Non minimal D-type conformal matter compactified on three punctured spheres
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Springer
Received: August 12, 2020 Accepted: September 22, 2020 Published: October 22, 2020
Evyatar Sabag Department of Physics, Technion, Haifa, 32000, Israel
E-mail: [email protected] Abstract: We study compactifications of 6d non minimal (Dp+3 , Dp+3 ) type conformal matter. These can be described by N M5-branes probing a Dp+3 -type singularity. We derive 4d Lagrangians corresponding to compactifications of such 6d SCFTs on three punctured spheres (trinions) with two maximal punctures and one minimal puncture. The trinion models are described by simple N = 1 quivers with SU(2N ) gauge nodes. We derive the trinion Lagrangians using RG flows between the aforementioned 6d SCFTs with different values of p and their relations to matching RG flows in their compactifications to 4d. The suggested trinions are shown to reduce to known models in the minimal case of N = 1. Additional checks are made to show the new minimal punctures uphold the expected S-duality between models in which we exchange two such punctures. We also show that closing the new minimal puncture leads to expected flux tube models. Keywords: Field Theories in Higher Dimensions, Supersymmetric Gauge Theory, Supersymmetry and Duality ArXiv ePrint: 2007.13567
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)139
JHEP10(2020)139
Non minimal D-type conformal matter compactified on three punctured spheres
Contents 1 Introduction
1
2 Trinion compactification of the Dp+3 SCFT 2.1 The trinion 2.2 Checks
3 3 7 11 11
A The N = 1 superconformal index
17
B S-duality proof for exchanging minimal punctures
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C The Dp+3 ’t Hooft anomaly predictions from 6d
22
1
13
Introduction
In the recent decade, following the influential work of [1] there has been a plethora of work relating compactifications of 6d SCFTs on a Riemann surface to Lagrangian 4d SCFTs. Such relations were understood for general Riemann surfaces with fluxes for several specific 6d SCFTs, including A1 and A2 (2, 0) [1, 2], A1 (2, 0) probing a Z2 singularity [3–5], the rank one E-string [6, 7], and for SO(8) and SU(3) minimal SCFTs [8]. In addition, recently such relations have been found for entire classes of 6d SCFTs for general Riemann surfaces with fluxes, including A1 (2, 0) probing a Zk singularity and A0 (2, 0) probing a DN +3 singularity [9, 10]. There are many more SCFTs for which only special surfaces Lagrangians are known. For example (2, 0) SCFTs probing higher rank E-string or ADE singularities on tori surfaces or genus zero surfaces with two punctures or less [11–15]. The relations between 4d and 6d SCFTs lead to many new understandings regarding dualities and their relation to geometry, as well as emergent IR symmetries [16]. One method to find 4d Lagrangians related to 6d compactifications is by using anomaly predictions from 6d [7]. These are used to predict the number of vector and hyper multiplets of the 4d theory assuming it is a conformal gauge theory with all the gauge couplings having vanishing one loop β f
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