Warped Passages (41 page)

But Ike later learned that the social structure in Heaven had not always been so secure. Originally, dangerous energetic infiltrators had threatened the hierarchical foundation of society. In Heaven, however, most problems can be solved. God had sent everyone a personal guardian angel, and the angels and their charges had heroically worked together to avert the threat to the hierarchy and preserve the ordered society that Ike could now enjoy.

Even so, Heaven was not entirely safe. The angels turned out to be free agents, with no contract binding them to a single generation. The fickle angels, who had so bravely rescued the hierarchy, now threatened to destroy Heaven’s family values. Ike was appalled. Despite Heaven’s well-advertised attractions, he was finding it a surprisingly stressful place.

“Super” words abound in physics terminology. We have superconducting, supercooling, supersaturated, superfluid, the Super conducting Supercollider (the SSC)—which would have been the highest-energy collider today had Congress not canceled it in 1993—and the list goes on. So you can imagine the excitement when physicists discovered that spacetime symmetry itself has a bigger, “super” version.

The discovery of
supersymmetry
was truly surprising. At the time when supersymmetric theories were first developed, physicists thought they knew all the symmetries of space and time. Spacetime symmetries are the more familiar symmetries that we saw in Chapter 9, which declare that you can’t tell where you are or which way you’re facing or what time it is solely from physical laws. The trajectory of a basketball, for example, doesn’t depend on which side of the court you’re on or if you play the game in California or New York.

In 1905, with the arrival of relativity theory, the list of spacetime symmetry transformations expanded to include those that change velocity (speed and direction of motion). But, physicists thought, that topped the list. No one believed that there could be other undiscovered symmetries involving space and time. Two physicists, Jeffrey Mandula and Sidney Coleman, codified this intuition in 1967 by proving that there could be no other such symmetries. However, they (and everyone else) had overlooked one possibility based on unconventional assumptions.

This chapter introduces
supersymmetry
, a strange new symmetry transformation that interchanges bosons and fermions. Physicists can now construct theories that incorporate supersymmetry. However, supersymmetry as a symmetry of nature is still hypothetical, since no one has yet discovered supersymmetry in the world around us. Nonetheless, physicits have two major reasons to think that it might exist in the world:

One reason is the superstring, which will be more thoroughly investigated in the chapter that follows. Superstring theory, which incorporates supersymmetry, is the only known version of string theory that has the potential to reproduce the particles of the Standard Model. String theory without supersymmetry doesn’t look as if it could possibly describe our universe.

The second reason is that supersymmetric theories have the potential to solve the hierarchy problem. Supersymmetry doesn’t necessarily explain the origin of the large ratio of the weak scale mass to the Planck scale mass, but it does eliminate the problematic enormous quantum contributions to the Higgs particle’s mass. The hierarchy problem is a serious conundrum for which very few suggestions have survived experimental and theoretical scrutiny. Before extra-dimensional theories were introduced as potential alternatives, supersymmetry was the lone candidate solution.

Because no one yet knows whether or not supersymmetry exists in the external world, all we can do at this point is evaluate candidate theories and their consequences. This way, when experiments reach higher energy, we’ll be prepared to figure out what the physical theory underlying the Standard Model really is. So let’s take a look at what could lie in store.

Fermions and Bosons: An Unlikely Match

In a supersymmetric world every known particle is paired with another—its supersymmetric partner, also known as a
superpartner
—with which it is interchanged by a supersymmetry transformation. A supersymmetry transformation turns a fermion into its partner boson and a boson into its partner fermion. We saw in Chapter 6 that fermions and bosons are particle types that are distinguished in quantum mechanical theories by their spin. Fermionic particles have half-integer spin, while bosonic particles have integer spin. Integer spin values are those numbers that ordinary objects spinning in space could take, whereas half-integer values are a peculiar feature of quantum mechanics.

All fermions in a supersymmetric theory can be transformed into
their partner bosons and the bosons can all be transformed into their partner fermions. Supersymmetry is a feature of the theoretical description of these particles. If you muck around with the equations that describe how particles behave by making a supersymmetry transformation that interchanges bosons and fermions, the equations will all end up looking the same. The predictions would all be identical to those you made before you did the transformation.

At first glance, such a symmetry defies logic. Symmetry transformations are supposed to leave systems unchanged. But supersymmetry transformations interchange particles that are manifestly different: fermions and bosons.

Although one would not expect a symmetry to mix things that are so different, several groups of physicists nevertheless proved that it could. In the 1970s, European and Russian physicists
^*
showed that a symmetry could interchange such different particles, and that the laws of physics could be the same before and after bosons and fermions were interchanged.

This symmetry is a little different from previous symmetries we have considered because the objects that it interchanges clearly have different properties. But the symmetry can nonetheless exist if bosons and fermions are present in equal numbers. As an analogy, imagine an equal number of different-size red marbles and green marbles, with one marble of each color in each size. Suppose you are playing a game with a friend, and you get the red marbles and your friend gets the green ones. If the marbles were exactly paired, neither color choice would give you an advantage. However, if there weren’t an equal number of red and green marbles of any given size, it wouldn’t be an even playing field. It would matter if you chose red or green, and the game would proceed differently if you and your friend were to switch colors. For there to be a symmetry, every size of marble must come in both red and green, and there must be the same number of marbles of each color of any given size.

Similarly, supersymmetry is possible only if bosons and fermions are exactly paired. You need the same number of boson and fermion particle types. And just as the marbles that were interchanged had to have identical sizes, the paired bosons and fermions must have the same mass and charges as each other, and their interactions must be controlled by the same parameters. In other words, each particle must have its own superpartner with similar properties. If a boson experiences strong interactions, so does its supersymmetric partner. If there are interactions involving some number of particles, there are related interactions involving their supersymmetry partners.

