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The SL(2, ℤ) dualization algorithm at work

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Comi, Riccardo 
Hwang, Chiung 
Marino, Fabio 
Pasquetti, Sara 


jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pRecently an algorithm to dualize a theory into its mirror dual has been proposed, both for 3jats:italicd</jats:italic>jats:inline-formulajats:alternativesjats:tex-math$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml=""> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 4 linear quivers and for their 4jats:italicd</jats:italic>jats:inline-formulajats:alternativesjats:tex-math$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml=""> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 1 uplift. This mimics the manipulations done at the level of the Type IIB brane setup that engineers the 3jats:italicd</jats:italic> theories, where mirror symmetry is realized as jats:italicS</jats:italic>-duality, but it is enirely field-theoretic and based on the application of genuine infra-red dualities that implement the local action of jats:italicS</jats:italic>-duality on the quiver. In this paper, we generalize the algorithm to the full duality group, which is SL(2jats:italic,</jats:italic> ℤ) in 3jats:italicd</jats:italic> and PSL(2jats:italic,</jats:italic> ℤ) in 4jats:italicd</jats:italic>. This also produces dualities for 3jats:italicd</jats:italic>jats:inline-formulajats:alternativesjats:tex-math$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml=""> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 3 theories with Chern-Simons couplings, some of which have enhanced jats:inline-formulajats:alternativesjats:tex-math$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml=""> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 4 supersymmetry, and their new 4jats:italicd</jats:italic>jats:inline-formulajats:alternativesjats:tex-math$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml=""> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 1 counterpart. In addition, we propose three ways to study the RG flows triggered by possible VEVs appearing at the last step of the algorithm, one of which uses a new duality that implements the Hanany-Witten move in field theory.</jats:p>



4902 Mathematical Physics, 5107 Particle and High Energy Physics, 49 Mathematical Sciences, 51 Physical Sciences

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Journal of High Energy Physics

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Springer Science and Business Media LLC