English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Pro

Presents the zaia usage as premium feature

ZAIA

Presents AI Discovery search usage as a premium feature

AI Discovery

Presents AI Discovery explain and summary usage as a premium feature

Content Analysis

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Presents the pdf analysis as premium feature

PDF Analysis

1500 Top-up

3000 Top-up

Zendy Basic

2500 Top-up

Zendy Unlimited

Presents the access of premium content as premium feature

Premium Content

Low--energy limits of N=2 supersymmetric field theories in the Higgs branchare described in terms of a non--linear 4--dimensional sigma--model on a \hktarget space, classically obtained as a \hk quotient of the original flathypermultiplet space by the gauge group. We review in a pedagogical way thisconstruction, and illustrate it in various examples, with special attentiongiven 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 instantonsingularity in the moduli space of one instanton on $\RR^4$. By explicitlyevaluating the metric, we show that this Higgs branch coincides with the Higgsbranch of a $U(1)$ N=2 SUSY theory with the number of flavors predicted by thesingularity structure of Seiberg--Witten's theory in the Coulomb phase. We findanother 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 ageometric interpretation due to Biquard et al. This duality may be relevant forunderstanding Seiberg's conjectured duality $N_c \leftrightarrow N_f-N_c$ inN=1 SUSY $SU(N_c)$ gauge theories.Comment: 32 pages, latex2e, no figures, uses amsfonts packag

Higgs Branch, Hyper-Kähler Quotient and Duality in SUSY N = 2 Yang–Mills Theories