Extended supersymmetry of semichiral sigma model in 4D

Briefly: Using a novel $(1,1)$ superspace formulation of semichiral sigma models with $4D$ target space, we investigate if an extended supersymmetry in terms of semichirals is compatible with having a $4D$ target space with torsion. In more detail: Semichiral sigma models have $(2,2)$ supersymmetry and Generalized K\"ahler target space geometry by construction. They can also support $(4,4)$ supersymmetry and Generalized Hyperk\"ahler geometry, but when the target space is four dimensional indications are that the geometry is restricted to Hyperk\"ahler. To investigate this further, we reduce the model to $(1,1)$ superspace and construct the extra (on-shell) supersymmetries there. We then find the conditions for a lift to $(2,2)$ super space and semichiral fields to exist. Those conditions are shown to hold for Hyperk\"ahler geometries. The $SU(2)\otimes U(1)$ WZW model, which has $(4,4)$ supersymmetry and a semichiral description, is also investigated. The additional supersymmetries are found in $(1,1)$ superspace but shown {\em not} to be liftable to a $(2,2)$ semichiral formulation.Comment: 23 pages. Resubmitted after compilation problem

Complex Geometry and Supersymmetry

I stress how the form of sigma models with (2, 2) supersymmetry differs depending on the number of manifest supersymmetries. The differences correspond to different aspects/formulations of Generalized K\"ahler Geometry.Comment: 9 pages, Proceedings of the Corfu Summer Institute 2011 School and Workshops on Elementary Particle Physics and Gravity September 4-18, 2011 Corfu, Greec

Limits of the D-brane action

For background geometries whose metric contain a scale $\gamma$ we reformulate the Born-Infeld D-brane action in terms of $\epsilon \equiv \gamma /(2\pi \alpha ')$. This may be taken as a starting point for various perturbative treatments of the theory. We study two limits that arise at zeroth order of such perturbations. In the first limit, that corresponds to the $g_s\to\infty$ with $\epsilon$ fix, we find a "string parton" picture, also in the presense of some background RR-fields. In the second limit, $\epsilon\to 0$, we find a topological model.Comment: 13 pages, Latex. Minor errors are corrected. To appear in JHE

C-theorem for two dimensional chiral theories

We discuss an extension of the $C$-theorem to chiral theories. We show that two monotonically decreasing $C$-functions can be introduced. However, their difference is a constant of the renormalization group flow. This constant reproduces the 't Hooft anomaly matching conditions.Comment: 7 pages, uses harvmac.te