# Why does string theory require holography?

String theory solves the high energy gravity problem by making it mushier:

Lisa Randall - Warped Passages - 14 - String Theory’s Origins

Strings—unlike quarks—have no hard scattering processes. They have more “mushy” interactions that take place over an extended region. This property means that string theory could potentially solve the problem of the graviton’s ridiculously high interaction rate, and correctly predict high-energy graviton interactions.

why isn't this mushy gravity interaction enough to describe high energy gravity without holography? what string gravity calculation can only be done with the help of holography? the answer structure should be: string gravity is flawed because... holography improves it because...

## Holography

Holography is projecting the mushy string graviton interaction from a $d-1$ dimensions hard gluon interaction, as discussed in this PDF:

The two corresponding lumps of energy modify the virtual cloud of gluons surrounding them, which in turn induces a net attraction between the lumps, precisely reproducing the correct gravitational force. In every physical sense, gravity and the extra direction of space making up the inside of the box do indeed emerge “holographically,” from the dynamics of the theory that lives fundamentally on the walls. This correspondence gives us our first concrete clue as to how space-time may emerge from more primitive building blocks.

The motivation for the holographic principle is independent of string theory. It is that the entropy of a black hole increases with its surface area rather than with its volume. So thermodynamically, a quantum theory with black holes in it, behaves like an ordinary quantum theory with one less dimension of space. This became the idea that a theory of quantum gravity should be equivalent to a nongravitational quantum field theory in one less dimension. Of course black hole entropy has not been measured; that it behaves this way is a theoretical deduction made by Bekenstein and Hawking, and then 't Hooft and Susskind made the holographic generalization.

Why interacting quantum strings turn out to embody the holographic principle, I don't know how to answer. In retrospect, we know a lot about how a gauge theory can give rise to a dual string theory, but I don't know how you would guess just from the basics of string theory, that it was equivalent to a lower-dimensional theory.

• the motivation must also be that something is missing in string gravity. can u add what that is? and how far holography goes in filling that gap – John Peterson Apr 7 '15 at 18:04
• @John Peterson - Sorry, I don't follow... Holography is not a choice in string theory. You can't have string theory and then decide to add holography, they believe holography is already implied. But it took several decades before this was discovered to be an implication of the theory. – Mitchell Porter Apr 8 '15 at 20:01
• why isn't string gravity a complete gravity model? without holography or anything more – John Peterson Apr 8 '15 at 21:33
• That's like saying "why does arithmetic need prime numbers?" The existence of prime numbers is not a starting point, but it follows logically from the definitions of counting, multiplication, etc. The point is that string theory was not designed with holography in mind, it was built step by step according to other criteria, but the resulting theory turned out to have the holographic property. – Mitchell Porter Apr 9 '15 at 2:59
• i clarified the question. if string gravity calculate everything we want without holography, holography is a pointless curiosity – John Peterson Apr 9 '15 at 20:58

You seem to be assuming that holography is a proposal on top of, or in addition to, string theory, when in fact holography is simply a fact of string theory in Anti-de Sitter space.

String theory in $AdS^5\times S^5$ is equivalent to a certain conformal field theory defined on the boundary of this space; this is a purely mathematical result about the behaviour of strings in this particular vacuum; it is true that there are reasons to suspect that this might be true even before studying strings in detail -- black hole thermodynamics strongly suggests that any quantum theory of gravity should be holographic -- but holography is not something one needs to add "by hand" to string theory: it is always there, at least in appropriate backgrounds.

It is nonetheless true that the $AdS/CFT$ correspondence is unproven, but it is a property that string theory either has or does not have, not an additional assumption layered on top.

Holography is a successful hypothesis at the moment. In my opinion it is an elegant and advanced way of analyzing the functions involved. Fourier transforms, for example analyze the possible frequencies in a signal. This does not mean that infinite tuning forks make up the signal. It is a useful model though in innumerable situations.

The observation of holographic correspondences in string theories may inspire people to new models for fundamental interactions. It remains to be seen.

• u say it's useful for analyzing gravity. but can we say more precisely why mushy gravity isn't enough by itself but should be projected from a hard gluon interaction? what's the shortcoming that we're trying to solve? – John Peterson Jan 11 '15 at 5:31
• Theorists are trying to find one quantized unifying theory for all fundamental interactions, it is the holy grail of physics since the middle of last century. – anna v Jan 11 '15 at 5:43
• making gravity emergent would reduce the fundamental forces to three, and I suppose that for some theorists this would be a very elegant theory. Elegance in the mathematics of theories is one of gauges used in evaluating theories. for example, that classical thermodynamics emerges from the microscopic interactions modeled with statistical mechanics is accepted as great progress in understanding the physics processes. – anna v Jan 11 '15 at 6:33

## Because it gives hints about the compactification

String gravity is flawed because it requires you to select a compactification to calculate with it, and the compactification is famously undetermined. There's no way to reverse engineer the standard model to find the compactification that correspond to it (see this video).

Holography improves it because it places constraints on the compactification, but it still leaves the compactification far from determined.