Friday, November 05, 2004

Albion and Bernard: talks

Yesterday, Albion Lawrence gave a pretty interesting and very well-prepared Duality Seminar on his work with John McGreevy (who is visiting us, too) about soft SUSY breaking terms from FI D-terms in type II string theory.
  • He explained the basic stuff how you construct N=1 vacua from type II strings on Calabi-Yau. Type II strings on Calabi-Yau have N=2 SUSY to start with, with hypermultiplets and vector multiplets whose number is given by the Hodge numbers, and you can add D-branes (D6-branes in type IIA or D(2k-1)-branes in type IIB), which breaks N=2 to N=1, and adds some adjoint or bifundamental chiral multiplets

  • They were always considering "modular" vacua in which different pieces of the Calabi-Yau are responsible for different things. The local physics near the locus of the Standard Model on the Calabi-Yau may be viewed as a non-compact Calabi-Yau - one that is eventually connected to the other modules...
  • Supersymmetry can be broken explicitly by some D-terms - well, the breaking seems explicit because its parameters are effectively non-dynamical, from the Standard Model viewpoint. It is being communicated from some hidden sector that actually breaks the SUSY...
  • The SUSY breaking terms have classical contributions, but they showed that the one-loop contributions cancel, and there were many other detailed insights about the story...


Ten minutes ago Bernard Julia finished a talk about the exciting topic of the mysterious duality, and the Borcherds and Borel algebras associated with del Pezzo surfaces and various supergravity theories. It was interesting to see a slightly different viewpoint on the mysterious duality which was re-discovered and extended by Iqbal, Neitzke, Vafa in

but whose basic point - the map between del Pezzo surfaces and the compactifications of M-theory - are already included in Manin's book, as Julia mentioned. Bernard showed us the magic triangle - the N=N supergravities (counted according to four-dimensional supersymmetries) in d=d dimensions have the same complexified noncompact U-duality group like N'=7-N theories in d'=9-d dimensions, or something roughly of this form. The exceptional groups appear at many places.

Julia's new structure added to the mysterious duality are the Borcherds algebras. Take the second cohomology of the del Pezzo, and treat it is a Cartan subalgebra of a superalgebra. Then you can define some graded algebra, generalizing the exceptional algebra E_k, and truncate it at some degree (which is always consistent because only non-negative degree generators exist). This satisfies Jacobi's identity, and it "knows" about the equations of motion for the p-forms in supergravity. This algebra (that was labeled by the term "p-gerbes") is non-Abelian, mixes various forms, and "knows" about the Chern-Simons terms as well, it seems.

Moreover, Julia has a proposal how to define a singular replacement of the del Pezzo (or an orbifold) with an associated Borcherds algebra that describes supergravities with less supersymmetry.

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