RECORD
Surface Operator, Bubbling Calabi-Yau and AGT Relation
High Energy Physics - Theory · Submitted 15 Jul 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that this aspect can be realized as the geometric transition in topological string theory, and the insertion of a surface operator leads to the bubbling of the toric Calabi-Yau geometry.
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
The abstract, sentence by sentence
Surface operators in N=2 four-dimensional gauge theories are interesting half-BPS objects. These operators inherit the connection of gauge theory with the Liouville conformal field theory, which was discovered by Alday, Gaiotto and Tachikawa. Moreover it has been proposed that toric branes in the A-model topological strings lead to surface operators via the geometric engineering. We analyze the surface operators by making good use of topological string theory. Starting from this point of view, we propose that the wave-function behavior of the topological open string amplitudes geometrically engineers the surface operator partition functions and the Gaiotto curves of corresponding gauge theories. We then study a peculiar feature that the surface operator corresponds to the insertion of the degenerate fields in the conformal field theory side. We show that this aspect can be realized as the geometric transition in topological string theory, and the insertion of a surface operator leads to the bubbling of the toric Calabi-Yau geometry.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Surface operators in N=2 four-dimensional gauge theories are interesting half-BPS objects. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | These operators inherit the connection of gauge theory with the Liouville conformal field theory, which was discovered by Alday, Gaiotto and Tachikawa. | background 1.00 | 0.03 | 0.03 | asserted 1.00 |
| s2 | Moreover it has been proposed that toric branes in the A-model topological strings lead to surface operators via the geometric engineering. | background 1.00 | 0.04 | 0.03 | hedged possibility 0.72 |
| s3 | We analyze the surface operators by making good use of topological string theory. | method 0.67 | 0.81 | 0.04 | asserted 0.88 |
| s4 | Starting from this point of view, we propose that the wave-function behavior of the topological open string amplitudes geometrically engineers the surface operator partition functions and the Gaiotto curves of corresponding gauge theories. | contribution 0.92 | 0.81 | 0.50 | speculative 0.46 |
| s5 | We then study a peculiar feature that the surface operator corresponds to the insertion of the degenerate fields in the conformal field theory side. | contribution 0.63 | 0.54 | 0.11 | asserted 0.87 |
| s6 | We show that this aspect can be realized as the geometric transition in topological string theory, and the insertion of a surface operator leads to the bubbling of the toric Calabi-Yau geometry. | result 0.92 | 0.91 | 0.50 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Surface operators in N=2 four-dimensional gauge theories are interesting half-BPS objects. These operators inherit the connection of gauge theory with the Liouville conformal field theory, which was discovered by Alday, Gaiotto and Tachikawa. Moreover it has been proposed that toric branes in the A-model topological strings lead to surface operators via the geometric engineering. We analyze the surface operators by making good use of topological string theory. Starting from this point of view, we propose that the wave-function behavior of the topological open string amplitudes geometrically engineers the surface operator partition functions and the Gaiotto curves of corresponding gauge theories. We then study a peculiar feature that the surface operator corresponds to the insertion of the degenerate fields in the conformal field theory side. We show that this aspect can be realized as the geometric transition in topological string theory, and the insertion of a surface operator leads to the bubbling of the toric Calabi-Yau geometry.
References
How the literature uses it
49 arXiv papers cite this in 85 sentences
Papers citing it · 51 sentences without a confident label
Builds on it 2 papers
-
Our mapping of the intersecting defects in <ref> with the most general Toda degenerate field insertion, which is labeled by the pair of representations $(ℛ',ℛ)$, completes [ref] , where one of the representations was taken to be trivial (see also [ref] ).
Intersecting Surface Defects and Two-Dimensional CFT · Introduction · 0.99
-
Here as a consistency check, we consider the single stack of toric brane insertion with only $n_s ≠0$ for the Abelian factor $U(1)_s$, they are labeled by a Young diagram with $n_s$ columns, this should be regarded as a slight generalization of the refined geometric transition involving single toric brane considered in [ref] .
On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories · Single Stack of Surface Operators : $n⃗=(0,0, …n_s, …0, 0)$ · 1.00
Uses its method or tool 4 papers
-
Using the gluing rule [ref] , one can truncate the toric diagram into two separate ones denoted by $T_1$ and $T_2$(as showing in Fig. 6b).
Note on refined topological vertex, Jack polynomials and instanton counting · $U(2)×U(2)$ theory · 0.98
-
Now we shall derive the quantum operator $𝖧(𝗑,𝗒)$ from the partition function of the topological string with the single brane by the method in [ref] .
