4d S-duality wall and SL(2, ℤ) relations


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Authors
Bottini, LE 
Hwang, C 
Pasquetti, S 
Abstract

jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pIn this paper we present various 4jats:italicd</jats:italic>jats:inline-formulajats:alternativesjats:tex-math$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 1 dualities involving theories obtained by gluing two jats:italicE</jats:italic>[USp(2jats:italicN</jats:italic>)] blocks via the gauging of a common USp(2jats:italicN</jats:italic>) symmetry with the addition of 2jats:italicL</jats:italic> fundamental matter chiral fields. For jats:italicL</jats:italic> = 0 in particular the theory has a quantum deformed moduli space with chiral symmetry breaking and its index takes the form of a delta-function. We interpret it as the Identity wall which identifies the two surviving USp(2jats:italicN</jats:italic>) of each jats:italicE</jats:italic>[USp(2jats:italicN</jats:italic>)] block. All the dualities are derived from iterative applications of the Intriligator-Pouliot duality. This plays for us the role of the fundamental duality, from which we derive all others. We then focus on the 3jats:italicd</jats:italic> version of our 4jats:italicd</jats:italic> dualities, which now involve the jats:inline-formulajats:alternativesjats:tex-math$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 4 jats:italicT</jats:italic>[SU(jats:italicN</jats:italic>)] quiver theory that is known to correspond to the 3jats:italicd S</jats:italic>-wall. We show how these 3jats:italicd</jats:italic> dualities correspond to the relations jats:italicS</jats:italic>jats:sup2</jats:sup> = jats:italic−</jats:italic>1, jats:italicS</jats:italic>jats:supjats:italic−</jats:italic>1</jats:sup>jats:italicS</jats:italic> = 1 and jats:italicSTS</jats:italic> = jats:italicT</jats:italic>jats:supjats:italic−</jats:italic>1</jats:sup>jats:italicS</jats:italic>jats:supjats:italic−</jats:italic>1</jats:sup>jats:italicT</jats:italic>jats:supjats:italic−</jats:italic>1</jats:sup> for the jats:italicS</jats:italic> and jats:italicT</jats:italic> generators of SL(2jats:italic,</jats:italic> ℤ). These observations lead us to conjecture that jats:italicE</jats:italic>[USp(2jats:italicN</jats:italic>)] can also be interpreted as a 4jats:italicd S</jats:italic>-wall.</jats:p>

Description
Keywords
Regular Article - Theoretical Physics, Duality in Gauge Field Theories, Supersymmetric Gauge Theory, Supersymmetry and Duality
Journal Title
Journal of High Energy Physics
Conference Name
Journal ISSN
1029-8479
1029-8479
Volume Title
2022
Publisher
Springer Science and Business Media LLC