Mirrors of 3d Sicilian theories

By F. Benini, Yuji Tachikawa, Dan Xie. 2010

212 citations recorded by the source corpus.

We consider the compactification of the 6d $$ \mathcal{N} = \left( {2,0} \right) $$ theories, or equivalently of M-theory 5-branes, on a punctured Riemann surface times a circle. This gives rise to what we call 3d $$ \mathcal{N} = 4 $$ Sicilian theories, and we find that their mirror theories are star-shaped quiver gauge theories. We also discuss an alternative construction of these 3d theories through 4d $$ \mathcal{N} = 4 $$ SYM on a graph, which allows us to obtain the 3d mirror via 4d S-duality.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d8f8e5ecb986582cef82397eabf3cfc393a923f4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Sergei Gukov
2. D. Gaiotto
3. Dan Xie
4. Abhijit Gadde
5. E. Witten
6. F. Benini
7. Shlomo S. Razamat
8. C. Vafa

In Nuclear and High Energy Physics

1. F. Benini
2. D. Gaiotto
3. Sergei Gukov
4. Yuji Tachikawa
5. Dan Xie
6. L. Rastelli
7. E. Witten
8. Abhijit Gadde

In Statistical and Nonlinear Physics

1. Yuji Tachikawa
2. Dan Xie
3. D. Gaiotto
4. E. Witten
5. Sergei Gukov
6. F. Benini
7. Abhijit Gadde
8. L. Rastelli

Citations in the corpus

• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories (2012, background): “The total quaternionic dimension of the Higgs branch is then [43]”
• Tinkertoys for Gaiotto duality (2010, methodology): “3D Mirrors To bolster our identification of the global symmetry groups of the interacting SCFTs that we have found, we will use an approach described by Benini, Tachikawa and Xie [16].”
• Reducing the 4d index to the S3 partition function (2011, background): “for example, in [22] it is claimed that mirror duals of TN [21] theories have Lagrangian description and are certain star shaped quiver gauge theories.”
• BPS spectra and 3-manifold invariants (2017, background): “ chiral with R-charge 2 + 2gadjoint chirals ( i;e i) g i=1 with R-charge 0: (3.120) When p= 0, the theory has N= 4 supersymmetry and coincides with the mirror description of the 3d reduction of T[ g] [73]. Having p6= 0 results in punits of RR 2-form ux after reducing the M5-branes rst on the circle ”
• Fivebranes and 3-manifold homology (2016, background): “This is due to the fact that the Coulomb branch of T [Σ× S1] has a hyper-Kähler quotient description [76].”
• General Argyres-Douglas theory (2012, methodology): “The form of the regular singularities can be checked using three dimensional mirror symmetry [40]: their 3d mirror have the shape of corresponding E type Dynkin diagram with rank N for each quiver node.”
• N=1 theories of class S_k (2015, background): “One interesting aspect of the dimensional reduction in class S1 was that the reduced theories possess a mirror description which was always Lagrangian, a star-shaped quiver with arms associated to the punctures of the original theory [46].”
• Bootstrapping the superconformal index with surface defects (2012, background): “The 3d theory which arise in the infrared from the circle reduction a 4d theory of class S has a nice mirror description [67] in terms takes of a star-shaped quiver: a central node connected to a set of linear quivers, where each linear quiver is associated to a puncture of the Riemann surface.”
• Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, background): “For instance, one can obtain a 2d N = (4, 4) quiver gauge theory description of M5-branes on × T 2 by first compactifying on × S1 (that in general gives a non-Lagrangian theory), then using the 3d mirror symmetry of [59] and finally compactifying on S1.”
• Tinkertoys for the DN series (2011, background): “Introduction Gaiotto duality [3,4,5,6,7,1,8,9,10] identifies a large class of 4D N = 2 SCFTs with compactifications of the 6D N = (2, 0) SCFT on a punctured Riemann surface, C.”
• Fivebranes and Knots (2011, background): “In fact, there are a family of half-BPS codimension two defects; see [36], [37], and [9].”
• Two-dimensional SCFTs from wrapped branes and c-extremization (2013, methodology): “cription of them. This should be feasible for 4d N= 4 SYM on (punctured) Riemann surfaces, because we have a Lagrangian description to begin with. A possible approach is to proceed along the lines of [94] and study 3d N= 8 SYM on a graph (whose \fattening" is the punctured Riemann surface), lik”
• 4d Index to 3d Index and 2d TQFT (2011, background): “In the limit p → ∞ the 4d theory reduces to a 3d theory (which by mirror symmetry is dual to a conventional quiver theory [40]), the 4d index reduces to the 3d index (section 3) and it is expected that the 2d TQFT lifts to a 3d TQFT, perhaps along the lines of [41].”