**Supersymmetry** (SUSY) was proposed in the early 1970s as a further symmetry in nature. The Standard Model divides particles into two camps called **fermions** and**bosons**. All the usual matter particles we observe – like electrons and quarks – are fermions. Every normal force carrying particle – like a photon or graviton – is a boson.

Roughly speaking, SUSY claims that there’s a way to replace fermions with bosons such that the laws of physics remain the same. Regardless of whether particles are strings or points, SUSY implies a connection between properties of bosonic and fermionic particles.

Supersymmetry tells us that every particle has a partner, which differs in **spin** by half a unit. All particles have spin. It’s a bit like the rate the Earth rotates on its axis. Spin is an intrinsic quantum mechanical property that does not change. If you change the spin of a photon, it is not a photon any more. Fermions have half-integer spin numbers – ½, 1½, 2½ etc. Bosons have integer spins – 0, 1, 2 etc. The force carriers of strong, weak and electromagnetic forces have spin 1 and the graviton spin 2.

But none of the particles that we ordinarily detect can be partners with each other. Physicists worked out that the new super-partners had to be much heavier than their counterparts, and gave them strange names like squarks, selectrons and photinos. No supersymmetric particles have been discovered so far, but evidence for supersymmetry at particle accelerators like the Large Hadron Collider at CERN would be a landmark for 21^{st} century physics.

Including SUSY makes a big difference to string theory. Supersymmetric string theory (or **superstring** theory) describes both bosons and fermions, and removes the impossible tachyon (hypothetical particle that always travels faster than the speed of light). Plus it only requires ten dimensions, compared to twenty-six for bosonic string theory. This is a lot closer to the four dimensions we usually experience.All modern work in string theory is based on the superstring. Originally there appeared to be five consistent and distinct superstring theories. It would take a revolution to realise that these were all smoothly connected. They are part of M-theory.

Extra dimensions are string theory’s most outlandish prediction. String theory demands that our cosy 4D view of the world is wrong. In fact the universe of strings must have ten dimensions! This is immediately at odds with our perception of reality, but we can resolve the paradox by requiring the six unseen dimensions to be incredibly small.

So what makes a **dimension**? Intuitively each dimension is an independent direction in which we can move. We live in three dimensions of space, “forward-backward”, “left-right” and “up-down”. There’s also a single time dimension, “past-future”, making 4 dimensions in total. But our perception of dimension is greatly affected by scale.

Imagine watching a faraway ship approaching port. It starts out looking like a zero-dimensional dot on the horizon. Soon you realise it has a mast pointing high into the sky: it now appears to be a one-dimensional line. Next, its sails come into view making it seem two-dimensional. As it nears the dock you finally notice that it has a long deck, the third dimension.

There’s nothing strange here. It’s just that at large distances we can’t resolve dimensions. So perhaps there could be extra dimensions, so small that we don’t perceive them. The process of curling up space to produce these tiny invisible dimensions is known as **compactification**.

Suppose you’re a squirrel living on an infinitely long tree trunk. The trunk is (more or less) a cylinder. You can move in two independent directions, “along” and “around”. One day you get bored and move to a thinner tree – the circumference of the trunk is greatly reduced.

Now your “around” dimension is much smaller than it used to be. It only takes a few steps to go all the way round the trunk. Any meaningful movement has to be done in the “along” dimension. You jump to a yet finer trunk. Now a single step takes you round the tree a hundred times! The “around” dimension has become far too small for you to detect.

As the tree trunks get narrower, the dimensions of your world reduce from two to one. In string theory this must happen for all six extra dimensions. We wrap them up so they are inconceivably tiny. Every time you move your hand through space you circle the six hidden dimensions a vast number of times.

The size of these compactified dimensions is similar to the length of a string, the **Planck scale**. This has two important consequences. Firstly it’s unlikely that we’ll be able to detect them by direct experiment. Nevertheless several possible tests have been suggested, though generally they rely on having a healthy slice of luck. Secondly the extra dimensions form a surface which strings can become caught up in.

The shape and size of strings is vital to modelling their vibrations and interactions. Therefore it’s important to understand how they wrap themselves around the six curled-up dimensions. The precise structure of the surface formed by compactification changes the physics arising from the strings.

It turns out there are many different ways of mushing up the extra dimensions into a tiny space. Which method gives rise to conventional physics? Nobody knows! Current research focuses on **Calabi-Yau manifolds**, a promising group of compactifications. But as of yet there is no definitive answer.