Triangle Seminars

Abstract:
I give an outline of the program of Shadrin and his collaborators, to give explicit formulas for correlators in topological gravity (with descendants), starting with a Batalin-Vilkovisky algebra. In particular, I will try to explain the relationship with Givental's work on Gromov-Witten invariants. No background is assumed.

Abstract:
This is the first of three lectures: see the Graduate Program webpage at http://www.strings.ph.qmw.ac.uk/ for more information.

Abstract:
Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS_5 x S 5 superstring world-sheet theory in terms of physical degrees of freedom we construct a Pohlmeyer-reduced version of the corresponding sigma model. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting gauge-fixed equations can be obtained from a Lagrangian of a non-abelian Toda type: a gauged WZW-model with an integrable potential coupled also to a set of 2d fermionic fields.
We show that in the special case of the AdS_2 x S2 superstring model the reduced theory is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.

Abstract:
Recently Romelsberger made some conjectures about an index for N=1 superconformal quantum field theories applied to certain Seiberg dual theories. Recent joint work by me and Hugh Osborn proves and extends these conjectures by employing certain q-series type identities. I will discuss the superconformal index, how it applies for more general N=1 dual theories and, briefly, the proof of these conjectures.