Gauge dependence of the one-loop divergences in 6D, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> abelian theory

Ivanov²,

et al. 2018

Physics Letters B

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We consider 6D, N = (1, 1) supersymmetric Yang-Mills theory formulated in N = (1, 0) harmonic superspace and analyze the structure of the two-loop divergences in the hypermultiplet sector. Using the N = (1, 0) superfield background field method we study the two-point supergraphs with the hypermultiplet legs and prove that their total contribution to the divergent part of effective action vanishes off shell.

“…This paper is a continuation and further development of our previous works on the structure of divergences in 6D, N = (1, 0) and N = (1, 1) gauge theories [1,2,3].…”

Section: Introductionmentioning

confidence: 67%

On the two-loop divergences of the 2-point hypermultiplet supergraphs for 6D, N=(1,1) SYM theory

Ivanov²,

et al. 2018

Physics Letters B

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“…Their non-abelian generalization is the Slavnov-Taylor identities [49,50]. The harmonic superspace Ward identities were constructed in [33] by making the transformation (2.18) in the generating functional (3.2). Using the notation…”

Section: Quantization Feynman Rules and Ward Identities In The Abelmentioning

confidence: 99%

“…5. The relevant expression was calculated in [33], and it has the form Figure 5: The harmonic supergraph representing the one-loop contribution to the three-point gauge-hypermultiplet function.…”

Section: One-loop Divergences and Their Gauge Dependencementioning

confidence: 99%

Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories

Ivanov²,

et al. 2019

Symmetry

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We review the recent progress in studying the quantum structure of 6D, 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) 1 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. Also 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. Also 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.

“…Like in our previous publications, we deal with the six-dimensional N = (1, 1) supersymmetric gauge theory formulated in N = (1, 0) harmonic superspace [17], [18], [19] (for the harmonic superspace approach, see [20], [21]). The theory is quantized in the framework of the harmonic superfield background method which was originally developed for 4D, N = 2 SYM theories in [22], [23], [24] 3 and then generalized to 6D, N = (1, 0) gauge theories in [8], [25], [26], [27].…”

Section: Introductionmentioning

confidence: 99%

“…The background superfield method for 4D, N = 2 gauge theories in harmonic superspace was worked out in[22] and generalized for six-dimensional gauge theory in N = (1, 0) harmonic superspace in the works[25],[26],[27].…”

mentioning

confidence: 99%

Low-energy 6D, N=(1,1) SYM effective action beyond the leading approximation

Ivanov²,

2020

Nuclear Physics B

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For 6D, N = (1, 1) SYM theory formulated in N = (1, 0) harmonic superspace as a theory of interacting gauge multiplet and hypermultiplet we construct the N = (1, 1) supersymmetric Heisenberg-Euler-type superfield effective action. The effective action is computed for the slowly varying on-shell background fields and involves, in the bosonic sector, all powers of a constant abelian strength.Note that 6D, N = (1, 1) SYM theory is non-renormalizable by power counting. However, it was found that this theory is on-shell finite at one and two loops [28], [29], [30], [31], [32], [33], [34], [35]. Recently, the aspects of renormalizability of the theory under consideration were studied by harmonic superspace techniques. It was shown that there is a gauge choice at which the one-loop divergences are completely canceled off shell [25], [26], [27]. Some two-loop harmonic supergraphs are also finite [36] 4 .1 These results were recently confirmed by the component calculations in [9]. 2 The relationships of the 6D, N = (1, 1) SYM theory with the low-energy dynamics of D5 branes are discussed in [14], [15], [16].3 Review of various applications of the background harmonic superfields for studying the effective actions of 4D, N = 2, 4 SYM theories was given in [6], [7]. 4 Gauge dependence of the one-loop divergences was studied in [37].