𝒩 = 1 Curves on Generalized Coulomb Branches of Supersymmetric Gauge Theories
We study the low energy effective dynamics of four-dimensional <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&...
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MDPI AG
2022-02-01
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| Online Access: | https://www.mdpi.com/2218-1997/8/2/101 |
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| author | Thomas Bourton Elli Pomoni Xinyu Zhang |
| author_facet | Thomas Bourton Elli Pomoni Xinyu Zhang |
| author_sort | Thomas Bourton |
| collection | DOAJ |
| description | We study the low energy effective dynamics of four-dimensional <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> superconformal theories on their generalized Coulomb branch. The low energy effective gauge couplings are naturally encoded in algebraic curves <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">X</mi></semantics></math></inline-formula>, which we derive for general values of the couplings and mass deformations. We then recast these IR curves <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">X</mi></semantics></math></inline-formula> to the UV or M-theory form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">C</mi></semantics></math></inline-formula>: the punctured Riemann surfaces on which the M5 branes are compactified giving the four-dimensional theories. We find that the UV curves <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">C</mi></semantics></math></inline-formula> and their corresponding meromorphic differentials take the same form as those for their mother four-dimensional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> theories of class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula>. They have the same poles, and their residues are functions of all the exactly marginal couplings and the bare mass parameters which we can compute exactly. |
| first_indexed | 2024-03-09T20:55:28Z |
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| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T20:55:28Z |
| publishDate | 2022-02-01 |
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| spelling | doaj.art-6593841d6ddf41d8bfae24ab414fb2eb2023-11-23T22:23:24ZengMDPI AGUniverse2218-19972022-02-018210110.3390/universe8020101𝒩 = 1 Curves on Generalized Coulomb Branches of Supersymmetric Gauge TheoriesThomas Bourton0Elli Pomoni1Xinyu Zhang2Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, GermanyDeutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, GermanyDeutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, GermanyWe study the low energy effective dynamics of four-dimensional <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> superconformal theories on their generalized Coulomb branch. The low energy effective gauge couplings are naturally encoded in algebraic curves <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">X</mi></semantics></math></inline-formula>, which we derive for general values of the couplings and mass deformations. We then recast these IR curves <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">X</mi></semantics></math></inline-formula> to the UV or M-theory form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">C</mi></semantics></math></inline-formula>: the punctured Riemann surfaces on which the M5 branes are compactified giving the four-dimensional theories. We find that the UV curves <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">C</mi></semantics></math></inline-formula> and their corresponding meromorphic differentials take the same form as those for their mother four-dimensional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> theories of class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">S</mi></semantics></math></inline-formula>. They have the same poles, and their residues are functions of all the exactly marginal couplings and the bare mass parameters which we can compute exactly.https://www.mdpi.com/2218-1997/8/2/101supersymmetrySeiberg-Witten curveclass 𝒮 |
| spellingShingle | Thomas Bourton Elli Pomoni Xinyu Zhang 𝒩 = 1 Curves on Generalized Coulomb Branches of Supersymmetric Gauge Theories Universe supersymmetry Seiberg-Witten curve class 𝒮 |
| title | 𝒩 = 1 Curves on Generalized Coulomb Branches of Supersymmetric Gauge Theories |
| title_full | 𝒩 = 1 Curves on Generalized Coulomb Branches of Supersymmetric Gauge Theories |
| title_fullStr | 𝒩 = 1 Curves on Generalized Coulomb Branches of Supersymmetric Gauge Theories |
| title_full_unstemmed | 𝒩 = 1 Curves on Generalized Coulomb Branches of Supersymmetric Gauge Theories |
| title_short | 𝒩 = 1 Curves on Generalized Coulomb Branches of Supersymmetric Gauge Theories |
| title_sort | 𝒩 1 curves on generalized coulomb branches of supersymmetric gauge theories |
| topic | supersymmetry Seiberg-Witten curve class 𝒮 |
| url | https://www.mdpi.com/2218-1997/8/2/101 |
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