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/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The present Lecture Notes have been prepared to back up a series of a fewseminars given by the author at the Albert Einstein Institute in Potsdam. TheseNotes aim at reviewing a research project conducted over the last six yearsabout a quite interesting and challenging topic, namely the use of thegeneralized Kronheimer construction and the generalized McKay correspondencefor the crepant resolution $Y^\Gamma_{[3]} \to \frac{\mathbb{C}^3}{\Gamma}$ oforbifold singularities, $\Gamma$ being s finite subgroup of $\mathrm{SU(3)}$,as a strategic tool to construct holographic dual pairs of $\mathcal{N}=1$gauge theories in $D=4$ and D3-brane solutions of type IIB supergravity. Theproject, developed by Ugo Bruzzo with the present author, in variousco-authorships with Massimo Bianchi, Anna Fino, Pietro Antonio Grassi, DimitryMarkushevich, Dario Martelli, Mario Trigiante and Umar Shahzad, is still goingon and there are a lot of interesting unanswered questions that are illustratedthroughout these Lecture Notes and particularly emphasized in its last chapter.The mathematical roots of this project are very robust and ramified indifferential geometry, group theory and algebraic geometry. A particularlychallenging issue is that of constructing Ricci flat metrics on the total spaceof line-bundles over compact K\"ahler manifolds of real dimension four. In thatdirection the symplectic action/angle formalism turns out to be a winningweapon. The ultimate goal is that of deducing all the aspects of holographicduality from finite group theory or, to be more precise, SU(3) finite subgroups

Lectures on resolutions \`a la Kronheimer of orbifold singularities,  McKay quivers for Gauge Theories on D3 branes, and the issue of Ricci flat  metrics on the resolved three-folds