Exact probes of orientifolds

TL;DR

This paper computes exact Wilson loop expectation values in certain super Yang-Mills theories, using these results to explore their holographic duals, geometries, and the role of orientifolds and discrete torsion.

Contribution

It provides exact calculations of Wilson loops in SO(N) and Sp(N) theories and clarifies their holographic dual geometries, including the effects of discrete torsion and orientifold contributions.

Findings

Wilson loop expectation values computed exactly for SO(N) and Sp(N) theories

Identification of discrete torsion with negativity in fermionic phase space distribution

Insights into string world-sheet contributions related to orientifolds and crosscaps

Abstract

We compute the exact vacuum expectation value of circular Wilson loops for Euclidean ${\cal N}=4$ super Yang-Mills with $G=SO(N),Sp(N)$, in the fundamental and spinor representations. These field theories are dual to type IIB string theory compactified on $AdS_5\times {\mathbb R} {\mathbb P}^5$ plus certain choices of discrete torsion, and we use our results to probe this holographic duality. We first revisit the LLM-type geometries having $AdS_5\times {\mathbb R} {\mathbb P}^5$ as ground state. Our results clarify and refine the identification of these LLM-type geometries as bubbling geometries arising from fermions on a half harmonic oscillator. We furthermore identify the presence of discrete torsion with the one-fermion Wigner distribution becoming negative at the origin of phase space. We then turn to the string world-sheet interpretation of our results and argue that for the quantities considered they imply two features: first, the contribution coming from world-sheets with a single crosscap is closely related to the contribution coming from orientable world-sheets, and second, world-sheets with two crosscaps don't contribute to these quantities.