Tiny graviton matrix theory/SYM correspondence: Analysis of BPS states

Abstract

In this paper we continue analysis of the Matrix theory describing the DLCQ of type IIB string theory on ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ (and/or the plane-wave) background, i.e. the tiny graviton matrix theory (TGMT) [M. M. Sheikh-Jabbari, J. High Energy Phys. 09 (2004) 017.]. We study and classify $1/2$, $1/4$, and $1/8$ BPS solutions of the TGMT which are generically of the form of rotating three-brane giants. These are branes whose shape are deformed three-spheres and hyperboloids. In lack of a classification of such ten-dimensional type IIb supergravity configurations, we focus on the dual $\mathcal{N}=4$ four-dimensional $1/2$, $1/4$, and one $1/8$ BPS operators and show that they are in one-to-one correspondence with the states of the same set of quantum numbers in TGMT. This provides further evidence in support of the matrix theory.