Probing bad theories with the dualization algorithm I
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866914738705793024 |
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| author | Giacomelli, Simone Hwang, Chiung Marino, Fabio Pasquetti, Sara Sacchi, Matteo |
| author_facet | Giacomelli, Simone Hwang, Chiung Marino, Fabio Pasquetti, Sara Sacchi, Matteo |
| contents | Recently an algorithm to build $SL(2,\mathbb{Z})$ duals, including mirror duals, of 3d $\mathcal{N}=4$ quiver theories and their 4d $\mathcal{N}=1$ uplift has been introduced. In this work we use this new tool to study the so-called bad theories. Our approach allows us to determine exactly indices/partition functions for generic values of fugacities/real mass and FI parameters revealing their surprising feature: the 4d index/3d partition function of a bad theory behaves as a sum of distributions rather than an ordinary function of the deformation parameters. We focus on the bad SQCD, with $U(N_c)$ gauge group in 3d and $USp(2N_c)$ in 4d, while in an upcoming paper we will consider linear quivers which, in the 3d case, have both unitary and special unitary bad nodes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05326 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Probing bad theories with the dualization algorithm I Giacomelli, Simone Hwang, Chiung Marino, Fabio Pasquetti, Sara Sacchi, Matteo High Energy Physics - Theory Recently an algorithm to build $SL(2,\mathbb{Z})$ duals, including mirror duals, of 3d $\mathcal{N}=4$ quiver theories and their 4d $\mathcal{N}=1$ uplift has been introduced. In this work we use this new tool to study the so-called bad theories. Our approach allows us to determine exactly indices/partition functions for generic values of fugacities/real mass and FI parameters revealing their surprising feature: the 4d index/3d partition function of a bad theory behaves as a sum of distributions rather than an ordinary function of the deformation parameters. We focus on the bad SQCD, with $U(N_c)$ gauge group in 3d and $USp(2N_c)$ in 4d, while in an upcoming paper we will consider linear quivers which, in the 3d case, have both unitary and special unitary bad nodes. |
| title | Probing bad theories with the dualization algorithm I |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2309.05326 |