Correlators of currents corresponding to the massive $p$-form fields in AdS/CFT correspondence

TL;DR

The paper advances the AdS/CFT dictionary for massive $p$-form fields by solving the bulk equations of motion in $AdS_{d+1}$, performing a holographic projection to derive the boundary action, and showing that the resulting two-point function of the dual conformal current has conformal dimension $\Delta=\frac{d}{2}+\nu$ with $\nu=\sqrt{m^2+( \frac{d}{2}-p)^2}$. The method generalizes known massless results and provides explicit nonlocal kernels for the boundary correlators, ensuring Ward identities are preserved. In the massless limit, the results agree with established formulas, validating the approach for a broader class of $p$-form fields in AdS/CFT. This work hence extends holographic techniques to massive higher-form fields and clarifies how internal compactification masses appear in boundary correlators.

Abstract

By solving the equations of motion of massive $p$-form potential in Anti-de-Sitter space and using the $AdS/CFT$ correspondence of Maldacena, the generating functional of two-point correlation functions of the currents is obtained. When the mass parameter vanishes the result agrees with the known massless case.