Supermatrix models for M-theory based on

Abstract

Taking seriously the hypothesis that the full symmetry algebra of M-theory is osp(1|32, R), we derive the supersymmetry transformations for all fields that appear in 11-and 12dimensional realizations and give the associated SUSY algebras. We study the backgroundindependent osp(1|32, R) cubic matrix model action expressed in terms of representations of the Lorentz groups SO(10, 2) and SO(10, 1). We explore further the 11-dimensional case and compute an effective action for the BFSS-like degrees of freedom. We find the usual BFSS action with additional terms incorporating couplings to transverse 5-branes, as well as a mass-term and an infinite tower of higher-order interactions.

On the Unitarity of D = 9, 10, 11 Conformal Supersymmetry

“…We list only the main so(D) component with signature following directly from the embedding formulae, e.g., (5) for so (10).…”

“…In the Dynkin labeling of the n − 1 fundamental irreps Λ k of su(n) are characterized for fixed k by a i = δ ik . The fundamental irreps Λ o t of so(D) are characterized for (10) spinor with r 4 = 1. We summarize the results in Table 1.…”

“…In these applications most prominent role play the superalgebras osp(1| 2n), cf., e.g., [1][2][3][4][5][6][7][8][9][10]. Initially, the superalgebra osp(1| 32) was put forward for D = 10 [1].…”

Curved-space classical solutions of a massive supermatrix model

“…). In the 11-dimensional case, this difficulty has been overcome in [21] through the addition of a mass term, and we thus expect this model to contain the massive IIB matrix model, the bosonic part of which has been studied in [17] to investigate perturbation theory around noncommutative curved-space backgrounds.…”

“…The IIB matrix model has N = 2 supersymmetry, which exhibits a particular structure that allows us to interpret the eigenvalues of the large N matrices describing the bosonic fields as space-time coordinates [7,8] (IIB matrix model is extensively reviewed in [9]). Another intriguing attempt for a constructive definition of superstring theory is a background-independent matrix model based on the Lie superalgebra osp(1|32, R) [11,13,15,16,21]. It is a natural generalization of the IIB matrix model, in which both bosons and fermions are unified into a single supermultiplet.…”