Quantum mirror curve of periodic chain geometry · Mirror curve of chain geometry · 1.00
-
Following the derivation outlined in [ref] one can also easily find the effective superpotential and the associated Gaiotto curve from the open string partition function.
On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories · Open string partition function · 0.95
Compares with it 4 papers
-
Firstly, our result for the new M-strings system must be mathematically equivalent to the 5d Nekrasov partition function derived in [ref] since physics does not depend on the selection of the preferred direction of the refined topological vertex.
Surface Operators from M-strings · Discussions · 0.84
-
This also means that in the NS limit we obtain the same Gaiotto curve of 4d supersymmetric gauge theory, with a shift in its parameters[ In the limit $ϵ_2 →0$ or superpotential becomes precisely that of (2.14) [ref] .].
On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories · Appendix B: Superpotenial from the open string partition function · 0.90
-
This reminds us of exactly the same shift of the spectral parameters in the Higgsed DIM network [ref] [ref] [ref] [ref] [Upon the completion of the present work, we noticed [ref] , which shows the universal $R$ matrix of DIM algebra plays a significant role in the Higgsed network calculus.
MacMahon KZ equation for Ding-Iohara-Miki algebra · Construction of the shift operator · 0.90
Cites it as background 14 papers
-
This phenomenon is known as the bubbling Calabi-Yau [ref] [ref] .
Geometric transition in Non-perturbative Topological string · Bubbling Calabi-Yau · 0.88
-
Such surface operators were first considered in [ref] and have been further studied in [ref] .
Affine sl(N) conformal blocks from N=2 SU(N) gauge theories · Introduction · 0.82
-
Recent papers on the extension of AGT relation with surface operator [ref] mainly considered the superconformal case.
Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String · Introduction · 0.93
What it cites · 73 sentences without a confident label
Builds on 3 papers
-
In this way the degeneration of parameters gives the five-dimensional Nekrasov partition for the $SU(2)$ gauge theory with four flavors in the presence of a surface operator: [equation] We can recast it into the Nekrasov partition function for the $N_f=4$ theory with an added insertion of the factor coming of the surface operator [equation] where we introduce the mass parameters [equation] This formula is the five-dimensional lift of the result of [ref] .
A & B model approaches to surface operators and Toda theories · Degenerate Käher moduli and bubbling · 0.91
-
This relation between ([ref]) and ([ref]) provides the extension of the asymptotically free AGT relation [ref] for surface operators.
Asymptotically free N=2 theories and irregular conformal blocks · Decoupling limit and pure $SU(2)$ Yang-Mills theory · 0.99
-
This relation between ([ref]) and ([ref]) provides the extension of the asymptotically free AGT relation [ref] for surface operators.
On non-conformal limit of the AGT relations · Decoupling limit and pure $SU(2)$ Yang-Mills theory · 0.99
Uses the method or tool of 10 papers
-
By using M2-brane construction of surface operators [ref] , we can obtain surface operators from toric A-branes of topological string theory via the Ooguri-Vafa duality [ref] .
Knot Invariants and Topological Strings · Introduction · 0.92
-
By using M2-brane construction of surface operators [ref] , we can obtain surface operators from toric A-branes of topological string theory via the Ooguri-Vafa duality [ref] .
Loop and surface operators in N=2 gauge theory and Liouville modular geometry · Introduction · 0.92
-
Then we apply the geometric transition [ref] which changes branes into the background geometry.
M-Theory and Topological Strings--I · Degenerate Käher moduli and bubbling · 0.97
Compares with 1 paper
-
This approach will be an alternative to the matrix model computation of the B-model in [ref] .
A & B model approaches to surface operators and Toda theories · Conclusion and Discussion · 0.93
Cites as background 21 papers
-
Last year, a mysterious relation which relates $𝒩=2$ gauge theories in four dimensions to conformal field theories in two dimension was discovered in [ref] .
Liouville Correlation Functions from Four-dimensional Gauge Theories · Introduction · 0.95
-
The refined topological vertex which was proposed by Iqbal, Kozcaz and Vafa in [ref] was based on the melting crystal dual picture of the A-model[An another refined vertex formalism had been proposed by Awata and Kanno [ref] .]
Instanton counting, Macdonald function and the moduli space of D-branes · Refined topological vertex · 0.89
-
The refined topological vertex which was proposed by Iqbal, Kozcaz and Vafa in [ref] was based on the melting crystal dual picture of the A-model[An another refined vertex formalism had been proposed by Awata and Kanno [ref] .]
The Refined Topological Vertex · Refined topological vertex · 0.89
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.