Perturbative computations in string field theory

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 {\tt hep-th/0311017} by Taylor and Zwiebach, and should be read as a supplement to those notes.Comment: 17 pages; 2003 TASI lecture notes, supplement to 2001 TASI lectures by Taylor and Zwiebac

Three-Index Symmetric Matter Representations of SU(2) in F-Theory from Non-Tate Form Weierstrass Models

We give an explicit construction of a class of F-theory models with matter in the three-index symmetric (4) representation of SU(2). This matter is realized at codimension two loci in the F-theory base where the divisor carrying the gauge group is singular; the associated Weierstrass model does not have the form associated with a generic SU(2) Tate model. For 6D theories, the matter is localized at a triple point singularity of arithmetic genus g=3 in the curve supporting the SU(2) group. This is the first explicit realization of matter in F-theory in a representation corresponding to a genus contribution greater than one. The construction is realized by "unHiggsing" a model with a U(1) gauge factor under which there is matter with charge q=3. The resulting SU(2) models can be further unHiggsed to realize non-Abelian G_2xSU(2) models with more conventional matter content or SU(2)^3 models with trifundamental matter. The U(1) models used as the basis for this construction do not seem to have a Weierstrass realization in the general form found by Morrison-Park, suggesting that a generalization of that form may be needed to incorporate models with arbitrary matter representations and gauge groups localized on singular divisors.Comment: 34 pages, 3 figure

D-Branes, Tachyons, and String Field Theory

In these notes we provide a pedagogical introduction to the subject of tachyon condensation in Witten's cubic bosonic open string field theory. We use both the low-energy Yang-Mills description and the language of string field theory to explain the problem of tachyon condensation on unstable D-branes. We give a self-contained introduction to open string field theory using both conformal field theory and overlap integrals. Our main subjects are the Sen conjectures on tachyon condensation in open string field theory and the evidence that supports these conjectures. We conclude with a discussion of vacuum string field theory and projectors of the star-algebra of open string fields. We comment on the possible role of string field theory in the construction of a nonperturbative formulation of string theory that captures all possible string backgrounds.Comment: 103 pages, 11 figures. Lectures presented at TASI 2001. v2: references added. v3: minor errors corrected; reference, discussion added regarding other results on open string spectrum in stable vacuu