Abstract
We review the recent progress in studying the quantum structure of 6 D , N = ( 1 , 0 ) , and N = ( 1 , 1 ) supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly N = ( 1 , 0 ) supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The N = ( 1 , 1 ) supersymmetric Yang–Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Furthermore, some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Furthermore, in the Abelian case, we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action.
Highlights
We briefly review some recent results [29,30,31,32,33,34] concerning the structure of the ultraviolet divergences and low-energy effective action in 6D, N = (1, 1) and N = (1, 0) SYM theories in the harmonic superspace approach
The pure 6D, N = (1, 0) SYM theory is described by the harmonic superspace action [20]:
If the hypermultiplet belongs to the adjoint representation, R = Adj, the action (13) describes N = (1, 1) SYM theory, which possesses a hidden N = (0, 1) supersymmetry in addition to the manifest N = (1, 0) one
Summary
The higher-dimensional supersymmetric gauge theories attract significant interest due to their remarkable properties in classical and quantum domains and profound links with string/brane theory. The quantum aspects of this formulation have not been worked out for the time being, and for this reason, we do not discuss this here.) The main purpose of this study is to reveal the structure of the off-shell divergences in the harmonic superspace approach and to find them explicitly in the lowest loops following the proposals of [8]. Such calculations can be done using either the formalism of harmonic supergraphs or the harmonic superspace generalization of the proper-time method of [37,38]. It is worth pointing out that such an effective action is closely related to the on-shell amplitudes in 6D maximally-extended supersymmetric Yang–Mills theories (see, e.g., [2] and the references therein) and to the so-called little strings [40,41,42]
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