Nonperturbative tests of three-dimensional dualities

By A. Kapustin, Brian Willett, Itamar Yaakov. 2010

308 citations recorded by the source corpus.

We test several conjectural dualities between strongly coupled superconformal field theories in three dimensions by computing their exact partition functions on a three sphere as a function of Fayet-Iliopoulos and mass parameters. The calculation is carried out using localization of the path integral and the matrix model previously derived for superconformal $$ \mathcal{N} = 2 $$ gauge theories. We verify that the partition functions of quiver theories related by mirror symmetry agree provided the mass parameters and the Fayet-Iliopoulos parameters are exchanged, as predicted. We carry out a similar calculation for the mirror of $$ \mathcal{N} = 8 $$ super-Yang-Mills theory and show that its partition function agrees with that of the ABJM theory at unit Chern-Simons level. This provides a nonperturbative test of the conjectural equivalence of the two theories in the conformal limit.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/87b0d462e0a5d4eb00584eb02cb487d9b7f01e68

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Citations in the corpus

Non-perturbative effects and the refined topological string (2013, background): “One first notices (see also [28]) that the matrix integral (2.”
Relation between the 4d superconformal index and the S3 partition function (2011, methodology): “It is used to confirm dualities among 3d theories [4, 5, 6, 7] and predictions of AdS4/CFT3 [8, 9, 10, 11, 12].”
Rigid supersymmetric theories in curved superspace (2011, methodology): “Even though we do not discuss it here in detail, it is clear that the same issue with lack of reflection positivity applies to non-conformal N = 2 theories on S(4) [1-3] and on S(3) [4-20].”
Summing up all genus free energy of ABJM matrix model (2011, background): “elated interesting developments; generalizations to quiver gauge theories [12], the F-maximization conjecture [13], computations of superconformal index [14], and tests of three-dimensional dualities [15]. 2 It is worthwhile to note that the shift (1.2) is closely related to the renormalization of t”
Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories (2011, methodology): “The localization techniques of [61] have been used as well to test field theory dualities in three-dimensional supersymmetric gauge theories [62, 63, 57, 60, 96], by showing that their partition functions agree as functions of the various parameters.”
Comments on Chern-Simons contact terms in three dimensions (2012, background): “Many other dualities have been shown to require relative Chern-Simons counterterms [33-43].”
SUSY gauge theories on squashed three-spheres (2011, methodology): “It has also been attracting wide attention from various other fields, for example Wilson loops [5, 6], 3D dualities [2], large-N duality of topological string [7] and the ABJM theory at strong coupling [8, 9, 10].”
The exact superconformal R-symmetry extremizes Z (2010, background): “After localization, this results in a term − i π ∫ S(3) ξTr (−σ/r) = 2πiξTr (σ)r(2), as in [22].”
ABJM theory as a Fermi gas (2011, methodology): “In the context of ABJM theory, it was used in [33] in order to prove the equivalence of (2.”
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, background): “1) as a mirror description of the ABJM theory in terms of the 3d U(N) N = 4 SYM with adjoint and fundamental hypermultiplets, which is isomorphic to 3d U(N) N = 8 SYM in the low-energy limit [51].”
Localization techniques in quantum field theories (2016, methodology): “See [54] for an introduction to the deformation theory of complex manifolds.”
From Weak to Strong Coupling in ABJM Theory (2010, result): “1 Similar results apply also to other 3d theories with N = 2 supersymmetry [4,6].”
Notes on SUSY gauge theories on three-sphere (2010, methodology): “In this paper we extend the result of [5, 8] so that the matter chiral multiplets with arbitrary R-charge assignment can be incorporated.”
3d dualities from 4d dualities (2013, background): “lies that the Euclidean partition function on S3 of the 3dversions of theories A and B should be the same, and usually this is considered as very strong evidence for the equivalence of these theories [23]. This type of relation between the 4dand 3ddualities was recently investigated in [3]. But we m”
Superconformal indices of three-dimensional theories related by mirror symmetry (2011, background): “The partition functions of three-dimensional supersymmetric field theories are studied in [25–35].”
Bootstrapping the superconformal index with surface defects (2012, background): “Four important classes of examples are expectation values of circular Wilson loops in 4d N = 2 theories on S4 [3], partition functions of 3d N = 2 theories on S3 [4, 5, 6], partition functions of N = 1 and N = 2 theories on S3 × S1 [7, 8] and partition functions of N = 2 theories on S2 × S1 [9, 10, ”
Comments on twisted indices in 3d supersymmetric gauge theories (2016, methodology): “A similar computation was done on S3 in [81].”