Re: Spontaneous supersymmetry breaking
- From: Igor Khavkine <igor.kh@xxxxxxxxx>
- Date: Sat, 12 Aug 2006 03:32:35 +0000 (UTC)
saju wrote:
Greetings,
Assuming that during the very early instances of the big bang there
did exist a supersymmetric 10-D universe, what triggered the symmetry
breaking and resulting 6-D compactification and particle creation ?
Does a drop in temperature because of the expansion after big bang cause
super symmetry to be broken ? Why ? If the answer is known, can it be
explained in "interested layman" terms please :) ?
Since supersymmetric particles have not yet been observed, it is not
known whether supersymmetry actually exists and has been broken. In
that sense, the answer is not known. However, the physical phenomenon
of spontaneous symmetry breaking (SSB), that the proponents of
supersymmetry are trying to leverage, is well known as well as widely
observed and studied.
The simplest example of SSB is a magnet. A magnet has a magnetic moment
because the spins of its electrons or nuclei have aligned such that
their sum gives a non-zero total magnetization. But if you heat up the
same magnet, after a certain temperature (called the Curie temperature,
incidentally), it looses its magnetization---the electron and nuclear
spin alignment is lost. Notice that temperature does play a crucial
role here.
So what happened? Recall that heat is motion. The higher the
temperature, the more microscopic motion will there be inside a solid.
The lower the temperature, the lower the total energy of the solid
wants to be.
At high temperature, everything is moving around. For instance, nuclear
or electronic spins are twirling and pointing in different directions,
ignoring what their neighbors are doing. Because they have no special
direction to point in, on average, the sum of individual spins will
come out to zero---no magnetization.
But at lower temperatures, the spins don't twirl around too much and
pay more attention to what their neighbors are doing. At some point,
the spins notice that they like to point in the same direction as their
neighbors (such configurations have lower energy). And, once the
temperature is low enough and the spins are rotating sufficiently
slowly, they notice that they'd like nothing better to do than for all
of them to point in the same direction (the state with the lowest
available energy).
But here's a puzzle. If we start with a heated magnet (such that it's
not magnetized) shaped like a sphere and then cool it down, once it
acquires a magnetization, which way will it point? After all, there's
nother special about any way in which the sphere is oriented.
Here we come back to the name of the phenomenon: spontaneous symmetry
breaking. The symmetry breaking corresponds to the fact that once the
sphere becomes magnetized, we can identify two special points on its
surface: the North and South poles. So, the rotational symmetry of the
sphere has been broken. The word spontaneous tells us that the answer
to the puzzle above is: very hard to know in advance.
Examining the transition between the non-magnetized and magnetized
states, we find that at the transition temperature the non-magnetized
state becomes unstable. It is unstable in the same way that a ball
sitting at the very apex of a hill. It is in equilibrium. As long as it
is not touched it will stay there for every. However, even the tiniest
gust of wind or the smallest tremble of the ground will send it
rolling. The ball can roll to the left or to the right depending on
what force had upset its equilibrium. Physicists say that the ball
spontaneously chooses the direction in which to roll. Same for the
magnet, the direction of the acquired magnetization could have been
influenced by any number of things, from the Earth's magnetic field to
the field generated by a nearby computer monitor.
To conclude, here are the ingredients for spontaneous symmetry
breaking. There needs to be a symmetry to the individual components of
the system. For example, in a magnet, spins are free to point in any
direction. At high enough temperatures, the system should be
describable as a collection of non-interacting individual components.
In this phase, the symmetry is unbroken. For example, this is the high
temperature non-magnetized phase of a magnet. Then, at low
temperatures, the individual components can no longer be considered
non-interacting and they tend to orient themselves in the same way as
their neighbors. In a magnet, at low temperature, individual spins like
to point in the same direction as their neighbors.
Lets come back to supersymmetry. Every particle is presumed to have a
fermion and a boson component. A continuous transformation (much like a
rotation) between the components is the symmetry in question. If the
interaction between two nearby particles energetically favors both of
them to be of the same statistics (bosonic or fermionic), then at low
enough temperature one would generically expect a symmetry-broken
phase, where each particle is either a fermion or a boson. So, in this
scenario, given the cooling of the universe as it expands, it is not
unreasonable to expect breaking of supersymmetry.
Hope this helps and was sufficiently in "interested layman terms".
Igor
.
- References:
- Spontaneous supersymmetry breaking
- From: saju
- Spontaneous supersymmetry breaking
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