STRING THEORY: CHALLENGES AND PROSPECTS John H. Schwarz

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STRING THEORY CHALLENGES AND PROSPECTS John
H. Schwarz

• October 2008

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• OUTLINE
• I. What is string theory?
• II. Challenges and Prospects

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I. What is String Theory?

• String theory arose in the late 1960s in an
  attempt to understand the strong nuclear force.
  This is the force that holds neutrons and protons
  together inside the nucleus.
• The theory must incorporate relativity and
  quantum mechanics. If the fundamental objects in
  the theory are loops or line segments, called
  strings, rather than point-like particles, it can
  account for features of the strong nuclear force.

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• The basic idea is that different motions of
  the string correspond to different types of
  particles. So, string theory has a unique
  fundamental object (namely, the string).
• The original string theory (1968-69), called
  the bosonic string theory, has several fatal
  shortcomings. A much better one, superstring
  theory (1971), overcomes these problems.

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BOSONIC STRING THEORY

• This theory describes bosons but not fermions.
  These are the two basic classes of particles in
  quantum theories.
• Consistency requires 26 dimensions (25 of them
  are spatial and 1 is time).
• It has various other mathematical and physical
  shortcomings, but it serves as a good warm-up
  exercise.

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SUPERSTRING THEORY

• Another string theory that contains both
  fermions and bosons was introduced in 1971 by
  Ramond, Neveu, and me. It requires 10 dimensions
  (9 1).
• Its development led to the discovery of
  supersymmetry, a symmetry that relates bosons and
  fermions. Strings with this symmetry are called
  superstrings.

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UNIFICATION

• Both string theories contain massless
  particles. One of them has just the right
  properties to be the graviton -- the particle
  responsible for the gravitational force.
• In 1974 Scherk and I proposed using string
  theory for unification of all forces (including
  gravity).

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EINSTEINS DREAM

• A unified theory was Einsteins focus in his
  later years. However, the approach he pursued
  involved trying to combine only electromagnetism
  and gravitation (general relativity).
• The nuclear forces were not yet understood,
  and Einstein was uneasy with quantum mechanics,
  even though he was one of its founders. So his
  efforts were doomed from the outset.

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THE SIZE OF STRINGS

• When strings were supposed to describe
  strongly interacting nuclear particles (hadrons)
  their typical size needed to be
• L 10-13 cm
• To describe gravity it needs to be roughly
  equal to the Planck length
• L hG/c3 1/2 10-33 cm
• Smaller by 20 orders of magnitude!

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• Advantages of String Theory
• for Unification
• Quantum corrections to Einsteins theory of
  gravity are infinite in point-particle theories.
  In contrast, string theory gives finite results.
• The extra spatial dimensions can curl up and
  become very small in a gravity theory, where the
  geometry of space and time is determined by the
  dynamics.

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FIVE THEORIES

Following various breakthroughs in 1984, we had
five consistent superstring theories Type I,
Type IIA, Type IIB, Heterotic HE and HO Each
of these is unique (without any free parameters)
and requires ten dimensions.
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DUALITIES

• String theory has many surprising truths. One
  of them is that different geometries for the
  extra dimensions can be physically equivalent!
  This is called T duality.
• e.g., a circle of radius R can be equivalent
  to a circle of radius L2/R, where L is the string
  length scale. Two such cases are
• HE ? HO and IIA ? IIB

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S DUALITY

• Another surprising discovery is S duality. It
  relates a theory with an interaction strength g
  to another one with interaction strength g
  1/g. Two examples are
• I ? HO and IIB ? IIB.
• Thus, since we know how to compute physical
  quantities when g is very small, we learn how
  these three theories behave when g is very large.

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• M-THEORY
• What happens to the other two theories (IIA
  and HE) when g is large?
• Answer They grow an 11th dimension of size
  gL. This new dimension is a circle in the IIA
  case and a line interval in the HE case.
• Taken together with the dualities, this
  implies that the five superstring theories are
  actually different facets of a unique
  underlying theory.

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Theres just one theory!
Courtesy of John Pierre
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BRANES

• In addition to fundamental strings,
  superstring theory predicts the existence of
  objects with p spatial dimensions, called
  p-branes. (The fundamental string is a 1-brane.)
• The values of p that can occur depend on the
  theory. Since the dimension of space is large (9
  or 10), the allowed values of p can also be
  large. For example, M-theory admits a 2-brane and
  a 5-brane.

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BRANE WORLDS

• Certain p-branes are called D-branes. They
  have the property that fundamental strings can
  end on them. One consequence is that quantum
  field theories, like the standard model, can live
  on these D-branes.
• In this setup elementary particles and all
  forces except gravity are restricted to the
  branes, while gravity acts in all ten dimensions.

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II. CHALLENGES AND PROSPECTS
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1. Explain Particle Physics

• The underlying theory is unique, but its
  equations have very many solutions. One of them
  should describe the microscopic quantum world of
  particle physics.
• Can we find it? Is it picked out by some
  beautiful principle, or is it just randomly
  chosen by our corner of the Universe?

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Facts to Explain

• Four-Dimensional Spacetime
• Yang--Mills Quantum Field Theory with SU(3) X
  SU(2) X U(1) gauge symmetry.
• Three families of quarks and leptons.
• The SU(2) X U(1) symmetry is broken to the
  electromagnetic U(1) symmetry by the Higgs
  mechanism. This gives mass to the quarks and
  leptons.

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2. Understand the Role of Supersymmetry

• Supersymmetry, which is an essential feature
  of superstring theory, implies that every
  particle has a superpartner.
• What are their masses?
• Is the LSP responsible for dark matter?
• Can superpartners be made in collisions?
• How is supersymmetry broken?

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With Supersymmetry
Courtesy of The Particle Adventure
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7 7 TeV proton proton collider
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Detectors
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3. Cosmology Origin and Evolution of the
Universe

• Trying to understand the whole Universe raises
  similar sorts of questions. How much of its
  origin, structure, and evolution can be deduced
  from first principles?
• Superstring cosmology has become a very active
  field of research.

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4. Understand Empty Space

• Empty space (or the vacuum) contains a
  mysterious substance called dark energy. It
  accounts for about 70 of the total energy of the
  Universe, and it causes the expansion of the
  Universe to accelerate.
• The density of this energy is 10(-120), when
  expressed in Planck units. How can we understand
  this number?

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5. Find a Compelling Formulation of the Theory

• We do not have a compelling formulation of the
  complete underlying theory. This may require some
  new principle.
• The existence of space and time is likely to
  be an emergent feature of specific solutions that
  is not built into the underlying theory.

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Spinoffs

• Mathematical discoveries
• Properties of high temperature nuclear matter
• Condensed matter systems, such as high
  temperature superconductors

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Conclusions

• String theory unifies disciplines as well as
  forces and particles.
• We have been exploring string theory for 40
  years, but there is a long way to go.
• I find it amazing that we might be able to answer
  such basic questions.