Such structures, referred to as [L.sub.[infinity]] or strongly homotopy Lie algebras, first appeared in the physics literature in closed string field theory  and in the mathematics literature in topology [2-4].
Indeed, it is to be expected that the gauge structure of exceptional field theory requires [L.sub.[infinity]] algebras with arbitrarily high brackets , as is also the case in closed string field theory .
Zwiebach, "Closed string field theory: quantum action and the Batalin-Vilkovisky master equation," Nuclear Physics B, vol.
Then, the amplitude for a closed string propagating between D- and gD-branes is given by <B(gD)[absolute value of [DELTA]]B(D)> = -<B(D)[absolute value of [DELTA]]B(D)>, where [DELTA] is an inverse of the closed string propagator.
The second is the gauge invariant overlap for closed string [24, 25].
where V is a closed string vertex operator and <I| is the identity string field.
I learned about open string and closed string theories.
* Closed string oscillations are sometimes called left movers and right movers.
The simplest vibration of a closed string
produces a graviton, the quantized particle of gravity.
Therefore, closed string theories are expected to remain commutative as long as the background is geometric.
Lust, "Asymmetric orbifolds, non-geometric fluxes and non-commutativity in closed string theory," Journal of High Energy Physics, vol.
Kong and Zhang studied the motion of relativistic closed strings
in the Minkowski space [R.sup.1+n] in ; particularly, the authors obtained a general solution formula for this system of nonlinear equations.