As a continuation of a general program started in two previous publications, in thepresent paper we study the Kähler quotient resolution of the orbifoldC3/Z4, comparingwith the results of a toric description of the same. In this way we determine thealgebraic structure of the exceptional divisor, whose compact component is the secondHirzebruch surfaceF2. We determine the explicit Kähler geometry of the smoothresolved manifoldY, which is the total space of the canonical bundle ofF2. We study indetailthechamberstructureofthespaceofstabilityparameters(correspondingingaugetheory to the Fayet–Iliopoulos parameters) that are involved in the construction of thedesingularizations either by generalized Kronheimer quotient, or as algebro-geometricquotients. The walls of the chambers correspond to two degenerations; one is a partialdesingularization of the quotient, which is the total space of the canonical bundle of theweighted projective spaceP[1,1,2], while the other is the product of the ALE spaceA1by a line, and is related to the full resolution in a subtler way. These geometrical resultswill be used to look for exact supergravity brane solutions and dual superconformalgauge theories.
Crepant resolutions of ℂ3∕Z4 and the generalized Kronheimer construction (in view of the gauge/gravity correspondence)
Fino A.;Fre P.;Grassi P.;
2019-01-01
Abstract
As a continuation of a general program started in two previous publications, in thepresent paper we study the Kähler quotient resolution of the orbifoldC3/Z4, comparingwith the results of a toric description of the same. In this way we determine thealgebraic structure of the exceptional divisor, whose compact component is the secondHirzebruch surfaceF2. We determine the explicit Kähler geometry of the smoothresolved manifoldY, which is the total space of the canonical bundle ofF2. We study indetailthechamberstructureofthespaceofstabilityparameters(correspondingingaugetheory to the Fayet–Iliopoulos parameters) that are involved in the construction of thedesingularizations either by generalized Kronheimer quotient, or as algebro-geometricquotients. The walls of the chambers correspond to two degenerations; one is a partialdesingularization of the quotient, which is the total space of the canonical bundle of theweighted projective spaceP[1,1,2], while the other is the product of the ALE spaceA1by a line, and is related to the full resolution in a subtler way. These geometrical resultswill be used to look for exact supergravity brane solutions and dual superconformalgauge theories.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
