Construction of the zero-energy state of -matrix theory: Near the origin

Abstract

We explicitly construct a (unique) Spin(9)×SU (2) singlet state, φ, involving only the fermionic degrees of freedom of the supersymmetric matrix-model corresponding to reduced 10-dimensional super Yang-Mills theory, resp. supermembranes in 11-dimensional Minkowski space. Any non-singular wavefunction annihilated by the 16 supercharges of SU (2) matrix theory must, at the origin (where it is assumed to be non-vanishing) reduce to φ.

Towards the ground state of the supermembrane

“…Performing the Taylor expansion of the ground state about X = 0, the 0th order term (i.e. the coordinate independent one) for the SU(2) model has been constructed explicitly [17] and proven to be unique [18,19] which confirmed earlier symbolic results using Mathematica [20]. The 1st order term is now also available and turns out to be unique as well [21].…”

“…The unique candidate for |φ which we denote here by |S , has been constructed in [17,20], and the unique candidate for |φ a i which satisfies (2.4) has also been constructed in [21]. Thus we have the starting points for the sequences m = 0 and 1.…”

Measure of the potential valleys of the supermembrane theory

“…For an (incomplete) list of contributions towards its solution, mainly in asymptotic regimes, c.f. [16,15,13,19,17,18,12].…”

Hamiltonian truncation study of supersymmetric quantum mechanics: S-matrix and metastable states

“…However, there are only 3 SO(9) × SU (2) invariants formed out of the bosonic coordinates, which will play the role of r,r variables in the N = 4 SQM analyzed in this paper. Furthermore, the 2 24 component fermionic wave function reduces to a few hundred irreducible representations of SO(9) × SU (2) [45,46], and the direct diagonalization of a truncated Hamiltonian could be manageable when restricted to a sector with fixed SO(9) angular momentum. We hope to report on this in the near future.…”