Toward Precision Holography in Type IIA with Wilson Loops

Abstract

We study the one-loop effective action of certain classical type IIA string configurations in $Ad{S}_4\times {\mathbb{CP}}^3$. These configurations are dual to Wilson loops in the $\mathcal{N}=6$ $U(N{)}_k\times U(N{)}_{-k}$ Chern-Simons theory coupled to matter whose expectation values are known via supersymmetric localization. We compute the one-loop effective actions using two methods: perturbative heat kernel techniques and full $\zeta$-function regularization. We find that the result of the perturbative heat kernel method matches the field theory prediction at the appropriate order while the $\zeta$-function approach seems to lead to a disagreement. We explore various issues that might be responsible for this state of affairs.

arXiv comment48 pages. v2: references added

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Cited by in corpus (15)

• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Supersymmetric Mixed Boundary Conditions in AdS${}_2$ and DCFT${}_1$ Marginal Deformations
• One-loop Holography with Strings in $Ad{S}_4\times {\mathbb{CP}}^3$
• Matching quantum string corrections and circular Wilson loops in $Ad{S}_4\times C{P}^3$
• Localization and Duality for ABJM Latitude Wilson Loops
• On three-point functions in ABJM and the latitude Wilson loop
• Fermionic Bogomolnyi-Prasad-Sommerfield Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal gauge theories
• Antisymmetric Wilson loops in N = 4 SYM: from exact results to non-planar corrections
• Semiclassical $p$-branes in hyperbolic space
• Note on generating functions and connected correlators of 1/2-BPS Wilson loops in $\mathcal{N}=4$ SYM theory
• Quantum corrections to minimal surfaces with mixed three-form flux
• Wilson Loops and Spherical Branes
• Combinatorics of Wilson loops in $\mathcal{N}=4$ SYM theory
• Vacuum configuration of winding superstrings from non-standard semiclassical quantization