Supergraph analysis of the one-loop divergences in 6D, N=(1,0) and N=(1,1) gauge theories

Abstract

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.

Original language	English
Pages (from-to)	127-158
Number of pages	32
Journal	Nuclear Physics B
Volume	921
DOIs	https://doi.org/10.1016/j.nuclphysb.2017.05.010
Publication status	Published - 1 Aug 2017

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.nuclphysb.2017.05.010

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Buchbinder, I. L., Ivanov, E. A., Merzlikin, B. S., & Stepanyantz, K. V. (2017). Supergraph analysis of the one-loop divergences in 6D, N=(1,0) and N=(1,1) gauge theories. Nuclear Physics B, 921, 127-158. https://doi.org/10.1016/j.nuclphysb.2017.05.010

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title = "Supergraph analysis of the one-loop divergences in 6D, N=(1,0) and N=(1,1) gauge theories",

abstract = "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.",

author = "Buchbinder, {I. L.} and Ivanov, {E. A.} and Merzlikin, {B. S.} and Stepanyantz, {K. V.}",

year = "2017",

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doi = "10.1016/j.nuclphysb.2017.05.010",

language = "English",

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pages = "127--158",

journal = "Nuclear Physics B",

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T1 - Supergraph analysis of the one-loop divergences in 6D, N=(1,0) and N=(1,1) gauge theories

AU - Buchbinder, I. L.

AU - Ivanov, E. A.

AU - Merzlikin, B. S.

AU - Stepanyantz, K. V.

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

AB - 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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