Check of AGT Relation for Conformal Blocks on Sphere

And.Morozov; V.Alba

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Check of AGT Relation for Conformal Blocks on Sphere

V.Alba, And.Morozov

High Energy Physics - Theory · Submitted 14 Dec 2009

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

The authors' main claim We studied the n-point case, and found out that our results confirm the AGT conjecture up to the third order expansions.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.63 · compares with prior results 0.81 · mentions code or data availability 0.02.

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The AGT conjecture identifying conformal blocks with the Nekrasov functions is investigated for the spherical conformal blocks with more than 4 external legs. The diagram technique which arises in conformal block calculation involves propagators and vertices. We evaluated vertices with two Virasoro algebra descendants and explicitly checked the AGT relation up to the third order of the expansion for the 5-point and 6-point conformal blocks on sphere confirming all the predictions of arXiv:0906.3219 relevant in this situation. We propose that U(1)-factor can be extracted from the matrix elements of the free field Vertex operators. We studied the n-point case, and found out that our results confirm the AGT conjecture up to the third order expansions.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The AGT conjecture identifying conformal blocks with the Nekrasov functions is investigated for the spherical conformal blocks with more than 4 external legs.	background 0.60	0.43	0.08	asserted 0.41
s1	The diagram technique which arises in conformal block calculation involves propagators and vertices.	background 0.76	0.08	0.02	asserted 1.00
s2	We evaluated vertices with two Virasoro algebra descendants and explicitly checked the AGT relation up to the third order of the expansion for the 5-point and 6-point conformal blocks on sphere confirming all the predictions of arXiv:0906.3219 relevant in this situation.	result 0.92	0.96	0.65	asserted 1.00
s3	We propose that U(1)-factor can be extracted from the matrix elements of the free field Vertex operators.	contribution 0.50	0.61	0.08	speculative 0.61
s4	We studied the n-point case, and found out that our results confirm the AGT conjecture up to the third order expansions.	result 0.99	0.96	0.67	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.81.

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The paper

Original abstract

The AGT conjecture identifying conformal blocks with the Nekrasov functions is investigated for the spherical conformal blocks with more than 4 external legs. The diagram technique which arises in conformal block calculation involves propagators and vertices. We evaluated vertices with two Virasoro algebra descendants and explicitly checked the AGT relation up to the third order of the expansion for the 5-point and 6-point conformal blocks on sphere confirming all the predictions of arXiv:0906.3219 relevant in this situation. We propose that U(1)-factor can be extracted from the matrix elements of the free field Vertex operators. We studied the n-point case, and found out that our results confirm the AGT conjecture up to the third order expansions.

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References

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

On combinatorial expansion of the conformal blocks arising from AGT conjecture
hep-th 2010-12 conditional novelty 7.0 of 10

An orthogonal basis in Vir ⊗ Heisenberg is constructed whose primary-field matrix elements equal the instanton-counting function Z_bif, yielding a CFT derivation of the AGT expansion of conformal blocks.
Entanglement Entropy at Large Central Charge
hep-th 2013-03 conditional novelty 6.0 of 10

At large central charge, the entanglement entropy of N disjoint intervals in a 2d CFT equals a sum of single-interval entropies selected by the dominant OPE channel, reproducing the Ryu-Takayanagi minimal-surface formula.
Integrable structure, W-symmetry and AGT relation
hep-th 2011-09 conditional novelty 6.0 of 10

A new basis of states for W_n conformal field theory makes the AGT correspondence between 2d conformal blocks and 4d U(n) Nekrasov partition functions manifest, term by term.
A & B model approaches to surface operators and Toda theories
hep-th 2010-04 conditional novelty 6.0 of 10

Multiple surface operator insertions in 4d N=2 quiver gauge theories are matched, order by order, to open topological string amplitudes with multiple toric branes and to degenerate-operator insertions in Toda conforma...
M5-branes, toric diagrams and gauge theory duality
hep-th 2011-12 accept novelty 5.0 of 10

The paper derives an explicit map between the parameters of 5D N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge theories, showing they describe the same low-energy physics.

Show 1 more citing papers

Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
hep-th 2011-03 conditional novelty 5.0 of 10

The prepotential and chiral correlators of N=2 SU(N) gauge theories in the Omega background follow from a difference equation that acts as a non-commutative Seiberg-Witten curve.

How the literature uses it

25 arXiv papers cite this in 35 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 · 26 sentences without a confident label

Compares with it 1 paper

As compared to [ref] , ([ref]) involves direct computation of the descendants three point functions.

Irregular conformal blocks, Painlev\'e III and the blow-up equations · Irregular conformal blocks and Barnes $G$-functions · 1.00

Cites it as background 8 papers

This procedure is extensively reviewed in the literature [ref] , and, in the 4-point case shown in Fig.[ref], it gives the following series expansion in powers of $q$ B( Δ_1, Δ_2, Δ_3, Δ_4, Δ, c | q ) = ∑_|Y| = |Y^'| q^|Y| γ_Δ_1 Δ_2 Δ(Y) Q_Δ^-1(Y,Y^') γ_ΔΔ_3 Δ_4(Y^')

Conformal blocks as Dotsenko-Fateev Integral Discriminants · Conformal block as Dotsenko-Fateev integral CITEMARK23Z · 0.98
Let us give some details [For a more extended and technical discussion see for example [ref] or the recent review [ref] .].

Non-perturbative studies of N=2 conformal quiver gauge theories · The 2d/4d correspondence · 0.95
In the light of the AGT conjecture, the extensive studies on $q$-expansion of the conformal blocks have been carried out in [ref] .

Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model · Matrix Model vs Conformal Block · 0.98

What it cites · 16 sentences without a confident label

Uses the method or tool of 1 paper

There is a useful diagram technique [ref] to calculate the conformal blocks.

CFT exercises for the needs of AGT · Introduction · 0.99

Compares with 1 paper

These formulae coincide with predictions of [ref] .

Liouville Correlation Functions from Four-dimensional Gauge Theories · Introduction · 0.97

Cites as background 14 papers

Recently Alday, Gaiotto and Tachikawa (AGT) proposed a conjecture [ref] which implies that some Liouville correlation functions are equal to an integral of the squared absolute value of the Nekrasov full partition functions.

Liouville Correlation Functions from Four-dimensional Gauge Theories · Introduction · 0.96
In particular, this conjecture implies that conformal blocks [ref] are equal to the instanton Nekrasov partition functions [ref] .

An Algorithm for the Microscopic Evaluation of the Coefficients of the Seiberg-Witten Prepotential · Introduction · 0.90
In particular, this conjecture implies that conformal blocks [ref] are equal to the instanton Nekrasov partition functions [ref] .

Status Report on the Instanton Counting · Introduction · 0.90

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