Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops

2007

418 citations recorded by the source corpus.

We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the $${\mathcal N=4}$$ supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure $${\mathcal N=2}$$ and the $${\mathcal N=2^*}$$ supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional $${\mathcal N=2}$$ superconformal gauge theory is treated similarly.

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

View Paper: https://www.semanticscholar.org/paper/8f2ca8fb3155af66802f8626a773c74311ab6a0e

Citations in the corpus

• Exact results for Wilson loops in superconformal Chern-Simons theories with matter (2009, neutral): “e R dsσ = trR e2πσo (3.8) Thus we have: Z= R dσo exp −4iπ2Tr σo 2 Zg 1−loop[σo] <W>= 1 Z R dσo exp −4iπ 2Tr σo trR eπσo Zg 1−loop[σo] (3.9) This is essentially the same result as was found in [4] for N = 2 and N = 4 SYM theory in four dimensions. For N = 4, it was shown that Z 1−loop = 1, so ”
• Exact results in D = 2 supersymmetric gauge theories (2012, neutral): “The Higgs branch expression for the partition function shares features with the localization computation of the partition function and Wilson loops [3], ’t Hooft loops [23] and domain walls [41] in four dimensional N = 2 gauge theories.”
• From Weak to Strong Coupling in ABJM Theory (2010, positive): “An important breakthrough, which is the underpinning of the present study, was the work of Kapustin, Willett and Yaakov [4], who use the localization techniques of [5] to reduce the calculation of certain quantities in the gauge theory on S3 to finite dimensional matrix integrals.”
• A topologically twisted index for three-dimensional supersymmetric theories (2015, neutral): “Most of the examples studied in the last few years are not topologically twisted [2] (see [3] for a nice review”
• General instanton counting and 5d SCFT (2014, neutral): “The usefulness of this partition function in the 4d and 5d SUSY partition functions on curved spaces was also shown in [4, 5] and [6–15].”
• The virtue of defects in 4D gauge theories and 2D CFTs (2010, neutral): “The main idea behind Pestun’s localization of correlation functions of 4d N = 2 theories on S4 is simple: as long as all the observables in the correlation function preserve a common superconformal symmetry Q, one can add a Q-exact term to the Lagrangian without changing the result.”
• The N=2$$ \mathcal{N}=2 $$ superconformal bootstrap (2014, neutral): “It is frequently the case that the partition function ZS4 can be computed exactly using supersymmetric localization [124].”
• Supersymmetric partition functions on Riemann surfaces (2016, neutral): “On the other hand, keeping some supersymmetry in the process allows one to apply techniques, such as supersymmetric localization [1, 2], to explicitly and exactly compute those partition functions.”
• Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, neutral): “expression on the Higgs branch is reminiscent of the S4 case [3], where the instanton partition function Z inst of Nekrasov [18] appears, although in that case Z inst is in the integrand of a matrix integral, while in our case Zvortex is related to a matrix integral.”
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, neutral): “This will lead us to perform a localization calculation [15–17] on the field theory side and derive a generalization of the supersymmetric Casimir energy [18].”
• Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, neutral): “(A similar reduction of the functional integral occurs in certain four-dimensional field theories [26].”
• Liouville Correlation Functions from Four-Dimensional Gauge Theories (2009, neutral): “It is natural in the framework of [4] to insert Wilson loops on the gauge theory side.”
• 4d Index to 3d Index and 2d TQFT (2011, neutral): “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(”
• Correlation functions of Coulomb branch operators (2016, neutral): “This partition function can be in turn evaluated exactly by supersymmetric localization, expanding upon Pestun’s computation of the undeformed N = 2 partition function [3].”
• Exact results in ABJM theory from topological strings (2009, neutral): “This is straightforward in the Gaussian matrix model which computes the vev of the 1/2 BPS Wilson loop in N = 4 SYM [3, 2, 1], but it is not for the model (2.”