Exact results in D = 2 supersymmetric gauge theories

By N. Doroud, Joaquim Gomis, B. Floch, Sungjay Lee. Journal of High Energy Physics, 2012

379 citations recorded by the source corpus.

We compute exactly the partition function of two dimensional \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = (2, 2) gauge theories on S2 and show that it admits two dual descriptions: either as an integral over the Coulomb branch or as a sum over vortex and anti-vortex excitations on the Higgs branches of the theory. We further demonstrate that correlation functions in two dimensional Liouville/Toda CFT compute the S2 partition function for a class of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} $\end{document} = (2, 2) gauge theories, thereby uncovering novel modular properties in two dimensional gauge theories. Some of these gauge theories flow in the infrared to Calabi-Yau sigma models — such as the conifold — and the topology changing flop transition is realized as crossing symmetry in Liouville/Toda CFT. Evidence for Seiberg duality in two dimensions is exhibited by demonstrating that the partition function of conjectured Seiberg dual pairs are the same.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/abbf9721c78003789654675e4e68fbed46a79f52

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Citations in the corpus

Two-dimensional SCFTs from wrapped branes and c-extremization (2013, background): “In particular, the S(2) partition function of N = (2, 2) GLSMs, as function of the R-symmetry, has been computed in [85, 86] and it would be interesting to understand if it is related to c-extremization.”
Supersymmetry on curved spaces and holography (2012, background): “In [30, 31] the partition function for N = (2, 2) theories on the two-spere has been calculated by supersymmetric localisation.”
The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere (2012, methodology): “The theory on S(5) is perfectly adapted for the localization technique, which has recently been applied to theories in two, three and four dimensions on spheres and other compact manifolds in for example [7]-[19].”
Comments on twisted indices in 3d supersymmetric gauge theories (2016, background): “2) closely follows previous localization computations in related contexts [13, 14, 15, 6, 7, 8, 12, 16].”
Seiberg-Witten theories on ellipsoids (2012, result): “Similar exact results have also been obtained for 3D N ≥ 2 gauge theories on round three-sphere [3, 4, 5], its orbifold [6, 7], and 2D theories on sphere [8, 9].”
Correlation functions of Coulomb branch operators (2016, background): “For some previous work on the partition function of SCFTs on spheres consult [1–3,19–22].”
Instantons on the 5-sphere and M5-branes (2012, background): “This was recently shown to be possible for supersymmetric partition functions on S(2) [23, 24].”
Supersymmetric field theories on three-manifolds (2012, background): “1 For related work in two and five dimensions, see [14-16] and [17-20], respectively.”
Two-Sphere Partition Functions and Gromov–Witten Invariants (2012, methodology): “The partition function for such a GLSM on S2, deformed appropriately by O( 1 R ) terms and localized onto the Coulomb branch, takes the form [22,23]8”
Black Holes in 4D N=4 Super-Yang-Mills Field Theory (2018, background): “In order to evaluate its large N limit, though, we find more convenient to recast it in a different form, called Bethe Ansatz formula [50, 51] (see also [62] for a 3d analog, and [63–67] for similar Higgs branch localization formulas).”
Exact Kähler potential from gauge theory and mirror symmetry (2012, methodology): “3), they are explicitly given by [6]”
A topologically twisted index for three-dimensional supersymmetric theories (2015, methodology): “This more general formulation makes contact with the “factorization” of 3d partition functions [14–17] (as well as with a similar factorization in two [18, 19] and four [20] dimensions).”