Wilson loops in $$ \mathcal{N} $$ = 4 SO(N) SYM and D-branes in AdS5 × ℝℙ5

Abstract

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>We study the half-BPS circular Wilson loop in <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 4 super Yang-Mills with orthogonal gauge group. By supersymmetric localization, its expectation value can be computed exactly from a matrix integral over the Lie algebra of SO(<jats:italic>N</jats:italic>). We focus on the large <jats:italic>N</jats:italic> limit and present some simple quantitative tests of the duality with type IIB string theory in AdS<jats:sub>5</jats:sub><jats:italic>×</jats:italic> ℝℙ<jats:sup>5</jats:sup>. In particular, we show that the strong coupling limit of the expectation value of the Wilson loop in the spinor representation of the gauge group precisely matches the classical action of the dual string theory object, which is expected to be a D5-brane wrapping a ℝℙ<jats:sup>4</jats:sup> subspace of ℝℙ<jats:sup>5</jats:sup>. We also briefly discuss the large <jats:italic>N</jats:italic>, large <jats:italic>λ</jats:italic> limits of the SO(<jats:italic>N</jats:italic>) Wilson loop in the symmetric/antisymmetric representations and their D3/D5-brane duals. Finally, we use the D5-brane description to extract the leading strong coupling behavior of the “bremsstrahlung function” associated to a spinor probe charge, or equivalently the normalization of the two-point function of the displacement operator on the spinor Wilson loop, and obtain agreement with the localization prediction.</jats:p>