SUPERSTRING THEORY: PAST, PRESENT, AND FUTURE John H. Schwarz

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SUPERSTRING THEORY PAST, PRESENT, AND FUTURE
John H. Schwarz

• PITP Showcase Conference
• May 13, 2005

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I. 1968 - 1993

• 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.
• A theory based on strings, rather than
  point-like particles, can account for various
  features of the strong nuclear force and the
  strongly interacting particles (hadrons).

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STRING DYNAMICS
For a point particle the motion makes the
invariant length of the world-line extremal.
For a string the motion makes the invariant area
of the world-sheet extremal.
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• The basic idea is that different quantum
  states of the string correspond to the different
  types of particles. So, there is a unique
  fundamental object (namely, the string).

This string theory can be quantized, but this is
consistent only for 26 spacetime dimensions (25
are spatial and 1 is time). The string spectrum
contains bosons only (no fermions). Moreover, one
of these bosons is a tachyon.
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• By adding fermionic coordinates to the
  world-sheet, another string theory that contains
  fermions (as well as bosons) was constructed
  in 1971 by Pierre Ramond, André Neveu, and me. It
  requires 10 dimensions.
• Its development led to supersymmetry, a new
  type of symmetry that relates bosons and
  fermions. Strings with this symmetry are called
  superstrings.

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• In addition to the unrealistic
  dimension and the tachyon, the string spectrum
  includes particles that are massless, whereas all
  hadrons have positive mass.
• In the early 1970s a better theory of the
  strong nuclear force, called quantum
  chromodynamics (or QCD), was developed. As a
  result, string theory fell out of favor.

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• UNIFICATION
• One of the massless particles has precisely
  the right properties to be the graviton -- the
  particle responsible for the gravitational force.
  
• In 1974 Joël Scherk and I proposed to use
  string theory for the unification of all forces
  (including gravity), rather than just the strong
  nuclear force. Thus we stumbled upon a possible
  realization of Einstein's dream.

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THE SIZE OF STRINGS

• When strings were supposed to describe 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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This proposal had two big benefits

• All prior attempts to describe quantum
  corrections to Einsteins theory of gravity
  assumed point particles. They gave nonsensical
  infinite results (nonrenormalizable ultraviolet
  divergences). String theory is UV finite.
• Extra spatial dimensions can be compact in
  string theory, where the geometry is determined
  by the dynamics.

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FIRST SUPERSTRING REVOLUTION

• In 1984 Michael Green and I discovered that
  superstring theory is free from certain expected
  quantum inconsistencies, called anomalies, for
  two special choices of the symmetry group
• SO(32) and E8 x E8
• This raised hopes that a realistic theory can
  be determined just by mathematical consistency.
  The known symmetries fit nicely inside E8 .

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MBG and JHS Aspen 1984
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FIVE THEORIES

• Subsequently, two new superstring theories
  with exactly these symmetries were constructed by
  the Princeton string quartet.

By the time the dust settled, there seemed to be
five consistent superstring theories I, IIA,
IIB, HE, HO each of which requires ten
dimensions.
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Calabi-Yau Compactification

• Certain six-dimensional manifolds, called
  Calabi-Yau spaces, solve the equations and give a
  supersymmetric field theory in the remaining four
  dimensions.
• If one starts with the HE theory, and chooses
  the right CY space, it is possible to come quite
  close to achieving a realistic supersymmetric
  extension of the Standard Model.

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• SPACE (or T) DUALITY
• It was discovered in the late 1980s that
  different geometries for the extra dimensions can
  be physically equivalent!
• For example, 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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II. 1994 - PRESENT

• The period of discovery in the mid-1990s is
  referred to as the
• Second Superstring Revolution
• Some of the most important contributors are
  pictured on the next slide

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Juan Maldacena Joe Polchinski
Nathan Seiberg
Andrew Strominger Cumrun Vafa
Edward Witten
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• STRENGTH (or S) DUALITY
• This is another duality that relates a theory
  with interaction strength g to one with strength
  1/g.
• Two examples are
• I ? HO and IIB ? IIB.
• Thus, since we know how to do calculations
  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 superstring
  theories IIA and HE when g is large?
• Answer They grow an eleventh 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 new
  objects, called p-branes.
• p is the number of spatial dimensions they
  occupy. (For example, the fundamental string is a
  1-brane.)
• Since the dimension of space is large (9 or
  10), the allowed values of p can also be large.

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BRANE WORLDS

• Certain p-branes are called D-branes. They
  have the property that strings can end on them.
  One consequence is that quantum field theories
  like the standard model can live on D-branes.
• One intriguing possibility is that the
  observable Universe is actually a set of
  3-branes, which is embedded in a space with 6
  additional spatial dimensions.

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ADS/CFT DUALITY

• In 1997 Maldacena proposed a new
  class of dualities (or equivalences) for
  example, between a certain 4d QFT called N 4
  super Yang-Mills theory and Type IIB superstring
  theory in the 10d geometry AdS5 X S5.
• The string theory is represented
  holographically by the QFT, which is associated
  to the conformal boundary of the 10d or 11d
  spacetime. Since the QFT is conformally invariant
  (CFT), this is called an AdS/CFT duality.

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III. SOME REMAINING PROBLEMS

• 1. Find a complete and compelling formulation of
  the theory
• We do not yet have a compelling
  formulation of the underlying theory. It may
  require some principle that has not yet been
  understood.
• The existence of space and time is probably
  an emergent feature of specific solutions that is
  not built into the underlying theory.

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• 2. Understand empty space
• The vacuum energy density, called dark energy,
  is observed to be about 70 of the total energy
  of the present Universe. It causes the expansion
  of the Universe to accelerate.
• This energy density is only about 10-122 when
  expressed in Planck units. Anthropic explanation
  If it were much larger, we wouldnt be here. Is
  there another explanation? I hope so.

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3. Explain elementary particle physics

• Superstring theory may be unique, but its
  equations have very many solutions (or quantum
  vacua). 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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4. Understand the role of supersymmetry

• Supersymmetry requires that every particle
  have a superpartner.
• What are their masses?
• Is the lightest superpartner (LSP) responsible
  for dark matter?
• Can superpartners be made in collisions?

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With Supersymmetry
Courtesy of The Particle Adventure
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5. Understand spacetime and quantum mechanics

• What prevents bad spacetime singularities?
• What ensures causality?
• What are the microscopic quantum states that
  are responsible for the entropy of black holes?
• Is quantum mechanics exact?
• What ensures that there is no loss of quantum
  coherence for processes involving black holes?

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Trying to understand the whole Universe raises
yet more questions. How much of its origin,
structure, and evolution can be deduced from
first principles?
6. Understand the origin and evolution of the
Universe
Observational cosmology is providing many facts
that need to be explained. Superstring cosmology
has recently become a very active field of
research.
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7. Develop mathematical techniques and concepts

• String theory is up against the frontiers of
  several branches of mathematics. Given our
  experience to date, I expect that future
  developments will require mathematical methods
  and concepts that do not currently exist.
• String theory is unifying disciplines as well
  as forces and particles.