Finiteness of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Super-Yang–Mills Effective Action in Terms of Dressed <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> Superfields
We argue in favor of the independence on any scale, ultraviolet or infrared, in kernels of the effective action expressed in terms of dressed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvari...
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MDPI AG
2023-11-01
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| Online Access: | https://www.mdpi.com/2571-712X/6/4/63 |
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| author | Igor Kondrashuk Ivan Schmidt |
| author_facet | Igor Kondrashuk Ivan Schmidt |
| author_sort | Igor Kondrashuk |
| collection | DOAJ |
| description | We argue in favor of the independence on any scale, ultraviolet or infrared, in kernels of the effective action expressed in terms of dressed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> superfields for the case of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> super-Yang–Mills theory. Under “scale independence” of the effective action of dressed mean superfields, we mean its “finiteness in the off-shell limit of removing all the regularizations”. This off-shell limit is scale independent because no scale remains inside these kernels after removing the regularizations. We use two types of regularization: regularization by dimensional reduction and regularization by higher derivatives in its supersymmetric form. Based on the Slavnov–Taylor identity, we show that dressed fields of matter and of vector multiplets can be introduced to express the effective action in terms of them. Kernels of the effective action expressed in terms of such dressed effective fields do not depend on the ultraviolet scale. In the case of dimensional reduction, by using the developed technique, we show how the problem of inconsistency of the dimensional reduction can be solved. Using Piguet and Sibold formalism, we indicate that the dependence on the infrared scale disappears off shell in both the regularizations. |
| first_indexed | 2024-03-08T20:27:41Z |
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| id | doaj.art-174f34637167474aa5912c3f0f6ed08e |
| institution | Directory Open Access Journal |
| issn | 2571-712X |
| language | English |
| last_indexed | 2024-03-08T20:27:41Z |
| publishDate | 2023-11-01 |
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| series | Particles |
| spelling | doaj.art-174f34637167474aa5912c3f0f6ed08e2023-12-22T14:30:43ZengMDPI AGParticles2571-712X2023-11-0164993100810.3390/particles6040063Finiteness of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Super-Yang–Mills Effective Action in Terms of Dressed <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> SuperfieldsIgor Kondrashuk0Ivan Schmidt1Departamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Casilla 110-V, Valparaiso 2390123, ChileDepartamento de Física, Universidad Técnica Federico Santa María, Avenida España 1680, Casilla 110-V, Valparaiso 2390123, ChileWe argue in favor of the independence on any scale, ultraviolet or infrared, in kernels of the effective action expressed in terms of dressed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> superfields for the case of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> super-Yang–Mills theory. Under “scale independence” of the effective action of dressed mean superfields, we mean its “finiteness in the off-shell limit of removing all the regularizations”. This off-shell limit is scale independent because no scale remains inside these kernels after removing the regularizations. We use two types of regularization: regularization by dimensional reduction and regularization by higher derivatives in its supersymmetric form. Based on the Slavnov–Taylor identity, we show that dressed fields of matter and of vector multiplets can be introduced to express the effective action in terms of them. Kernels of the effective action expressed in terms of such dressed effective fields do not depend on the ultraviolet scale. In the case of dimensional reduction, by using the developed technique, we show how the problem of inconsistency of the dimensional reduction can be solved. Using Piguet and Sibold formalism, we indicate that the dependence on the infrared scale disappears off shell in both the regularizations.https://www.mdpi.com/2571-712X/6/4/63<i>R</i>-operationgauge symmetry<i>N</i> = 4 supersymmetrySlavnov–Taylor identity |
| spellingShingle | Igor Kondrashuk Ivan Schmidt Finiteness of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Super-Yang–Mills Effective Action in Terms of Dressed <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> Superfields Particles <i>R</i>-operation gauge symmetry <i>N</i> = 4 supersymmetry Slavnov–Taylor identity |
| title | Finiteness of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Super-Yang–Mills Effective Action in Terms of Dressed <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> Superfields |
| title_full | Finiteness of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Super-Yang–Mills Effective Action in Terms of Dressed <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> Superfields |
| title_fullStr | Finiteness of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Super-Yang–Mills Effective Action in Terms of Dressed <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> Superfields |
| title_full_unstemmed | Finiteness of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Super-Yang–Mills Effective Action in Terms of Dressed <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> Superfields |
| title_short | Finiteness of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Super-Yang–Mills Effective Action in Terms of Dressed <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> Superfields |
| title_sort | finiteness of inline formula math display inline semantics mrow mi mathvariant script n mi mo mo mn 4 mn mrow semantics math inline formula super yang mills effective action in terms of dressed inline formula math display inline semantics mrow mi mathvariant script n mi mo mo mn 1 mn mrow semantics math inline formula superfields |
| topic | <i>R</i>-operation gauge symmetry <i>N</i> = 4 supersymmetry Slavnov–Taylor identity |
| url | https://www.mdpi.com/2571-712X/6/4/63 |
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