Thomas Quella, (Amsterdam U.)
Conformally invariant sigma-models on superspaces are two-dimensional supersymmetric quantum field theories which play a prominent role in a number of recent developments in mathematical physics. Apart from their applications in string theory and condensed matter physics (especially disordered systems) they also provide a geometric road towards logarithmic conformal field theories. Last but not least, they arise as critical continuum limits of certain super spin chains.
In my talk I will review recent progress on this subject, with special emphasis on supergroups and supercosets as superspaces. It will first be sketched how superspace sigma models arise in string theory in the context of the AdS/CFT correspondence and the quantization of strings on flux backgrounds. Employing the examples of superspheres and projective superspaces (the supertwistor space employed by Witten being a special case) it will then be indicated how exact spectra of anomalous critical dimensions can be calculated as a function of some geometric modulus. These results are then used to argue for new and highly non-trivial dualities between geometric and non-geometric supersymmetric conformal field theories such as supersphere sigma-models and OSP Gross-Neveu models.
Arnold Sommerfeld Center