Killing spinors and Supersymmetry on AdS

TL;DR

This paper constructs supersymmetric theories on AdS_5, clarifies the Killing spinor equations involving USp(2N) matrices, and confirms particle masses align with AdS/CFT predictions, ensuring proper symmetry transformations.

Contribution

It introduces the correct form of Killing spinor equations with USp(2N) matrices and verifies mass spectra match AdS/CFT expectations.

Findings

Confirmed particle masses agree with AdS/CFT predictions

Identified the role of USp(2N) matrices in Killing spinor equations

Established proper isometry transformations for AdS_d

Abstract

In this paper we construct several supersymmetric theories, including SU(N) gauge theory, on AdS_5 background. We discuss the proper definition of the Killing equation for the symplectic Majorana spinors required in AdS_5 supersymmetric theories. We find that the symplectic Killing spinor equation involves a matrix M in the USp(2N) indices whose role was not recognized previously. Using the correct Killing spinors we explicitly confirm that the particle masses in the constructed theories agree with the predictions of the AdS/CFT correspondence. Finally, we establish correct O(d-1,2) isometry transformations required to keep the Lagrangian invariant on AdS_d.