superparticle and super-Yang–Mills theory in harmonic superspace

Abstract

We study the N =4 harmonic superparticle model, both with and without central charge and quantize it. Since the central charge breaks the U (4) R-symmetry group of the N =4 superalgebra down to U Sp(4), we consider the superparticle dynamics in N =4 harmonic superspace with U Sp(4)/(U (1) × U (1)) harmonic variables. We show that the quantization of a massive superparticle with central charge leads to a superfield realization of the N =4 massive vector multiplet in N =4 harmonic superspace. In the massless case without central charge the superparticle quantization reproduces three different multiplets: the N =4 SYM multiplet, the N =4 gravitino multiplet and N =4 supergravity multiplet. The SYM multiplet is described by six analytic superfield strengths with different types of analyticity. We show that these strengths solve the N =4 SYM constraints and can be used for the construction of actions in N =4 harmonic superspace.

Towards harmonic superfield formulation of N=4, USp(4) SYM theory with the central charge

“…, which are inert under supersymmetry and take the values in the fundamental representation of USp(4) [19], [18] (see Appendix B for details) 10 . Using the harmonics u…”

“…and so on, allowing us to define a reality condition in harmonic superspace [19], [18]. With the help of the harmonics u…”

“…Some superspace aspects of the theory under consideration have been discussed in the earlier papers [16], [17], [18]. The paper [16] is devoted to construction of the above theory in terms of N = 1 superfields where the component constraint from [1] has been written in N = 1 superfield form.…”

“…Here the superfield constraints, originating from the Bianchi identities and determining the correct USp(4) vector multiplet with the central charge have been formulated and solved in terms of some superfield strengths. In the papers [18] the aspects of a N = 4 SYM theory in harmonic superspace with the central charge were studied and applied for the construction of Abelian low-energy effective action. In the present paper we prove that the constraint for the auxiliary field, introduced in [1] for non-Abelian theory, automatically follows from the N = 4 superfield constraints stipulated by the Bianchi identities, obtained in [17].…”

“…Using the covariant derivatives and solving the Bianchi identities, we can immediately write down the supersymmetry transformations (2) By analogy with the case of the N = 2 models with the intrinsic central charge [12]- [15], the equations (14,18,19) can be called the generalized Dirac equation, the Yang-Mills equation and the Klein-Gordon equation respectively. Thus the central charge plays the role of 'fifth coordinate'.…”