8 Beyond the Standard Model
511
separation of long and short distances is a corner stone of the renormalization group
approach, this is not evident in the case of gravity. One possible implication of this
behavior is that in gravitational systems the amount of information stored in a spatial
volume is proportional to the boundary’s surface area rather then to the bulk volume.
String theory provides explicit and concrete realizations of this amazing behavior.
A system of strings moving in particular ten dimensional space-times (of the anti
de Sitter type) are equivalent to special highly symmetric supersymmetric nonAbelian gauge theories living in four dimensions and experiencing no gravitational
forces. Moreover modifying the backgrounds on which the strings propagate by
adding defects to them, one finds that strings propagating on certain backgrounds are
equivalent to gauge theories in which color is confined. String theory methods are
used to perform difficult calculations in hadronic physics. String theory, which was
born out of hadronic physics, has returned to pay back its original debt! In addition,
remarkable structures have been uncovered in supersymmetric gauge theories using
string theory methods. Attempts have been made to confront strings with other
singularities. Why should strings respond to singularities in any other way than
particles do? A Talmudic story helps explain the manner in which extended objects
modify problems associated with point particles. During a seminar, the following
question came up: Assume a pigeon (a very valuable animal at the time) is found
somewhere, to whom does it belong? The rule is, finders-keepers, as long as the
pigeon is found further away, than some determined distance, from the entrance to
an owned pigeon-hole. A student raised his hand and asked: “The pigeon is, after all,
an extended object, what if one of its legs is nearer than the prescribed distance to
the pigeon-hole but the other leg is further away?” The student was ejected from
his place of study for raising the question. Strings definitely turn out to soften
some harsh singularities which are time independent (called time like singularities).
Strings are also found to punch through singularities which form at particular times
such as a big crunch. The analysis of such systems is still at very early stages,
still I would like to note a very interesting feature in common up the present to all
attempts to study using string theory methods universes that are spatially closed. In
these cases the compact universe is found to be immersed in one way or another in
a non compact universe. The study of strings near these singularities could well be
essential to appreciate their properties at short distances. A key ingredient driving
some researchers is a new panoramic vista opening up to them. For some it is the
precise calculations of experimentally measurable quantities, for others it is the
Magic.
8.4.6 Magic
The universe as viewed with string probes is full of magic ambiguities and
symmetries unheard of before. In fact most mathematical concepts used to describe
the universe are veiled under symmetry. There are cases for which each of the
following concepts becomes ambiguous: distances, the number of dimensions,
511
separation of long and short distances is a corner stone of the renormalization group
approach, this is not evident in the case of gravity. One possible implication of this
behavior is that in gravitational systems the amount of information stored in a spatial
volume is proportional to the boundary’s surface area rather then to the bulk volume.
String theory provides explicit and concrete realizations of this amazing behavior.
A system of strings moving in particular ten dimensional space-times (of the anti
de Sitter type) are equivalent to special highly symmetric supersymmetric nonAbelian gauge theories living in four dimensions and experiencing no gravitational
forces. Moreover modifying the backgrounds on which the strings propagate by
adding defects to them, one finds that strings propagating on certain backgrounds are
equivalent to gauge theories in which color is confined. String theory methods are
used to perform difficult calculations in hadronic physics. String theory, which was
born out of hadronic physics, has returned to pay back its original debt! In addition,
remarkable structures have been uncovered in supersymmetric gauge theories using
string theory methods. Attempts have been made to confront strings with other
singularities. Why should strings respond to singularities in any other way than
particles do? A Talmudic story helps explain the manner in which extended objects
modify problems associated with point particles. During a seminar, the following
question came up: Assume a pigeon (a very valuable animal at the time) is found
somewhere, to whom does it belong? The rule is, finders-keepers, as long as the
pigeon is found further away, than some determined distance, from the entrance to
an owned pigeon-hole. A student raised his hand and asked: “The pigeon is, after all,
an extended object, what if one of its legs is nearer than the prescribed distance to
the pigeon-hole but the other leg is further away?” The student was ejected from
his place of study for raising the question. Strings definitely turn out to soften
some harsh singularities which are time independent (called time like singularities).
Strings are also found to punch through singularities which form at particular times
such as a big crunch. The analysis of such systems is still at very early stages,
still I would like to note a very interesting feature in common up the present to all
attempts to study using string theory methods universes that are spatially closed. In
these cases the compact universe is found to be immersed in one way or another in
a non compact universe. The study of strings near these singularities could well be
essential to appreciate their properties at short distances. A key ingredient driving
some researchers is a new panoramic vista opening up to them. For some it is the
precise calculations of experimentally measurable quantities, for others it is the
Magic.
8.4.6 Magic
The universe as viewed with string probes is full of magic ambiguities and
symmetries unheard of before. In fact most mathematical concepts used to describe
the universe are veiled under symmetry. There are cases for which each of the
following concepts becomes ambiguous: distances, the number of dimensions,