# How does the holographic principle apply to the $n$ dimensional space of String Theory?

The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon. In a larger sense, the theory suggests that the entire universe can be seen as a two-dimensional information on the cosmological horizon, such that the three dimensions we observe are an effective description only at macroscopic scales and at low energies.

99.999% of string theory is beyond me, (other than what I have read in the better popsci books) but I have one (very naive) question regarding the above Wikipedia excerpt. Holographic Principle

In the simplest terms, am I wrong in assuming that on a macro scale, we can understand this principle in the most general terms as saying that a 3D volume can be treated as a 2D surface? I do follow the general idea of duality in basic math situations.

If that's the case, what happens to the $n$ dimensional space that string theory needs to operate in, i.e. how many dimensions can we "reduce" it to, if the holographic principle does apply at micro levels in the same way as I think it applies to the macro world?

There are related posts regarding this question, but can anybody provide as general i.e. simple, as possible an answer?

If it's a short answer that just points out reading I should do or a basic misunderstanding, that fine by me.

It seems the keyword OP is searching for is AdS/CFT correspondence. The holographic principle in string theory is realized between a gravity theory in an $n$ dimensional AdS bulk manifold $M$ and a gauge CFT on an $n\!-\!1$ dimensional boundary $\partial M$.
In the most famous example, the 10 dimensional target space of superstring theory is a product of a small internal compact $S^5$ and a $AdS_5$ spacetime, so the dimension $n=5$ is five here.