Exact results for Wilson loops in superconformal Chern-Simons theories with matter

By A. Kapustin, Brian Willett, Itamar Yaakov. 2009

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We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a single complex supersymmetry, and exist in any $$\mathcal{N}= 2 $$ theory, though the localization requires superconformal symmetry. We present explicit results for the cases of pure Chern-Simons theory with gauge group U(N), showing agreement with the known results, and ABJM, showing agreement with perturbative calculations. Our method applies to other theories, such as Gaiotto-Witten theories, BLG, and their variants.

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

View Paper: https://www.semanticscholar.org/paper/5c2a0409c42f7f7617150b00dbd58daaaeb14072

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Citations in the corpus

Supersymmetric field theories on three-manifolds (2012, background): “Following [1-4], much work has focused on supersymmetric theories on round and squashed spheres [5-13].”
Comments on 3d Seiberg-like dualities (2011, methodology): “5 Dualities for U(n) theories and S(3) b partition function Recently it was understood that the partition function ZS3 for any N = 2 superconformal theory on a 3-sphere can be reduced to an ordinary integral using localization techniques [53, 54, 55].”
4d Index to 3d Index and 2d TQFT (2011, background): “Recent studies have uncovered powerful techniques (mostly based on localization) to extract exact results for 3d and 4d supersymmetric gauge theories, including the 4d N ≥ 1 superconformal index on S(1) × S(3) [1, 2], the 4d N ≥ 2 partition function on S(4) [3], the 3d N ≥ 2 partition function on S(”
Nonperturbative tests of three-dimensional dualities (2010, methodology): “According to [5] the contribution of the N = 2 vector multiplet is given precisely by (2.”
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, ”
Localization on Hopf surfaces (2014, neutral): “14) can be included in the deformation term by replacing δV → δ′V ′, with δ′ = δ + δB, where δB is the BRST transformation, and V ′ = V + Tr γ̄∇τ a [35].”
Topological Strings from Quantum Mechanics (2014, positive): “Using localization, this partition function can be expressed in terms of a matrix integral [2].”
From Weak to Strong Coupling in ABJM Theory (2010, methodology): “In [4] the one-loop determinant is evaluated up to a multiplicative constant,”
Refined stable pair invariants for E-, M- and [p, q]-strings (2013, background): “The topological string on the del Pezzo surfaces captures [15] the topological sector [16] of three-dimensional ABJM theories proposed for the description of multiple M2-branes[17] even at strong coupling and recently it was found that the 1 = 0 sector of the refined topological string encodes the n”
The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere (2012, background): “This theory on S(5) does not have the same status as the corresponding superconformal theories in the 4D and 3D cases on S(4) and S(3), originally considered in [7] and [8], respectively.”
Localization techniques in quantum field theories (2016, methodology): “5) 11In fact, [13] generalizes the construction to squashed rotationally-invariant spheres which preserve only an su(1|1) superalgebra.”
Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions (2012, background): “Similarly, it would be interesting if (as in supersymmetric theories [61]) one could find a way to compute exactly the free energy of our theories on a Euclidean S(3) (at least in the large N limit), as this could provide another useful test of the duality; this free energy for our theories at weak ”
The virtue of defects in 4D gauge theories and 2D CFTs (2010, methodology): “To see this, we note that such factors arise in the one-loop determinant for 3d N = 2 gauge multiplets on S(3) computed in [40] in a similar context of equivariant localization, based on the same isometries as for the S(4) computation we have here.”
A topologically twisted index for three-dimensional supersymmetric theories (2015, background): “As first observed in [14] and later elaborated upon in [15, 16], both the S3 partition function of [29], the S2×S1 supersymmetric index of [47, 48] and the lens space index of [49] “factorize” into building elements which can be interpreted as the partition function on R(2)Ω×S(1) in an Ω-background.”
Nonperturbative aspects of ABJM theory (2011, methodology): “In the calculation of the superstring free energies we have used the large N dual description of ABJM theory in terms of a matrix model [2], and we have formulated a general strategy to extract spacetime instantons from matrix models which generalizes previous results in, for example, [15, 17].”
Exact results on the ABJM Fermi gas (2012, methodology): “Subsequently, it was shown in [8] that the localization technique [9], which reduces the partition function defined by infinite-dimensional path integral to a finite-dimensional matrix model, is applicable to supersymmetric Chern-Simons theories.”
Chern-Simons theory and S-duality (2011, background): “The S transformation (and its inverse) corresponds to the basic building block represented by the mass-deformed theory T [SU(2)], whereas the T k transformation corresponds to a deformation of the Lagrangian by a Chern-Simons term at level k [74, 75].”
Index for three dimensional superconformal field theories with general R-charge assignments (2011, methodology): “This is based on the fact that the path integral of a three-dimensional N = 2 superconformal field theory in S(3) can be reduced to a matrix integral by using the localization method[5].”