High Energy Physics - Theory · arXiv:hep-th/0512124 v3 · submitted 12 Dec 2005
Toric Sasaki-Einstein manifolds and Heun equations
The paper says
“By combining knowledge of the explicit symplectic potential and the exponents, we show that the ground states, or equivalently holomorphic functions, have one-to-one correspondence with integral lattice points in the convex polyhedral cone.”
from the abstract · picked out as the main claim by a classifier
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The paper
Abstract
Symplectic potentials are presented for a wide class of five dimensional toric Sasaki-Einstein manifolds, including L^a,b,c which was recently constructed by Cvetic et al. The spectrum of the scalar Laplacian on L^a,b,c is also studied. The eigenvalue problem leads to two Heun's differential equations and the exponents at regular singularities are directly related to toric data. By combining knowledge of the explicit symplectic potential and the exponents, we show that the ground states, or equivalently holomorphic functions, have one-to-one correspondence with integral lattice points in the convex polyhedral cone. The scaling dimensions of the holomorphic functions are simply given by scalar products of the Reeb vector and the integral vectors, which are consistent with R-charges of BPS states in the dual quiver gauge theories.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.38 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v3). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| Symplectic potentials are presented for a wide class of five dimensional toric Sasaki-Einstein manifolds, including L^{a,b,c} which was recently constructed by Cvetic et al. The spectrum of the scalar Laplacian on L^{a,b,c} is also studied. | contribution 0.99 | 0.85 | 0.09 | asserted 1.00 |
| The eigenvalue problem leads to two Heun's differential equations and the exponents at regular singularities are directly related to toric data. | result 0.81 | 0.85 | 0.10 | asserted 1.00 |
| By combining knowledge of the explicit symplectic potential and the exponents, we show that the ground states, or equivalently holomorphic functions, have one-to-one correspondence with integral lattice points in the convex polyhedral cone. | result 0.97 | 0.94 | 0.54 | asserted 1.00 |
| The scaling dimensions of the holomorphic functions are simply given by scalar products of the Reeb vector and the integral vectors, which are consistent with R-charges of BPS states in the dual quiver gauge theories. | result 0.56 | 0.85 | 0.30 | asserted 0.57 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00
What was examined, and what was not
Sources read
- arXiv listing abstract v3
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
How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,803 input tokens, $0.0002 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
Cited by 8 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Brane Tilings and Exceptional Collections hep-th · Feb 2006
- Superconformal Indices, Sasaki-Einstein Manifolds, and Cyclic Homologies hep-th · Jul 2012
- Spin-2 spectrum of defect theories hep-th · Mar 2011
- On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check hep-th · Nov 2010
- String Gyratons in Supergravity hep-th · Mar 2006
- Index for Supergravity on AdS_5 \times T^{1,1} and Conifold Gauge Theory hep-th · Feb 2006
- Triangle Anomalies from Einstein Manifolds hep-th · Jan 2006
- Brane Tilings and Their Applications hep-th · Mar 2008
How the literature uses it
10 arXiv papers cite this in 17 sentences
Papers citing it · 13 sentences without a confident label
Uses its method or tool 1 paper
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We apply a $SL(3;ℤ)$ transformation $T$ (see also [ref] ) [equation] to bring the vectors $v_i=Tv_i^'$ in the form [ref] [ref] [equation]
Toric data and Killing forms on homogeneous Sasaki-Einstein manifold $T^{1,1}$ · Symplectic and complex coordinates on conifold $C(T^1,1)$ · 0.85
Cites it as support 1 paper
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This correspondence motivates the interpretation of the $α_k(z_i)$ as the holographic wavefunctions of the operators $X_k$ associated with the corresponding flavor node [ref] .
N-ification of Forces: A Holographic Perspective on D-brane Model Building · Adding the flavor D7-branes · 0.97
Cites it as background 2 papers
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To our knowledge, the most general study of the spectrum of the scalar Laplacian has been done in [ref] .
Strings on conifolds from strong coupling dynamics: quantitative results · Coherent states and orthogonality · 0.87
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They arise in a variety of physical contexts, for instance as eigenvalue equations in the background of the Kerr-Newman-de Sitter black hole [ref] , of large AdS black holes in five dimensions [ref] , of the toric Sasaki-Einstein manifolds $L^a,b,c$ [ref] , or in the study of RG flows between 2D CFTs [ref] and of slowly-rotating homogeneous stars [ref] (for more physics applications see the references in [ref] ).
Spin-2 spectrum of defect theories · Heun's equation · 0.94
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