# The Holographic Principle and M-theory

To them, I said,

the truth would be literally nothing

but the shadows of the images.

the truth would be literally nothing

but the shadows of the images.

*-Plato, The Republic (Book VII)***Holography Through the Ages**

However, some prisoners may escape from the cave; they may go out into the light of the sun and behold true reality. When they try to go back into the cave and tell the other captives the truth, they are mocked as madmen.

Of course, to Plato this story was just meant to symbolize mankind's struggle to reach enlightenment and understanding through reasoning and open-mindedness. We are

*all*initially prisoners and the tangible world is our cave. Just as some prisoners may escape out into the sun, so may some people amass knowledge and ascend into the light of true reality.

What is equally interesting is the

*literal*interpretation of Plato's tale: The idea that reality could be represented completely as `shadows' on the walls.

**The Holographic Principle and Modern Physics**

*Holographic Principle*, consists of two basic assertions:

**Assertion 1**The first assertion of the Holographic Principle is that all of the information contained in some region of space can be represented as a `Hologram' - a theory which `lives' on the boundary of that region. For example, if the region of space in question is the DAMTP Tearoom, then the holographic principle asserts that all of the physics which takes place in the DAMTP Tearoom can be represented by a theory which is defined on the walls of the Tearoom.

**Assertion 2**The second assertion of the Holographic Principle is that the theory on the boundary of the region of space in question should contain at

*most*one degree of freedom per Planck area.

A

*Planck area*is the area enclosed by a little square which has side length equal to the Planck length, a basic unit of length which is usually denoted

*L*

_{p}. The Planck length is a fundamental unit of length, because it is the parameter with the dimensions of length which can be constructed out of the basic constants

*G*(Newton's constant for the strength of gravitational interactions), (Planck's constant from quantum mechanics), and

*c*(the speed of light). A quick calculation reveals that

*L*

_{p}is very small indeed:

**Man ponders shadow, or shadow ponders itself?**

*are*the shadows on the wall. The `room' is some larger, five-dimensional spacetime and our four-dimensional world is just the boundary of this larger space. If we try to move away from the wall, we are moving into an extra dimension of space - a fifth dimension. In fact, people have recently been trying to think of ways in which we might actually experimentally `probe' this fifth dimension.

At the heart of many of these exciting ideas is a version of the Holographic Principle known as the adS/CFT correspondence.

**Are YOU a Hologram? M-theory and the adS/CFT correspondence**

*anti-de Sitter*space (adS). Five-dimensional anti-de Sitter space has a boundary which is four-dimensional, and in a certain limit looks like flat spacetime with one time and three space directions. The adS/CFT correspondence states that the physics of gravity in five-dimensional anti-de Sitter space, is equivalent to a certain supersymmetric Yang-Mills theory which is defined on the boundary of adS. This Yang-Mills theory is thus a `hologram' of the physics which is happening in five dimensions. The Yang-Mills theory has gauge group

*SU*(

*N*), where

*N*is very large, and it is said to be `supersymmetric' because it has a symmetry which allows you to exchange bosons and fermions. The hope is that this theory will eventually teach us something about QCD (quantum chromodynamics), which is a gauge theory with gauge group

*SU*(3). QCD describes interactions between quarks. However, QCD has much less symmetry than the theory defined on the boundary of adS; for example, QCD has no supersymmetry. Furthermore, we still don't know how to incorporate a crucial property of QCD, known as

*asymptotic freedom*.

Here in DAMTP, we have been working to see if the adS/CFT correspondence can be generalized. Working with collaborators in such far-flung places as the United States, Canada, and Durham, we have managed to show that the duality is still true even when you replace adS with more complicated five-dimensional spacetimes. In particular, we have calculated what happens when you put electric charge in adS, or rotation in adS, or even what happens when you put a certain exotic charge known as `NUT-charge' into adS.