A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories

Yasuhiko Yamada

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A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories

Yasuhiko Yamada

High Energy Physics - Theory · Submitted 1 Nov 2010

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

The authors' main claim We give an explicit differential equation which is expected to determine the instanton partition function in the presence of the full surface operator in N=2 SU(N) gauge theory.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.31 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.18 · mentions code or data availability 0.02.

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We give an explicit differential equation which is expected to determine the instanton partition function in the presence of the full surface operator in N=2 SU(N) gauge theory. The differential equation arises as a quantization of a certain Hamiltonian system of isomonodromy type discovered by Fuji, Suzuki and Tsuda.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We give an explicit differential equation which is expected to determine the instanton partition function in the presence of the full surface operator in N=2 SU(N) gauge theory.	contribution 0.97	0.91	0.72	hedged possibility 0.71
s1	The differential equation arises as a quantization of a certain Hamiltonian system of isomonodromy type discovered by Fuji, Suzuki and Tsuda.	method 0.75	0.23	0.12	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.97.

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The paper

Original abstract

We give an explicit differential equation which is expected to determine the instanton partition function in the presence of the full surface operator in N=2 SU(N) gauge theory. The differential equation arises as a quantization of a certain Hamiltonian system of isomonodromy type discovered by Fuji, Suzuki and Tsuda.

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References

Forward citations

Cited by 4 Pith papers

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

Surface Defects and Resolvents
hep-th 2013-07 accept novelty 7.0 of 10

The effective twisted superpotential of a large class of BPS surface defects is obtained by replacing traces of the bulk scalar in the 2d one-loop result with the exact 4d resolvent, reproducing and extending brane-co...
Spectral Duality in Integrable Systems from AGT Conjecture
hep-th 2012-04 conditional novelty 6.0 of 10

The N-site Heisenberg XXX spin chain and a reduced gl(N) Gaudin model are shown to be spectrally dual, with matching spectral curves and Seiberg-Witten differentials, and with a claimed matching of their quantized Bax...
Quantum Hitchin Systems via beta-deformed Matrix Models
hep-th 2011-04 conditional novelty 6.0 of 10

In the Nekrasov-Shatashvili limit, the Schwinger-Dyson loop equations of the beta-deformed Dotsenko-Fateev matrix model yield the Schroedinger-type equations whose potentials are the quantum Hitchin Hamiltonians on th...
On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
hep-th 2010-11 conditional novelty 4.0 of 10

Inserting the simplest degenerate operator into a conformal block yields a Schrödinger-like equation whose Bohr-Sommerfeld periods generate the one-parameter deformed Seiberg-Witten prepotential.

How the literature uses it

11 arXiv papers cite this in 18 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 · 10 sentences without a confident label

Cites it as background 6 papers

The AGT conjecture [ref] establishes explicit relations between the basic formulas in several principal branches of modern theory and naturally attracts an increasing attention [ref] - [ref] .

On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles · Introduction · 0.99
In this paper we study the AGT correspondence [ref] at the level of integrable systems [ref] [See also [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] .].

Spectral Duality in Integrable Systems from AGT Conjecture · Introduction · 0.98
The AGT relation [ref] - [ref] is an explicit formulation of duality between the $2d$ and $4d$ descriptions of conformal $6d$ theory of self-dual 2-forms, compactified on a Riemann surface [ref] .

Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals · Introduction · 0.99

What it cites · 36 sentences without a confident label

Compares with 1 paper

For instance, the specialization of the primary fields $V_χ$, $χ=κΛ_1, κΛ_N-1$ in [ref] for the simple punctures agrees with the choice of the spectral type $(N-1,1)$.

Affine sl(N) conformal blocks from N=2 SU(N) gauge theories · Summary and discussions · 0.81

Cites as background 5 papers

In [ref] , Alday and Tachikawa formulated a combinatorial formula[We will recapitulate it in section 2, eq.([ref]).] for the instanton partition function $Z_inst$ in the presence of the full surface operator in $N=2$ $SU(N)$ gauge theory, based on a result [ref] about the affine Laumon space.

Yangians and cohomology rings of Laumon spaces · Introduction · 0.84
In [ref] , Alday and Tachikawa formulated a combinatorial formula[We will recapitulate it in section 2, eq.([ref]).] for the instanton partition function $Z_inst$ in the presence of the full surface operator in $N=2$ $SU(N)$ gauge theory, based on a result [ref] about the affine Laumon space.

Affine SL(2) conformal blocks from 4d gauge theories · Introduction · 0.84
For $SU(N)$ case, the relation to affine $SL(N)$ conformal blocks was studied in [ref] .

Affine sl(N) conformal blocks from N=2 SU(N) gauge theories · Introduction · 0.89

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