arXiv subjects
Publications and source records attributed to B. Pioline.
We review in detail the recently discovered phenomenon of partial spontaneous breaking of supersymmetry in the case of a N=2 pure gauge U(1) theory, and recall how the standard lore no-go theorem is evaded. We discuss the extension of this mechanism to theories with charged matter, and surprisingly find that the gauging forbids the existence of a magnetic Fayet-Iliopoulos term.
Low--energy limits of N=2 supersymmetric field theories in the Higgs branch are described in terms of a non--linear 4--dimensional sigma--model on a \hk target space, classically obtained as a \hk quotient of the original flat hypermultiplet space by the gauge group. We review in a pedagogical way this construction, and illustrate it in various examples, with special attention given to the singularities emerging in the low--energy theory. In particular, we thoroughly study the Higgs branch singularity of Seiberg--Witten $SU(2)$ theory with $N_f$ flavors, interpreted by Witten as a small instanton singularity in the moduli space of one instanton on $\RR^4$. By explicitly evaluating the metric, we show that this Higgs branch coincides with the Higgs branch of a $U(1)$ N=2 SUSY theory with the number of flavors predicted by the singularity structure of Seiberg--Witten's theory in the Coulomb phase. We find another example of Higgs phase duality, namely between the Higgs phases of $U(N_c)\; N_f$ flavors and $U(N_f-N_c)\; N_f$ flavors theories, by using a geometric interpretation due to Biquard et al. This duality may be relevant for understanding Seiberg's conjectured duality $N_c \leftrightarrow N_f-N_c$ in N=1 SUSY $SU(N_c)$ gauge theories.