One reason physicists find supersymmetry so exciting is that if it
is
discovered in our world, it will be the first new spacetime symmetry to be found in almost a century. That’s why it’s “super.” I won’t give the mathematical explanation, but just knowing that supersymmetry exchanges particles of different spin is enough to deduce a connection. Because their spins are different, bosons and fermions transform differently when they rotate in space. Supersymmetry transformations must involve space and time in order to compensate for this distinction.
²³

But don’t think that this means you should be able to picture what a single supersymmetry transformation looks like in physical space. Even physicists understand supersymmetry only in terms of its mathematical description and its experimental consequences. And these, as we’ll soon see, could be spectacular.

Superhistory

You can skip this if you like. It’s a historical section that won’t introduce any concepts that will be essential later on. But the development of supersymmetry is an interesting story, in part because it nicely demonstrates the versatility of good ideas and the way string theory and model building sometimes have a productive, symbiotic relationship. String theory motivated the search for supersymmetry, and the superstring—the best string theory candidate for the real world—was identified only because of insights from supergravity, the supersymmetric theory that includes gravity.

The French-born physicist Pierre Ramond put forward the first supersymmetric theory in 1971. He wasn’t working with the four dimensions that we (used to) think we live in, but in two: one of space and one of time. Ramond’s goal was to find a way to include fermions in string theory. For technical reasons, the original version of string theory contained only bosons, but fermions are essential to any theory that hopes to describe our world.

Ramond’s theory contained two-dimensional supersymmetry and evolved into the fermionic string theory he developed with André Neveu and John Schwarz. Ramond’s theory was the first supersymmetric theory to appear in the Western world: Gol’fand and Likhtman in the Soviet Union had simultaneously discovered supersymmetry, but their papers were hidden from the West behind the Iron Curtain.

Since four-dimensional quantum field theory was on much more solid footing than string theory, the obvious question was whether supersymmetry is possible in four dimensions. But because supersymmetry is intricately woven into the fabric of spacetime, it was not a straightforward task to generalize from two to four dimensions. In 1973, the German physicist Julius Wess and the Italian-born physicist Bruno Zumino developed a four-dimensional supersymmetric theory. In the Soviet Union, Dmitri Volkov and Vladimir Akulov independently derived another four-dimensional supersymmetric theory, but once again the Cold War forestalled any exchange of ideas.

Once these pioneers had worked out a four-dimensional supersymmetric theory, more physicists paid attention. However, the Wess-Zumino model of 1973 couldn’t accommodate all the Standard Model particles; no one yet knew how to add force-carrying gauge bosons to a four-dimensional supersymmetric theory. The Italian theorists Sergio Ferrara and Bruno Zumino solved this difficult problem in 1974.

On a train trip from Cambridge to London, where we had just attended the Strings 2002 conference, Sergio told me how finding the right theory would have been an impossibly difficult problem had it not been for the formalism of
superspace
, an abstract extension of spacetime that has additional
fermionic dimensions
. Superspace is an extremely complicated concept, and I shall not attempt a description of it. The important point here is that this entirely different type of dimension—which is not a dimension of space—played a crucial
role in supersymmetry’s development. This purely theoretical device continues to simplify supersymmetry calculations today.

The Ferrara-Zumino theory told physicists how to include electromagnetism and the weak and strong forces in a supersymmetric theory. However, supersymmetric theories did not yet include gravity. So the remaining question for a supersymmetric theory of the world was whether it could incorporate this remaining force. In 1976, three physicists, Sergio Ferrara, Dan Freedman, and Peter van Nieuwenhuizen, solved this problem by constructing
supergravity
, a complicated supersymmetric theory that contains gravity and relativity.

The interesting thing is that while supergravity was being formulated, string theory was marching forward independently. In one of the key theoretical developments in string theory, Ferdinando Gliozzi, Joel Scherk, and David Olive discovered a stable string theory as an outgrowth of the fermionic string theory that Ramond, along with Neveu and Schwarz, had developed. Fermionic string theory turned out to contain a type of particle that no one had previously encountered except in supergravity theories. The new particle had identical properties to the supersymmetric partner of the graviton known as the
gravitino
, and this is indeed what it turned out to be.

Because of the concurrent development of supergravity, physicists seized on and pursued this common element of the two theories, and soon realized that supersymmetry was present in fermionic string theory. With that, the superstring was born.

We’ll return to string theory and the theory of the superstring in the following chapter. For now, we’ll focus on the other important application of supersymmetry: its consequences for particle physics and the hierarchy problem.

The Supersymmetric Extension of the Standard Model

Supersymmetry would be most economical and compelling if it paired known particles with each other. However, for this to be true the Standard Model would have to contain equal numbers of fermions and bosons—but it doesn’t satisfy this criterion. That tells us that if
our universe is supersymmetric, it must contain many new particles. In fact, it must contain at least twice the number of particles that experimenters have so far observed. All the fermions of the Standard Model—the three generations of quarks and leptons—must be paired with new, as yet undiscovered bosonic superpartners. And the gauge bosons—the particles that communicate the forces—must have superpartners, too.

In a supersymmetric universe, the partners of quarks and leptons would be new bosons. Physicists, who enjoy whimsical (but systematic) nomenclature, call them
squarks
and
sleptons
. In general, the bosonic supersymmetric partner of a fermion has the same name as the fermion, but with an “s” at the beginning. Electrons are paired with
selectrons
, for example, and top quarks with
stop squarks
. Every fermion has a bosonic superpartner, its allied sfermion.