October 1996 | T. Banks, W. Fischler, S.H. Shenker, L. Susskind
This paper proposes a conjecture that uncompactified eleven-dimensional M-theory is equivalent to the N = ∞ limit of a supersymmetric matrix quantum mechanics describing D0 branes. The conjecture is supported by several correspondences between the two theories. The matrix model is rich enough to describe the properties of the entire Fock space of massless well-separated particles of the supergravity theory. In a particular kinematic situation, the leading large-distance interaction of these particles is exactly described by supergravity. The model appears to be a nonperturbative realization of the holographic principle. Membrane states required by M-theory are contained as excitations of the matrix model. The membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime.
The paper discusses the infinite momentum frame and the holographic principle, showing that in this frame, string theory can be formulated in Hamiltonian form. The infinite momentum frame is the only frame in which it has proved possible to formulate string theory in Hamiltonian form. The description of M-theory in this frame is also in the infinite momentum frame. The paper reviews the features of the infinite momentum frame formulation of relativistic quantum mechanics and discusses the Galilean symmetry and Supergalilean group.
The paper then discusses M-theory and D0 branes, showing that D0 branes are candidate partons for an infinite momentum limit description of M-theory. The D0 branes carry the quantum numbers of the first massive KK modes of the basic eleven-dimensional supergravity multiplet, including 44 gravitons, 84 components of a 3-form, and 128 gravitinos. These particles are referred to as supergravitons. As 11-dimensional objects, these are all massless. As a consequence, they are BPS saturated states in the 10-dimensional theory. Their 10-D mass is 1/R.
The paper then discusses D0 brane mechanics, showing that the infinite momentum limit of M-theory is the theory of D0 branes. The quantum mechanics of the system is described by a Lagrangian that has been extensively studied in another context. The Lagrangian is invariant under the gauge symmetry and the Supergalilean group. The Hamiltonian has the form of a trace of terms involving the matrices and their conjugates. The paper discusses the properties of the Hamiltonian and the implications for the dynamics of D0 branes.
The paper then presents a conjecture that M-theory formulated in the infinite momentum frame is exactly equivalent to the N → ∞ limit of the supersymmetric quantum mechanics described by the Hamiltonian. The calculation of any physical quantity in M-theory can be reduced to a calculation in matrix quantum mechanics followed by an extrapolation to large N. The paper offers evidence for this surprising conjecture, showing that the single particle spectrum of the theory matches the superThis paper proposes a conjecture that uncompactified eleven-dimensional M-theory is equivalent to the N = ∞ limit of a supersymmetric matrix quantum mechanics describing D0 branes. The conjecture is supported by several correspondences between the two theories. The matrix model is rich enough to describe the properties of the entire Fock space of massless well-separated particles of the supergravity theory. In a particular kinematic situation, the leading large-distance interaction of these particles is exactly described by supergravity. The model appears to be a nonperturbative realization of the holographic principle. Membrane states required by M-theory are contained as excitations of the matrix model. The membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime.
The paper discusses the infinite momentum frame and the holographic principle, showing that in this frame, string theory can be formulated in Hamiltonian form. The infinite momentum frame is the only frame in which it has proved possible to formulate string theory in Hamiltonian form. The description of M-theory in this frame is also in the infinite momentum frame. The paper reviews the features of the infinite momentum frame formulation of relativistic quantum mechanics and discusses the Galilean symmetry and Supergalilean group.
The paper then discusses M-theory and D0 branes, showing that D0 branes are candidate partons for an infinite momentum limit description of M-theory. The D0 branes carry the quantum numbers of the first massive KK modes of the basic eleven-dimensional supergravity multiplet, including 44 gravitons, 84 components of a 3-form, and 128 gravitinos. These particles are referred to as supergravitons. As 11-dimensional objects, these are all massless. As a consequence, they are BPS saturated states in the 10-dimensional theory. Their 10-D mass is 1/R.
The paper then discusses D0 brane mechanics, showing that the infinite momentum limit of M-theory is the theory of D0 branes. The quantum mechanics of the system is described by a Lagrangian that has been extensively studied in another context. The Lagrangian is invariant under the gauge symmetry and the Supergalilean group. The Hamiltonian has the form of a trace of terms involving the matrices and their conjugates. The paper discusses the properties of the Hamiltonian and the implications for the dynamics of D0 branes.
The paper then presents a conjecture that M-theory formulated in the infinite momentum frame is exactly equivalent to the N → ∞ limit of the supersymmetric quantum mechanics described by the Hamiltonian. The calculation of any physical quantity in M-theory can be reduced to a calculation in matrix quantum mechanics followed by an extrapolation to large N. The paper offers evidence for this surprising conjecture, showing that the single particle spectrum of the theory matches the super