A string theory realization of special unitary quivers in 3 dimensions
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Springer
September November November November
16, 14, 25, 27,
2020 2020 2020 2020
Andrés Collinuccia and Roberto Valandrob,c a
Service de Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles, Belgium b Dipartimento di Fisica, Università di Trieste, Strada Costiera 11, I-34151 Trieste, Italy c INFN, Sezione di Trieste, Via Valerio 2, I-34127 Trieste, Italy
E-mail: [email protected], [email protected] Abstract: We propose a string theory realization of three-dimensional N = 4 quiver gauge theories with special unitary gauge groups. This is most easily understood in type IIA string theory with D4-branes wrapped on holomorphic curves in local K3’s, by invoking the Stückelberg mechanism. From the type IIB perspective, this is understood as simply compactifying the familiar Hanany-Witten (HW) constructions on a T 3 . The mirror symmetry duals are easily derived. We illustrate this with various examples of mirror pairs. Keywords: Duality in Gauge Field Theories, Supersymmetric Gauge Theory, Brane Dynamics in Gauge Theories, D-branes ArXiv ePrint: 2008.10689
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)157
JHEP11(2020)157
A string theory realization of special unitary quivers in 3 dimensions
Contents 1
2 The Stückelberg mechanism in string theory
2
3 Strategy
4
4 IIA perspective
4
5 IIB perspective 5.1 Special unitary linear quivers 5.2 Mirror symmetry
6 6 8
6 Examples 6.1 Enhancement of the Higgs branch 6.2 SU(N) with Nf flavors for Nf ≥ 2N 6.3 Homogeneous linear quivers 6.4 Ascending linear quivers
9 9 10 11 12
7 An outlier: SU(2) with two flavors
13
1
Introduction
Hanany and Witten [1] showed us how to build quiver gauge theories in three dimensions with eight supercharges, and unitary gauge groups. The setting was type IIB string theory, with D3-branes suspended between NS5-branes, D5-branes, and various arrangements thereof. Because type IIB theory enjoys S-duality, this allowed them to easily derive for each theory they considered, an IR dual theory related to it via 3d mirror symmetry, as conceived in [2]. Alternative string theory setups were considered in the works [3, 4]. It is then natural to wonder, what the mirror duals of quivers with special unitary gauge groups are. In order to render a unitary gauge group special unitary, Witten devised a field theory method in [5], whereby he essentially gauges the topological U(1) global symmetry present. The coupling then acts like a Stückelberg mass term for the original photon. In [1], Hanany and Witten apply this method to various examples. This requires them to introduce an auxiliary hypermultiplet with an appropriate coupling to the photon. Through this method, they are able to derive various mirror pairs. More elaborate examples of this can be found in [6], and more generally even, in [7]. However, there is a vexing issue that persists: to our knowledge, no systematic direct method has
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