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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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EINSTEIN’S DREAM A unified theory was Einstein’s 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/c 3 ] 1/2 ~ 10 -33 cm Smaller by 20 orders of magnitude!

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Advantages of String Theory for Unification: Quantum corrections to Einstein’s 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 L 2 / 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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There’s just one theory! Courtesy of John Pierre

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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. BRANES

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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.

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