Obtaining the Maxwell-Boltzmann distribution from the string-theoretical thermal path integral?

Question

Can the Maxwell-Boltzmann distribution be obtained as the zero-mode part of the string-theoretical thermal path integral? And if this is indeed the case, can somebody explain this in some mathematical detaills to me?

Comments

If this question is nonsense I blame @LubošMotl for it, as it was him who made a corresponding comment at the beginning of this post (directly above the paragraph titled "Field theory"). So he better come here and explain this ... ;-)!

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The statement Lubos is making is that the dynamics of the low-energy theory is what Maxwell is describing with Maxwell equations and thermodynamics, and that if string theory is correct, as Motl assumes, the theories Maxwell gave us are a description of the dynamics of nearly massless part of the string spectrum.

Answer 1

There is no string thermal path-integral, gravity is incompatible with a uniform constant energy density. Constant energy density, constant temperature, leads to gravitational collapse when the volume is too big. This is why you can't have a consistent string thermal equilibrium state.

One consequence of this is that it is not possible to speak about thermal analogs of T-duality clearly in flat space-time, as people sometimes try to do, using imaginary time periodic path integrals. The presence of a thermal energy density curves space, and constant energy density is inconsistent.

The closest analog of a pure thermal state in a gravitational theory is a deSitter space, because semiclassically this space has a constant temperature, and a uniform cosmological constant. This type of state is not easy to incorporate into string theory, there is no consensus on how to do it.