Pith. Sign in

RECORD

A New Construction of Einstein-Sasaki Metrics in D >= 7

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
H. Lu, C.N. Pope, J.F. Vazquez-Poritz

High Energy Physics - Theory · Submitted 23 Dec 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using a canonical construction, these metrics all yield Einstein-Sasaki metrics in dimensions D=2n+5 \ge 7.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDhep-th/0512306 (version 2)
Pith IDBPBQLMZQ, Pith's permanent record of this paper and its review
CitationC.N. Pope, H. Lu, J.F. Vazquez-Poritz. "A New Construction of Einstein-Sasaki Metrics in D >= 7." arXiv:hep-th/0512306 (2005). https://pith.science/paper/BPBQLMZQ
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,979 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.62 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.24 · compares with prior results 0.22 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We construct explicit Einstein-Kahler metrics in all even dimensions D=2n+4 \ge 6, in terms of a $2n$-dimensional Einstein-Kahler base metric. These are cohomogeneity 2 metrics which have the new feature of including a NUT-type parameter, in addition to mass and rotation parameters. Using a canonical construction, these metrics all yield Einstein-Sasaki metrics in dimensions D=2n+5 \ge 7. As is commonly the case in this type of construction, for suitable choices of the free parameters the Einstein-Sasaki metrics can extend smoothly onto complete and non-singular manifolds, even though the underlying Einstein-Kahler metric has conical singularities. We discuss some explicit examples in the case of seven-dimensional Einstein-Sasaki spaces. These new spaces can provide supersymmetric backgrounds in M-theory, which play a role in the AdS_4/CFT_3 correspondence.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We construct explicit Einstein-Kahler metrics in all even dimensions D=2n+4 \ge 6, in terms of a $2n$-dimensional Einstein-Kahler base metric. contribution 0.95 0.95 0.29 asserted 1.00
s1 These are cohomogeneity 2 metrics which have the new feature of including a NUT-type parameter, in addition to mass and rotation parameters. contribution 0.57 0.88 0.12 asserted 1.00
s2 Using a canonical construction, these metrics all yield Einstein-Sasaki metrics in dimensions D=2n+5 \ge 7. result 0.46 0.84 0.47 asserted 1.00
s3 As is commonly the case in this type of construction, for suitable choices of the free parameters the Einstein-Sasaki metrics can extend smoothly onto complete and non-singular manifolds, even though the underlying Einstein-Kahler metric has conical singularities. result 0.90 0.46 0.11 asserted 0.56
s4 We discuss some explicit examples in the case of seven-dimensional Einstein-Sasaki spaces. contribution 0.93 0.91 0.06 asserted 0.98
s5 These new spaces can provide supersymmetric backgrounds in M-theory, which play a role in the AdS_4/CFT_3 correspondence. interpretation 1.00 0.30 0.15 hedged possibility 0.84

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We construct explicit Einstein-Kahler metrics in all even dimensions D=2n+4 \ge 6, in terms of a $2n$-dimensional Einstein-Kahler base metric. These are cohomogeneity 2 metrics which have the new feature of including a NUT-type parameter, in addition to mass and rotation parameters. Using a canonical construction, these metrics all yield Einstein-Sasaki metrics in dimensions D=2n+5 \ge 7. As is commonly the case in this type of construction, for suitable choices of the free parameters the Einstein-Sasaki metrics can extend smoothly onto complete and non-singular manifolds, even though the underlying Einstein-Kahler metric has conical singularities. We discuss some explicit examples in the case of seven-dimensional Einstein-Sasaki spaces. These new spaces can provide supersymmetric backgrounds in M-theory, which play a role in the AdS_4/CFT_3 correspondence.

Human review

How Pith checks papers → · Full audit of this paper →

References
How the literature uses it

3 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Compares with it 1 paper
  • One can check from the form of the toric diagram that the $A^p,q,r$ are a subset of a more general family of Sasaki–Einstein manifolds with cohomogeneity two and $U(1)^4$ symmetry discussed in [ref] in different coordinates; the family depends on six integers and has a toric diagram with six external points.

    Parameter spaces of massive IIA solutions · The toric diagram · 0.91

Cites it as background 1 paper
  • Recently, the study of Sasaki-Einstein manifolds [ref] has led to infinitely many explicit metrics on (non-compact) Calabi-Yau cones.

    Instantons on Calabi-Yau cones · Introduction · 0.82

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.