Tiny Graviton Matrix Theory: DLCQ of IIB Plane-Wave String Theory, A Conjecture

TL;DR

The work proposes that DLCQ of type IIB strings on the maximally supersymmetric plane-wave background in a sector with $J$ units of light-cone momentum is governed by a $0+1$-dimensional supersymmetric $U(J)$ matrix quantum mechanics with $PSU(2|2)\times PSU(2|2)\times U(1)$ symmetry, called the Tiny Graviton Matrix Theory, whose Hamiltonian is the quantized 3-brane action on the same background.Evidence is provided via the theory’s vacua (including giant-graviton-like fuzzy $S^3$ and the $X=0$ vacuum), detailed spectra about these vacua, and an analysis of effective couplings, all of which align with expectations for plane-wave strings and their BMN sector.An extension to DLCQ of strings on $AdS_5\times S^5$ is discussed, proposing that the same Hamiltonian with $R_- = \sqrt{g_s N}$ and gauge group $U(N)$ describes the system in the large-$N$ limit, with a smooth string theory emergence as $N\to\infty$ and links to string-bit formulations.

Abstract

We conjecture that the discrete light-cone quantization (DLCQ) of strings on the maximally supersymmetric type IIB plane-wave background in the sector with J units of light-cone momentum is a supersymmetric 0+1 dimensional U(J) gauge theory (quantum mechanics) with PSU(2|2)x PSU(2|2)x U(1) superalgebra. The conjectured Hamiltonian for the plane-wave matrix (string) theory, the tiny graviton matrix theory, is the quantized (regularized) three brane action on the same background. We present some pieces of evidence for this conjecture through analysis of the Hamiltonian, its vacua, spectrum and coupling constant. Moreover, we discuss an extension of our conjecture to the DLCQ of type IIB strings on AdS_5 x S^5 geometry.