Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories (original) (raw)

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We study the six-dimensional [Formula: see text] and [Formula: see text] supersymmetric Yang–Mills (SYM) theories in the component formulation. The one-loop divergencies of effective action are calculated. The leading one-loop low-energy contributions to bosonic sector of effective action are found. It is explicitly demonstrated that the contributions to effective potential for the constant background scalar fields are absent in the [Formula: see text] SYM theory.

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We consider the harmonic superspace formulation of higher-derivative 6D, N = (1, 0) supersymmetric gauge theory and its minimal coupling to a hypermultiplet. In components, the kinetic term for the gauge field in such a theory involves four space-time derivatives. The theory is quantized in the framework of the superfield background method ensuring manifest 6D, N = (1, 0) supersymmetry and the classical gauge invariance of the quantum effective action. We evaluate the superficial degree of divergence and prove it to be independent of the number of loops. Using the regularization by dimensional reduction, we find possible counterterms and show that they can be removed by the coupling constant renormalization for any number of loops, while the divergences in the hypermultiplet sector are absent at all. Assuming that the deviation of the gauge-fixing term from that in the Feynman gauge is small, we explicitly calculate the divergent part of the one-loop effective action in the lowest order in this deviation. In the approximation considered, the result is independent of the gauge-fixing parameter and agrees with the earlier calculation for the theory without a hypermultiplet.

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We study the one-loop effective action for 6D, N = (1, 0) supersymmetric Yang-Mills (SYM) theory with hypermultiplets and 6D, N = (1, 1) SYM theory as a subclass of the former, using the off-shell formulation of these theories in 6D, N = (1, 0) harmonic superspace. We develop the corresponding supergraph technique and apply it to compute the one-loop divergences in the background field method ensuring the manifest gauge invariance. We calculate the two-point Green functions of the gauge superfield and the hypermultiplet, as well as the three-point gauge-hypermultipet Green function. Using these Green functions and exploiting gauge invariance of the theory, we find the full set of the off-shell one-loop divergent contributions, including the logarithmic and power ones. Our results precisely match with those obtained earlier in [1, 2] within the proper time superfield method.

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We study the gauge dependence of one-loop divergences in a general matter-coupled 6D, N = (1, 0) supersymmetric gauge theory in the harmonic superspace formulation. Our analysis is based on the effective action constructed by the background superfield method, with the gauge-fixing term involving one real parameter ξ 0. A manifestly gauge invariant and N = (1, 0) supersymmetric procedure for calculating the one-loop effective action is developed. It yields the one-loop divergences in an explicit form and allows one to investigate their gauge dependence. As compared to the minimal gauge, ξ 0 = 1, the divergent part of the general-gauge effective action contains a new term depending on ξ 0. This term vanishes for the background superfields satisfying the classical equations of motion, so that the S-matrix divergences are gauge-independent. In the case of 6D, N = (1, 1) SYM theory we demonstrate that some divergent contributions in the non-minimal gauges do not vanish off shell, as opposed to the minimal gauge.

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We study the off-shell structure of the two-loop effective action in 6D,mathcalN\\mathcal{N}mathcalN N = (1, 1) supersymmetric gauge theories formulated in mathcalN\\mathcal{N}mathcalN N = (1, 0) harmonic superspace. The off-shell effective action involving all fields of 6D,mathcalN\\mathcal{N}mathcalN N = (1, 1) supermultiplet is constructed by the harmonic superfield background field method, which ensures both manifest gauge covariance and manifest mathcalN\\mathcal{N}mathcalN N = (1, 0) supersymmetry. We analyze the off-shell divergences dependent on both gauge and hypermultiplet superfields and argue that the gauge invariance of the divergences is consistent with the non-locality in harmonics. The two-loop contributions to the effective action are given by harmonic supergraphs with the background gauge and hypermultiplet superfields. The procedure is developed to operate with the harmonic-dependent superpropagators in the two-loop supergraphs within the superfield dimensional regularization. We explicitly calculate the ga...

Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

Journal of High Energy Physics, 2020

We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, mathcalN\mathcal{N}mathcalN N = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and mathcalN\mathcal{N}mathcalN N = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

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There are currently many string inspired conjectures about the structure of the low-energy effective action for super Yang-Mills theories which require explicit multi-loop calculations. In this paper, we develop a manifestly covariant derivative expansion of superspace heat kernels and present a scheme to evaluate multiloop contributions to the effective action in the framework of the background field method. The crucial ingredient of the construction is a detailed analysis of the properties of the parallel displacement propagators associated with Yang-Mills supermultiples in N -extended superspace.