N = 4 SYM low-energy effective action in N = 4 harmonic superspace
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= 4 SYM LowEnergy Effective Action in ᏺ = 4 Harmonic Superspace1 I. B. Samsonov Laboratory of Mathematical Physics, Tomsk Polytechnic University, Tomsk, 634050 Russia email: [email protected] Abstract—We apply the ᏺ = 4 harmonic superspace with USp(4) harmonic variables for describing the ᏺ = 4 SYM lowenergy effective action. Scale invariance and gauge symmetry fix the leading term in the low energy effective action uniquely, up to a constant. The value of the remaining constant can be fixed by the topological quantization condition for the Wess–Zumino term which is present in the component structure of this action. DOI: 10.1134/S1063779612050346 1
1. INTRODUCTION AND SUMMARY
The problem of lowenergy effective action in ᏺ = 4 SYM theory is very interesting for its applications to the D3brane dynamics in string theory (see, e.g., [1]), but it can be considered by its own due to its wonderful properties. Indeed, the ᏺ = 4 SYM model is a rare example of completely finite quantum field theory which respects the superconformal symmetry not only on the classical but also on the quantum level. The maximally extended supersymmetry and superconfor mal invariance restrict the quantum dynamics so strong that the leading terms in the effective action can be obtained without employing the perturbative calcu lations. In the present work we demonstrate that the ᏺ = 4 harmonic superspace approach is very useful for studying the leading terms in the ᏺ = 4 SYM effective action. The ᏺ = 4 gauge multiplet consists of ᏺ = 2 gauge multiplet and hypermultiplet which are naturally described within the ᏺ = 2 harmonic superspace approach [2]. In this superspace, half of supersymme tries of the ᏺ = 4 gauge theory are realized explicitly while another half are hidden. Therefore it is quite nontrivial to respect these hidden supersymmetries on the quantum level as the symmetries of the effective action. For instance, the part of the ᏺ = 4 SYM effec tive action in the sector of ᏺ = 2 gauge multiplet was known long ago, [3, 4], but it took several years to find a hypermultiplet completion of this action which is compatible with hidden ᏺ = 2 supersymmetries [5]. Our aim is to develop such a superspace description of the lowenergy effective action which makes all the supersymmetries of the ᏺ = 4 theory manifest. 1 The article is published in the original.
In the present work we consider the ᏺ = 4 har monic superspace with USp(4) harmonic variables [6, 7]. As we will show, the ᏺ = 4 superfield strength in this superspace is described by single chargeless ana lytic superfield. It is very easy to construct a scale invariant action with this superfield. By considering the component structure of this action we show that it takes into account all terms in the ᏺ = 4 lowenergy effective action up to the fourderivative order on mass shell. In particular, we derive the WessZumino and F 4/X 4 terms. 2. ᏺ = 4 SUPERGAUGE MULTIPLET IN ᏺ = 4 USp(4) HARMONIC SUPERSPACE Conventional ᏺ = 4 superspace is parametrized by i the coordinates (
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