Abstract
Quiver gauge theories with a large number of nodes host a wealth of Wilson loop operators. Expectation values are obtained, using supersymmetric localization, for Wilson loops in the antisymmetric representations associated with each individual gauge node, for a sample of 5d long quiver gauge theories whose UV fixed points have holographic duals in Type IIB. The sample includes the TN theories and the results are uniformly given in terms of Bloch-Wigner functions. The holographic representation of the Wilson loops is identified. It comprises, for each supergravity solution, a two-parameter family of D3-branes which exactly reproduce the field theory results and identify points in the internal space with the faces of the associated 5-brane web. The expectation values of (anti)fundamental Wilson loops exhibit an enhanced scaling for many operators, which matches between field theory and supergravity.
Highlights
The 3d road map paper [1])
Expectation values are obtained, using supersymmetric localization, for Wilson loops in the antisymmetric representations associated with each individual gauge node, for a sample of 5d long quiver gauge theories whose UV fixed points have holographic duals in Type IIB
The expectation values offundamental Wilson loops exhibit an enhanced scaling for many operators, which matches between field theory and supergravity
Summary
For gauge theories of the form (2.1) with L large, Wilson loops are labeled by the effectively continuous coordinate z along the quiver, defined in (2.2). To uniformly label the antisymmetric representations it is convenient to introduce a parameter k valued in [0, 1] and defined for the tth gauge node by k ≡ k/Nt. A concise notation for the Wilson loops is. Expectation values for these operators will be obtained for a sample of 5d long quiver gauge theories, in the limit where all gauge couplings become infinitely strong. The expectation values for fundamental and anti-fundamental Wilson loops will differ only for the YN theories which involve a Chern-Simons term.
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