On the two-loop divergences of the 2-point hypermultiplet supergraphs for 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>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> SYM theory

We exploit the 6D,$$ \mathcal{N} $$ N = (1, 0) and $$ \mathcal{N} $$ N = (1, 1) harmonic superspace approaches to construct the full set of the maximally supersymmetric on-shell invariants of the canonical dimension d = 12 in 6D,$$ \mathcal{N} $$ N = (1, 1) supersymmetric Yang-Mills (SYM) theory. Both single- and double-trace invariants are derived. Only four single-trace and two double-trace invariants prove to be independent. The invariants constructed can provide the possible counterterms of $$ \mathcal{N} $$ N = (1, 1) SYM theory at four-loop order, where the first double-trace divergences are expected to appear. We explicitly exhibit the gauge sector of all invariants in terms of $$ \mathcal{N} $$ N = (1, 0) gauge superfields and find the absence of $$ \mathcal{N} $$ N = (1, 1) supercompletion of the F6 term in the abelian limit.

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“…The explicit quantum harmonic superfield calculations confirming this statement were performed in[36,37].…”

mentioning

confidence: 73%

Higher-dimensional invariants in 6D super Yang-Mills theory

Buyucli¹,

Ivanov

2021

J. High Energ. Phys.

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“…The main advantage of such a formulation is the possibility to keep manifest N = (1, 0) supersymmetry at all steps of quantum calculations. In our recent papers [44][45][46][47][48][49][50] we developed the harmonic superfield approach for calculating the lowest off-shell quantum corrections in various 6D, N = (1, 0) and N = (1, 1) supersymmetric theories. In the present paper we apply this superfield technique for studying the one-loop effective action in 6D, N = (1, 0) higher-derivative gauge theory of ref.…”

Section: Jhep08(2020)169mentioning

confidence: 99%

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

Buchbinder

Ivanov²,

Мерзликин

et al. 2020

J. High Energ. Phys.

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We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ 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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“…Although 6D, N = (1, 1) non-abelian SYM theory is non-renormalizable by power counting, it was proved that it is on-shell finite at one and two loops [28][29][30][31][32][33][34][35]. Moreover, it was recently shown that this theory is one-loop finite even off-shell [36][37][38] and that the two-loop diagrams with hypermultiplet legs are also off-shell finite [39].…”

Section: Jhep09(2018)039mentioning

confidence: 99%

Leading low-energy effective action in 6D, $$ \mathcal{N}=\left(1,1\right) $$ SYM theory

Buchbinder

Ivanov²,

Мерзликин

2018

J. High Energ. Phys.

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We elaborate on the low-energy effective action of 6D, N = (1, 1) supersymmetric Yang-Mills (SYM) theory in the N = (1, 0) harmonic superspace formulation. The theory is described in terms of analytic N = (1, 0) gauge superfield V ++ and analytic ω-hypermultiplet, both in the adjoint representation of gauge group. The effective action is defined in the framework of the background superfield method ensuring the manifest gauge invariance along with manifest N = (1, 0) supersymmetry. We calculate leading contribution to the one-loop effective action using the on-shell background superfields corresponding to the option when gauge group SU(N) is broken to SU(N −1)×Υ(1) ⊂ SU(N). In the bosonic sector the effective action involves the structure ∼ F 4 X 2 , where F 4 is a monomial of the fourth degree in an abelian field strength F M N and X stands for the scalar fields from the ω-hypermultiplet. It is manifestly demonstrated that the expectation values of the hypermultiplet scalar fields play the role of a natural infrared cutoff.

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

Cited by 14 publications

References 39 publications

Higher-dimensional invariants in 6D super Yang-Mills theory

Higher-dimensional invariants in 6D super Yang-Mills theory

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

Leading low-energy effective action in 6D, $$ \mathcal{N}=\left(1,1\right) $$ SYM theory

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