Progress in String Theory

The following sections are included:

• FOREWORD

• CONTENTS

The following sections are included:

• Introduction

• Worldsheet Models of Closed Strings
  • The N = (2, 2) non-linear σ-model
  • The A model
  • The B model
  • Mirror symmetry

• Boundaries
  • The A-model
    • A-branes
    • Open strings for one A-brane
    • Open strings for many A-branes
  • The B-model
    • B-branes
    • Open strings for B-branes
    • A failure of mirror symmetry

• Some Mathematical Tools
  • Categories of sheaves
    • Holomorphic functions
    • Sheaves
    • Locally free sheaves
    • Kernels and cokernels
    • Abelian categories
    • Coherent sheaves
  • Cohomology
    • Čech cohomology
    • Spectral sequences
    • Dolbeault cohomology
    • Sheaf cohomology

• The Category of B-branes
  • Deformations and complexes
  • Open strings
  • The derived category
  • Coherent sheaves
  • More deformations
  • Anti-branes and K-theory
  • Mirror symmetry restored?

• Stability
  • A-branes
    • Special Lagrangians
    • A geometrical decay
    • Tachyon condensates
  • B-branes
    • Triangles
    • Categorical mirror symmetry at last
    • П-stability
    • Multiple decays
    • μ-stability

• Applications
  • The quintic threefold
    • Periods
    • 4-branes
    • Exotic B-branes
    • Monodromy
  • Flops
  • Orbifolds
    • The McKay correspondence
    • The Douglas-Moore construction
    • θ-stability
    • Periods
    • Monodromy
    • Examples of stability

• Conclusion

• Acknowledgments

• References

We give a short introduction to the AdS/CFT correspondence and its plane wave limit.

In this review we describe our current understanding of the properties of open string tachyons on an unstable D-brane or brane-antibrane system in string theory. The various string theoretic methods used for this study include techniques of two dimensional conformal field theory, open string field theory, boundary string field theory, non-commutative solitons etc. We also describe various attempts to understand these results using field theoretic methods. These field theory models include toy models like singular potential models and p-adic string theory, as well as more realistic version of the tachyon effective action based on Dirac-Born-Infeld type action. Finally we study closed string background produced by the ‘decaying’ unstable D-branes, both in the critical string theory and in the two dimensional string theory, and describe the open string completeness conjecture that emerges out of this study. According to this conjecture the quantum dynamics of an unstable D-brane system is described by an internally consistent quantum open string field theory without any need to couple the system to closed strings. Each such system can be regarded as a part of the ‘hologram’ describing the full string theory.

I review basic forces on moduli that lead to their stabilization, for example in the supercritical and KKLT models of de Sitter space in string theory, as well as an AdS₄ × S³ × S³ model I include which is not published elsewhere. These forces come from the classical dilaton tadpole in generic dimensionality, internal curvature, fluxes, and branes and orientifolds as well as non-perturbative effects. The resulting (A)dS solutions of string theory make detailed predictions for microphysical entropy, whose leading behavior we exhibit on the Coulomb branch of the system. Finally, I briefly review recent developments concerning the role of velocity-dependent effects in the dynamics of moduli. These lecture notes are based on material presented at various stages in the 1999 TASI, 2002 PiTP, 2003 TASI, and 2003 ISS schools.

The duality cascade, and its dual description as string theory on the warped deformed conifold, brings together several sophisticated topics, some of which are not widely known. These lectures, which contain a number of previously unpublished results, and are intended for experts as well as students, seek to explain the physics of duality cascades. Seiberg duality is carefully introduced, with detailed attention to the physical implications of duality away from the far infrared. The conifold is briefly introduced and strings on the conifold (the Klebanov-Witten model) are discussed. Next, fractional branes are introduced. The duality cascade is then constructed in field theory and in its dual supergravity description. Among the newly published results: it is shown why supergravity sees the cascade as smooth; how the two holomorphic couplings (dilaton and integrated two-form in supergravity) are related to the three physical couplings in the gauge theory; that there are actually twice as many approximate fixed points in the cascade as might be naively expected. These notes are based on lectures given at TASI 2003 and at the 2003 PIMS Summer School on Strings, Gravity & Cosmology.

These notes describe how perturbative on-shell and off-shell string amplitudes can be computed using string field theory. Computational methods for approximating arbitrary amplitudes are discussed, and compared with standard world-sheet methods for computing on-shell amplitudes. These lecture notes are not self-contained; they contain the material from W. Taylor's TASI 2003 lectures not covered in the recently published “TASI 2001” notes hep-th/0311017 by Taylor and Zwiebach, and should be read as a supplement to those notes.

The following sections are included:

• STUDENT SEMINARS

• STUDENT PARTICIPANTS

• LECTURERS

• DIRECTORS

• LOCAL ORGANIZING COMMITTEE

• PICTURES