Unconstrained off-shell N=3 supersymmetric Yang-Mills theory

Abstract

Harmonic superspace is used to build up an unconstrained off-shell formulation of N=3 supersymmetry Yang-Mills theory. The theory is defined in an analytic N=3 superspace having M4(X)SU(3)/(U(1)(X)U(1)) as an even part. The basic objects are the analytic potentials which serve as gauge connections entering harmonic derivatives. The action is an integral over analytic superspace. The Lagrange density is surprisingly simple and it is gauge invariant up to total harmonic derivative. The equations of motion are integrability conditions on the internal space SU(3)/U(1)(X)U(1). It is the infinite set of auxiliary fields that allows the authors to overcome the 'N=3 barrier'.

Superconformal symmetry in three dimensions

“…The formalism is powerful for applications whenever there exist off-shell superfield formulations for superconformal theories, and such formulations are known in four-dimensions for N = 1, 2, 3 [7][8][9][10][11] and in three-dimensions for N = 1, 2, 3, 4 [12][13][14][15][16][17][18][19]. In fact within the formalism Osborn elaborated the analysis of N = 1 superconformal symmetry for fourdimensional quantum field theories [20], and recently Kuzenko and Theisen determine the general structure of two-and three-point functions of the supercurrent and the flavour current of N = 2 superconformal field theories [21].…”

Untitled

“…The generalization to N = 3 was given in Ref. [9] and later on to general N in Refs. [16] (under the name of "(N, p, q) superspace").…”

Superbrane actions and geometrical approach

“…The variation of the actions (19) and (21) with respect to the auxiliary fields F ab , H abc (x) and v a (x) produces algebraic expressions for the Lagrange multipliers Q (n) , which thus do not describe independent degrees of freedom of the models. Note also that, at least for the Dirichlet branes with p ≤ 4, one can invert the equations for Q p−1 in terms of F ab , express the latter in terms of the former and substitute them in the action.…”

“…To compute the κ-transformation of the actions (19) and (21) we should also know the κ-variations of the Lorentz-harmonic fields u a b , which are genuine worldvolume fields. However these variations are multiplied by algebraic field equations such as (16) and (20) and, therefore, they can be appropriately chosen to compensate possible terms proportional to the algebraic equations that arise from the variation of other terms.…”

“…Thus by construction the actions (19) and (21) are integrals of (p + 1)-forms L p+1 and one can show that their κ-variation has the following general structure [17]:…”