A Mysterious Zero in AdS(5) x S(5) Supergravity

TL;DR

This paper demonstrates that all states in AdS(5) x S(5) supergravity have zero eigenvalues for all Casimir operators of its symmetry group, revealing a deep group-theoretical property linked to higher-dimensional structures and 2T-physics.

Contribution

It refines oscillator methods to compute Casimir eigenvalues and proves the universal zero eigenvalue property for supergravity states, connecting it to 12-dimensional structures.

Findings

All supergravity states have zero Casimir eigenvalues.

The zero eigenvalue is a group-theoretical fact in AdS(5) x S(5) supergravity.

This property is linked to a hidden 12-dimensional structure with (10,2) signature.

Abstract

It is shown that all the states in AdS(5) x S(5) supergravity have zero eigenvalue for the all Casimir operators of its symmetry group SU(2,2|4). To compute this universal zero in supergravity we refine the oscillator methods for studying the lowest weight unitary representations of SU(N,M|R,S). We solve the reduction problem when one multiplies an arbitrary number of super doubletons. This enters in the computation of the quadratic Casimir eigenvalues of the lowest weight representations. We apply the results to SU(2,2|4) that classifies the Kaluza-Klein towers of ten dimensional type IIB supergravity compactified on AdS(5) x S(5). We show that the vanishing of the SU(2,2|4) Casimir eigenvalues for all the states is indeed a group theoretical fact in AdS(5) x S(5) supergravity. By the AdS-CFT correspondence, it is also a fact for gauge invariant states of super Yang-Mills theory with four supersymmetries in four dimensions. This non-trivial and mysterious zero is very interesting because it is predicted as a straightforward consequence of the fundamental local Sp(2) symmetry in 2T-physics. Via the 2T-physics explanation of this zero we find a global indication that this special supergravity hides a twelve dimensional structure with (10,2) signature.