Singularity, Sasaki-Einstein manifold, Log del Pezzo surface and $\mathcal{N}=1$ AdS/CFT correspondence: Part I

Xie, Dan; Yau, Shing–Tung

doi:10.48550/arxiv.1903.00150

Cited by 5 publications

(7 citation statements)

References 66 publications

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“…a SE metric on its base. 11 (The role of K-stability in the holographic context has recently been stressed in [55][56][57], and in the field theory context in [58,59]. )…”

Section: Four-dimensional Models and Ads/cftmentioning

confidence: 99%

New 3d $$ \mathcal{N} $$ = 2 SCFT’s with N3/2 scaling

Amariti

Fazzi

Mekareeya

et al. 2019

J. High Energ. Phys.

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We construct several novel examples of 3d N = 2 models whose free energy scales as N 3/2 at large N . This is the first step towards the identification of field theories with an M-theory dual. Furthermore, we match the volumes extracted from the free energy with the ones computed from the Hilbert series. We perform a similar analysis for the 4d N = 1 parents of the 3d models, matching the volume extracted from the a central charge to that obtained from the Hilbert series. For some of the 4d models, we show the existence of a Sasaki-Einstein metric on the internal space of the candidate type IIB gravity dual.

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“…a SE metric on its base. 11 (The role of K-stability in the holographic context has recently been stressed in [55][56][57], and in the field theory context in [58,59]. )…”

Section: Four-dimensional Models and Ads/cftmentioning

confidence: 99%

New 3d $$ \mathcal{N} $$ = 2 SCFT’s with N3/2 scaling

Amariti

Fazzi

Mekareeya

et al. 2019

J. High Energ. Phys.

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“…These results are related to the idea of "stability". For reference, recent work on this subject include [49,50].…”

Section: Reduction To the Exceptional Divisormentioning

confidence: 99%

Resolution a la Kronheimer of $\mathbb{C}^3/Γ$ singularities and the Monge-Ampere equation for Ricci-flat Kaehler metrics in view of D3-brane solutions of supergravity

Bianchi,

Bruzzo,

Fré

et al. 2021

Preprint

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In this paper we analyze the relevance of the generalized Kronheimer construction for the gauge-gravity correspondence. We begin with the general structure of D3-brane solutions of type IIB supergravity on smooth manifolds Y Γ that are supposed to be the crepant resolution of quotient singularities C 3 /Γ with Γ a finite subgroup of SU (3). We emphasize that non trivial 3-form fluxes require the existence of imaginary self-dual harmonic forms ω 2,1 . Although excluded in the classical Kronheimer construction they may be reintroduced by means of mass deformations. Next we concentrate on the other essential item for the D3-brane construction, namely, the existence of a Ricci-flat metric on Y Γ . We study the issue of Ricci-flat Kähler metrics on such resolutions Y Γ , with particular attention to the case Γ = Z4. We advance the conjecture that on the exceptional divisor of Y Γ the Kronheimer Kähler metric and the Ricci-flat one, that is locally flat at infinity, coincide. The conjecture is shown to be true in the case of the Ricci-flat metric on totK WP [112] that we construct, i.e. the total space of the canonical bundle of the weighted projective space WP [112], which is a partial resolution of C 3 /Z4. For the full resolution we have Y Z 4 = tot K F 2 , where F2 is the second Hizebruch surface. We try to extend the proof of the conjecture to this case using the one-parameter Kähler metric on F2 produced by the Kronheimer construction as initial datum in a Monge-Ampère (MA) equation. We exhibit three formulations of this MA equation, one in terms of the Kähler potential, the other two in terms of the symplectic potential but with two different choices of the variables. In both cases one can establish a series solution in powers of the variable along the fibers of the canonical bundle. The main property of the MA equation is that it does not impose any condition on the initial geometry of the exceptional divisor, rather it uniquely determines all the subsequent terms as local functionals of this initial datum. Although a formal proof is still missing, numerical and analytical results support the conjecture. As a by-product of our investigation we have identified some new properties of this type of MA equations that we believe to be so far unknown.U.B.'s research is partly supported by PRIN "Geometry of Algebraic Varieties" and INdAM-GNSAGA. He is a member of the VBAC group.

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“…There exists alternative geometric construction for a large class of 4d SCFTs from Calabi-Yau 3-fold singularities [101,102], some of which includes a subset of Γ(G) theories [34]. In this way, the construction of N = 1 SCFTs either directly from F-theory on Calabi-Yau fourfolds, or indirectly from compactifications of the 6d (1, 0) SCFTs, provides a promising avenue for a top-down realization of the a = c theories studied in this paper.…”

Section: Towards a Geometric Constructionmentioning

confidence: 99%

Infinitely many 4d N=1 SCFTs with a=c

Kang,

Lawrie,

Lee

et al. 2021

Preprint

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We study a rich set of four-dimensional N = 1 superconformal field theories (SCFTs) with both central charges identical: a = c. We construct them via the diagonal N = 1 gauging of the flavor symmetry G of a collection of N = 2 Argyres-Douglas theories of type D p (G), with or without additional adjoint chiral multiplets. In this way, we construct infinitely-many theories that flow to interacting SCFTs with a = c in the infrared. Finally, we briefly highlight the features of the SCFTs without a = c that arise from generalizing this construction.

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Singularity, Sasaki-Einstein manifold, Log del Pezzo surface and $\mathcal{N}=1$ AdS/CFT correspondence: Part I

Cited by 5 publications

References 66 publications

New 3d $$ \mathcal{N} $$ = 2 SCFT’s with N3/2 scaling

New 3d $$ \mathcal{N} $$ = 2 SCFT’s with N3/2 scaling

Resolution a la Kronheimer of $\mathbb{C}^3/Γ$ singularities and the Monge-Ampere equation for Ricci-flat Kaehler metrics in view of D3-brane solutions of supergravity

Infinitely many 4d N=1 SCFTs with a=c

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