Nonperturbative definition of string and M-theory

5 problems

• Background-independent definition of M-theory

  Open

  Each known exact definition of string theory assumes a fixed shape of spacetime at infinity. A definition that does not assume a background is missing.

• Does BFSS matrix theory recover eleven-dimensional Lorentz invariance

  Partially resolved

  A quantum mechanics of N by N matrices is conjectured to equal M-theory when N becomes infinite. Whether it reproduces full eleven-dimensional relativity beyond protected calculations is unknown.

• Nonperturbative content of closed superstring field theory

  Open

  String field theory writes string theory like an ordinary field theory and fixes many subtle quantities. Whether it defines string theory beyond the weak-coupling series is unknown.

• Worldsheet string theory dual to free $N=4$ super-Yang-Mills

  Partially resolved

  Gauge theory with many colors and no interaction at all should still be equivalent to a string theory in curved space with strings of zero tension. Finding that string theory explicitly would show from first principles how gauge fields turn into strings.

• Do four expanding spacetime dimensions emerge in the IKKT model

  Contested

  A model built from ten large matrices is proposed as a complete definition of one string theory. Whether it produces a universe with three large expanding space directions is unknown.