Supergravity on $AdS_{4/7} \times S^{7/4}$ and M Branes

TL;DR

This paper investigates the duality between certain superconformal field theories and 11-dimensional supergravity on specific AdS spaces, revealing necessary adjustments to Kaluza-Klein masses for consistency.

Contribution

It provides a detailed calculation of operator dimensions in 3D and 6D superconformal theories via supergravity duals, identifying key rescaling and shifting of Kaluza-Klein masses.

Findings

Operator dimensions match supergravity predictions after rescaling masses.

Rescaling and shifting of Kaluza-Klein masses are essential for duality consistency.

Supports the validity of AdS/CFT correspondence in these models.

Abstract

We calculate the dimensions of operators in three and six dimensional superconformal field theories by using the duality between these theories at large N and D=11 supergravity on $AdS_{4/7} \times S^{7/4}$. We find that for the duality relations to work the Kaluza--Klein masses given in the supergravity literature must be rescaled and/or shifted.