take on the form at n-point, fm,n = gm,n(g,N) ∏ 1 t [p],ai,p i e ?m 4π g2 +m θ 2π K(εi, ki) , (1.1) with ai,p labeling the power of the invariant (both negative and positive). The helicity content containing the factors εi ·kj and εi ·εj is represented by the function K(εi, kj). The kinematic invariants t [p] i are defined by t [p] i = (ki + ki+1 + . . .+ ki+p?1) 2 , (1.2) for an ordering of the external legs in the cyclic fashion (1, 2, . . . , n). The coefficients gm,n enter as a result of the integration of the non-trivial gauge field configuration a