$\mathcal{N}=4$ line defect correlators of type BCD

TL;DR

This paper derives exact formulas for line defect correlators in $ =4$ super Yang-Mills theories with orthogonal and symplectic groups, linking them to gravity dual spectra via combinatorial methods.

Contribution

It provides the first exact closed-form expressions for these correlators using group character combinatorics, including generalized Murnaghan-Nakayama rules.

Findings

Exact correlator formulas for orthogonal and symplectic gauge groups

Large N correlators match gravity dual spectra

Connection between defect correlators and string/D-brane fluctuations

Abstract

We analyze the line defect correlation functions decorating the supersymmetric indices of $\mathcal{N}=4$ super Yang-Mills theories with orthogonal and symplectic gauge groups. We obtain exact closed-form expressions for the correlators by means of combinatorial methods associated with the group characters, including the generalized Murnaghan-Nakayama rules. The exact results for the large $N$ correlators lead to the gravity indices for the gravity dual spectrum of the fluctuations of the fundamental string wrapping $AdS_2$ and those of the fat string, the D5-brane wrapping $AdS_2$ $\times$ $\mathbb{RP}^4$.