Framing and localization in Chern-Simons theories with matter

Abstract

Supersymmetric localization provides exact results that should match QFT computations in some regularization scheme. The agreement is particularly subtle in three dimensions where complex answers from localization procedure sometimes arise. We investigate this problem by studying the expectation value of the 1/6 BPS Wilson loop in planar ABJ(M) theory at three loops in perturbation theory. We reproduce the corresponding term in the localization result and argue that it originates entirely from a non-trivial framing of the circular contour. Contrary to pure Chern-Simons theory, we point out that for ABJ(M) the framing phase is a non-trivial function of the couplings and that it potentially receives contributions from vertex-like diagrams. Finally, we briefly discuss the intimate link between the exact framing factor and the Bremsstrahlung function of the 1/2-BPS cusp.

24 pages, 7 figures; v2: published version

References in corpus (6)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual
• Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM

Cited by in corpus (23)

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• BPS Wilson loops in $\mathcal{N}\ge 2$ superconformal Chern-Simons-matter theories
• String theory duals of Wilson loops from Higgsing
• The quantum 1/2 BPS Wilson loop in $\mathcal{N}=4$ Chern-Simons-matter theories
• New BPS Wilson loops in $\mathcal{N}\text{= 4}$ circular quiver Chern-Simons-matter theories
• A matrix model for the latitude Wilson loop in ABJM theory
• Interpolating Wilson loops and enriched RG flows
• A note on multiply wound BPS Wilson loops in ABJM
• Localization and Duality for ABJM Latitude Wilson Loops
• On three-point functions in ABJM and the latitude Wilson loop
• 1/3 BPS loops and defect CFTs in ABJM theory
• Wilson loops and defect RG flows in ABJM
• ABJM $\theta$-Bremsstrahlung at four loops and beyond: non-planar corrections
• Conformal and non-conformal hyperloop deformations of the 1/2 BPS circle
• An exact limit of ABJM
• Interpolating Bremsstrahlung function in ABJM
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Framing fermionic Wilson loops in ABJ(M)
• Equivariant and supersymmetric localization in QFT
• A network of hyperloops