8 Beyond the Standard Model
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vacuum energy and perhaps may thus decay from one to the other. In particular
bubbles may form within one configuration, bubbles that contain in them a lower
energy configuration. Some researchers would like to see the universe itself, or
the bubbles that form in it, as eternal tourists who will end up visiting many of
these metastable states. Some suspect that many of these metastable states are
stable. Some would encourage brave sailors to take to sea again, as they did in
the 1980s, and charter this unknown geography, some are trying to make this
endeavor quantitative by counting vacua which have a given property, such as a
given cosmological constant. This subject is still at its infancy, many hopes and
opinions are currently expressed, it would be nice if this issue will turn out to fall
within the realm of solvable problems.
The challenges to string theory on the experimental side have been to reproduce
the standard model. This has not been done to this day. Many new ideas and
insights have been added. Bounds have been shifted several times, one has felt
being very near to obtaining the desired model, each new approach seemed to bring
one nearer to that goal, but obtaining one completely worked-out example, which
is the standard model, remains a challenge for string theorists. Another important
issue is that of the value of the cosmological constant. It is usually stated that the
small value of the cosmological constant is a major problem. These arguments are
centered around some version of a low energy effective field theory. That theory
could be valid below a few tens of electron volt thus describing only aspects of
electromagnetism or it could be at a TeV scale describing both the electroweak
interactions. The arguments goes on to say that the vacuum energy of such an
effective theory should be, on dimensional arguments grounds, proportional to the
scale of the cutoff, (the cutoff is set at that energy beyond which the ingredients of
the physics start to change) that is evs or TeVs in the above examples. In either
case, the value of this vacuum energy, which is the source of the cosmological
constant, is larger by an astonishing number than the known bounds on the value
of the cosmological constant. The argument is not correct as stated, it is not only the
cutoff that contributes to the cosmological constant, all scales do actually contribute
to the vacuum energy and if a cutoff should be invoked, it is the highest one, such as
the Planck scale, that should be chosen. Moreover, this argument does not take into
account the possibility that the fundamental theory has a certain symmetry which
could be the guardian of vanishingly small value of the cosmological constant. Such
a symmetry exists, it is called scale invariance, and it has shown to be a guardian
in several settings. Scale invariance is associated with the absence of a scale in the
theory. There are many classical systems which have this symmetry and there are
also quantum systems which retain it. In a finite, scale invariant theory not only
does the vacuum energy get contributions from all scales, they actually add up
to give rise to a vanishing vacuum energy. This remains the case even when the
symmetry is spontaneously broken. Being a consequence of a symmetry, the vacuum
energy contribution to the cosmological constant vanishes also is the appropriate
effective theory. What does string theory have to say about that? String theory
could well be a finite theory, it is not scale invariant, as it contains a string scale,
if that scale would be spontaneously generated perhaps one would be nearer to
509
vacuum energy and perhaps may thus decay from one to the other. In particular
bubbles may form within one configuration, bubbles that contain in them a lower
energy configuration. Some researchers would like to see the universe itself, or
the bubbles that form in it, as eternal tourists who will end up visiting many of
these metastable states. Some suspect that many of these metastable states are
stable. Some would encourage brave sailors to take to sea again, as they did in
the 1980s, and charter this unknown geography, some are trying to make this
endeavor quantitative by counting vacua which have a given property, such as a
given cosmological constant. This subject is still at its infancy, many hopes and
opinions are currently expressed, it would be nice if this issue will turn out to fall
within the realm of solvable problems.
The challenges to string theory on the experimental side have been to reproduce
the standard model. This has not been done to this day. Many new ideas and
insights have been added. Bounds have been shifted several times, one has felt
being very near to obtaining the desired model, each new approach seemed to bring
one nearer to that goal, but obtaining one completely worked-out example, which
is the standard model, remains a challenge for string theorists. Another important
issue is that of the value of the cosmological constant. It is usually stated that the
small value of the cosmological constant is a major problem. These arguments are
centered around some version of a low energy effective field theory. That theory
could be valid below a few tens of electron volt thus describing only aspects of
electromagnetism or it could be at a TeV scale describing both the electroweak
interactions. The arguments goes on to say that the vacuum energy of such an
effective theory should be, on dimensional arguments grounds, proportional to the
scale of the cutoff, (the cutoff is set at that energy beyond which the ingredients of
the physics start to change) that is evs or TeVs in the above examples. In either
case, the value of this vacuum energy, which is the source of the cosmological
constant, is larger by an astonishing number than the known bounds on the value
of the cosmological constant. The argument is not correct as stated, it is not only the
cutoff that contributes to the cosmological constant, all scales do actually contribute
to the vacuum energy and if a cutoff should be invoked, it is the highest one, such as
the Planck scale, that should be chosen. Moreover, this argument does not take into
account the possibility that the fundamental theory has a certain symmetry which
could be the guardian of vanishingly small value of the cosmological constant. Such
a symmetry exists, it is called scale invariance, and it has shown to be a guardian
in several settings. Scale invariance is associated with the absence of a scale in the
theory. There are many classical systems which have this symmetry and there are
also quantum systems which retain it. In a finite, scale invariant theory not only
does the vacuum energy get contributions from all scales, they actually add up
to give rise to a vanishing vacuum energy. This remains the case even when the
symmetry is spontaneously broken. Being a consequence of a symmetry, the vacuum
energy contribution to the cosmological constant vanishes also is the appropriate
effective theory. What does string theory have to say about that? String theory
could well be a finite theory, it is not scale invariant, as it contains a string scale,
if that scale would be spontaneously generated perhaps one would be nearer to