BFSS

BFSS refers to the BFSS matrix model, a proposal by Banks, Fischler, Shenker, and Susskind for a nonperturbative definition of M-theory in the infinite momentum frame. Introduced in 1996, it describes the quantum mechanics of N by N Hermitian matrices and is built as the dimensional reduction of ten-dimensional super Yang–Mills theory to one time dimension. The model is formulated in terms of nine bosonic matrices X^i(t) (i = 1,…,9) representing spatial coordinates and their fermionic superpartners, forming a supersymmetric quantum mechanics with 16 supercharges.

Physically, the BFSS model arises as the low-energy effective theory on the worldvolume of D0-branes in type IIA string theory. Its bosonic potential is generated by commutators of the matrices, typically written as a sum of Tr([X^i, X^j]^2). The theory is governed by a dimensionful coupling and is interpreted as describing the dynamics and interactions of D0-branes, including their gravitational and gauge interactions in a light-cone frame.

The central claim of the BFSS conjecture is that, in the appropriate discrete light-cone quantization limit and large N, this quantum mechanics provides a complete nonperturbative definition of M-theory in eleven dimensions. The proposal has spurred extensive study of D0-brane dynamics, black hole physics in matrix models, and connections to gauge/gravity dualities. While influential, the BFSS model is not proven as a final formulation of M-theory and remains a subject of ongoing research and scrutiny.