quantum gravity is a magnet


Luca Mazzucato


News from the March 2011 workshop on “Higher Spins and Holography” at SCGP, organized by Michael Douglas, Shlomo Razamat and the author.

We used to believe that string theory was a crucial element in studying quantum gravity through the holographic principle. Surprising theoretical discoveries show that quantum gravity may come with no strings attached and look like a magnet! Latest news from the SCGP workshop on ”Higher Spins and Holography”.

FUTURE – Let us keep an eye out: the new superstring revolution is around the corner. In the last years, theoretical physicists have been able to invent new “holographic” tools to attack their nemesis: quantum gravity. Discovering along the way a surprising fact: the regime of strong quantum gravity is described by a magnet, heated to the critical temperature at which it looses it magnetization!

All of this, and much more, was discussed for the first time at the recent workshop on “Higher Spin Theories and Holography”, held at the SCGP. The world’s leading experts, gathered for a week, have formulated a new coherent framework with surprising results.

The modern theory of gravitation goes under the name of the theory of general relativity and was discovered by Einstein a century ago. Gravity describes the way in which space and time, and our entire universe is evolving under the presence of matter, which bends its structures. Imagine spacetime as a sheet hanging, covered with sand (small particles that travel in a vacuum), but locked to a support on the four sides, holding it in tension. If you put a brick (represeting a star) on the sheet, this will form a hole and all the sand will fall into the pit. The gravity generated by the star draws all the particles that pass nearby. If you focus too much mass at the same point, the sheet tears open and all the sand falls off the sheet: it created a black hole that swallowed up all matter that gravitated around it!

The classical theory of Einstein explains very well the effect of the brick, but fails to explain exactly what happens when you “tear the sheet open”. The force of gravity becomes so strong that quantum effects are crucial and the theory of Einstein is not reliable anymore.

Here comes the string, which in addition to the “graviton” contains a series of higher vibration modes, that describe very massive particles. In everyday life, we fail to see these massive particles, even in the collisions of high energy protons, the LHC in Geneva (unless we have a real stroke of luck). But in the extreme setting near a black hole, these particles become crucial to understand what happens. Welcome to the quantum realm of gravity.

So far, we have lacked the theoretical tools to understand the “stringy” effects of these massive particles. A trick often used by theoretical physicists to study complicated phenomena is to “put them in a box,” making a sort of a thought experiment. In the case of spacetime, we would need a giant box that contains the whole universe! With a little effort, string theorists have realized that there is a “cosmological” version of the box: a universe with a negative cosmological constant (a.k.a. Anti-de Sitter spacetime).

The universe we live in (called de Sitter spacetime during its period of accelerated expansion) has a positive cosmological constant, which acts as a kind of pressure that increases the rate of expansion. Changing the sign of the cosmological constant (hence the prefix “anti-“) creates a new kind of hypothetical universe, contained in a box of infinite size. And like most boxes, the box of anti-de Sitter has instructions written on the cover, too!

The curious fact is that, once we confine the gravity inside a box, though infinitely large, theoretical physicists realized that gravity is a really holographic phenomenon. Do you remember those “Transformers” stickers in the early eighties, those strange metallic designs that project a three dimensional image when you look at them from different directions? Well, gravity works the same way: it is not nothing but a holographic illusion. At this point the question is: in what language are the instructions on the “holographic cover” written, and what do they tell us about gravity inside the box?

Until now, the hypothetical holographic universes available to physicists were populated by strings of all kinds. Due to the mathematical complexity inherent in string theory, progress has always been very difficult. The new ideas presented at Stony Brook point instead to a new direction: we have finally discovered a holographic universe entirely consistent, but with no strings in sight! This is the first example of “no strings attached” holography and a confirmation of how the concept of holography, guessed by Stephen Hawking studying black holes, is so fundamental that it transcends string theory itself.

In essence, a regime of extreme quantum gravity has been discovered in which spacetime is populated not only by the graviton, but there appear an infinite number of other particles of increasingly larger spin, which replace the notorious massive strings. The interactions among these particles are much simpler than those among strings, and thanks to this discovery we can finally face quantum gravity in all its beauty!

According to the holographic principle, gravity inside the box is a hologram, which is projected from the lid of the box. To understand gravity in the quantum regime we can now use a trick. Instead of looking at the nuts and bolts of gravity inside the box, we can study the cover of the box, where there is no gravitational pull at all. Using a “holographic dictionary”, we can translate the instructions on the cover into new properties of quantum gravity. As the reader might suspect, though, the devil is in the details – those of the dictionary! The results presented at Stony Brook are the very first entries of this amazing holographic dictionary, thanks to which we stumbled upon a big surprise.

The lid of the Anti-de Sitter spacetime, where the hurdles of quantum gravity are translated into a language more accessible to physicists, is nothing but a magnet at its phase transition (in technical terms, an Ising model). Very similar to the magnets attached to your refrigerator, if you heat them up to the critical temperature at which they loose their magnetization… We can answer now our rethorical question: yes, quantum gravity is a magnet!