Graduate Do higher dimensional branes have wave functions?

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Higher dimensional branes, such as the super membrane and NS5/M5 branes, raise questions about the existence of wave functions. While these branes become unstable upon quantization, this does not necessarily imply they lack wave functions. Discussions often overlook the wave functions of higher-dimensional branes like M2 or D6. Instead, the wave function of a brane is effectively represented by the quantum field theory describing its vibrations. Thus, references to a brane's "worldvolume theory" can be interpreted as discussions of its wave function.
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Do higher dimensional branes, like the super membrane (which is a 2D brane) or the NS5/M5 brane, have wave functions? I know that they become unstable once they are quantized, but does that mean that they do not have wave functions? You will never here about any thing regarding an M2 wave function, or a D6 wave function, or any brane with more than one dimension having a wave function.
 
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The wavefunction of a brane is described by the quantum field theory of the brane's vibrations. So whenever they talk about the "worldvolume theory" of a brane, they are in effect talking about its wavefunction.
 
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