The renormalization structure of 6D,N=(1,0) supersymmetric higher-derivative gauge theory (original) (raw)
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Symmetry, 2019
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 su...
Supergraph analysis of the one-loop divergences in 6 D ,N=(1,0)andN=(1,1)gauge theories
Nuclear Physics B, 2017
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.
On two-loop divergences of effective action in 6D, mathcalN\\mathcal{N}mathcalN = (1, 1) SYM theory
Journal of High Energy Physics
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...
On gauge dependence of the one-loop divergences in 6D, N=(1,0) and N=(1,1) SYM theories
Physics Letters B, 2019
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.
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.
One-loop divergences in 6D, N mathcalN\mathcal{N}mathcalN = (1, 0) SYM theory
Journal of High Energy Physics, 2017
We consider, in the harmonic superspace approach, the six-dimensional N = (1, 0) supersymmetric Yang-Mills gauge multiplet minimally coupled to a hypermultiplet in an arbitrary representation of the gauge group. Using the superfield proper-time and background-field techniques, we compute the divergent part of the one-loop effective action depending on both the gauge multiplet and the hypermultiplet. We demonstrate that in the particular case of N = (1, 1) SYM theory, which corresponds to the hypermultiplet in the adjoint representation, all one-loop divergencies vanish, so that N = (1, 1) SYM theory is one-loop finite off shell.
Gauge dependence of the one-loop divergences in 6D, N=(1,0) abelian theory
Nuclear Physics B, 2018
We study the gauge dependence of the one-loop effective action for the abelian 6D, N = (1, 0) supersymmetric gauge theory formulated in harmonic superspace. We introduce the superfield ξ-gauge, construct the corresponding gauge superfield propagator, and calculate the one-loop two-and three-point Green functions with two external hypermultiplet legs. We demonstrate that in the general ξ-gauge the two-point Green function of the hypermultiplet is divergent, as opposed to the Feynman gauge ξ = 1. The three-point Green function with two external hypermultiplet legs and one leg of the gauge superfield is also divergent. We verified that the Green functions considered satisfy the Ward identity formulated in N = (1, 0) harmonic superspace and that their gauge dependence vanishes on shell. Using the result for the two-and three-point Green functions and arguments based on the gauge invariance, we present the complete divergent part of the one-loop effective action in the general ξ-gauge.
On the two-loop divergences in 6D, calN=(1,1){\cal N}=(1,1)calN=(1,1) SYM theory
2021
We continue studying 6D,N = (1, 1) supersymmetric Yang-Mills (SYM) theory in the N = (1, 0) harmonic superspace formulation. Using the superfield background field method we explore the two-loop divergencies of the effective action in the gauge multiplet sector. It is explicitly demonstrated that among four two-loop background-field dependent supergraphs contributing to the effective action, only one diverges off shell. It is also shown that the divergences are proportional to the superfield classical equations of motion and hence vanish on shell. Besides, we have analyzed a possible structure of the two-loop divergences on general gauge and hypermultiplet background. joseph@tspu.edu.ru eivanov@theor.jinr.ru merzlikin@tspu.edu.ru stepan@m9com.ru
Modern Physics Letters A, 2019
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.