RECORD
Instanton Calculus, Topological Field Theories and N=2 Super Yang-Mills Theories
High Energy Physics - Theory · Submitted 29 Mar 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim As a consequence, instanton-dominated Green's functions in N=2 Super Yang-Mills can be equivalently computed either using the constrained instanton method or making reference to the topological twisted version of the theory.
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
The results obtained by Seiberg and Witten for the low-energy Wilsonian effective actions of N=2 supersymmetric theories with gauge group SU(2) are in agreement with instanton computations carried out for winding numbers one and two. This suggests that the instanton saddle point saturates the non-perturbative contribution to the functional integral. A natural framework in which corrections to this approximation are absent is given by the topological field theory built out of the N=2 Super Yang-Mills theory. After extending the standard construction of the Topological Yang-Mills theory to encompass the case of a non-vanishing vacuum expectation value for the scalar field, a BRST transformation is defined (as a supersymmetry plus a gauge variation), which on the instanton moduli space is the exterior derivative. The topological field theory approach makes the so-called "constrained instanton" configurations and the instanton measure arise in a natural way. As a consequence, instanton-dominated Green's functions in N=2 Super Yang-Mills can be equivalently computed either using the constrained instanton method or making reference to the topological twisted version of the theory. We explicitly compute the instanton measure and the contribution to $u=<\Tr \phi^2>$ for winding numbers one and two. We then show that each non-perturbative contribution to the N=2 low-energy effective action can be written as the integral of a total derivative of a function of the instanton moduli. Only instanton configurations of zero conformal size contribute to this result. Finally, the 8k-dimensional instanton moduli space is built using the hyperkahler quotient procedure, which clarifies the geometrical meaning of our approach.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The results obtained by Seiberg and Witten for the low-energy Wilsonian effective actions of N=2 supersymmetric theories with gauge group SU(2) are in agreement with instanton computations carried out for winding numbers one and two. | background 0.73 | 0.13 | 0.19 | asserted 0.98 |
| s1 | This suggests that the instanton saddle point saturates the non-perturbative contribution to the functional integral. | interpretation 1.00 | 0.15 | 0.15 | hedged possibility 1.00 |
| s2 | A natural framework in which corrections to this approximation are absent is given by the topological field theory built out of the N=2 Super Yang-Mills theory. | method 0.46 | 0.19 | 0.13 | asserted 0.98 |
| s3 | After extending the standard construction of the Topological Yang-Mills theory to encompass the case of a non-vanishing vacuum expectation value for the scalar field, a BRST transformation is defined (as a supersymmetry plus a gauge variation), which on the instanton moduli space is the exterior derivative. | method 0.88 | 0.83 | 0.08 | asserted 1.00 |
| s4 | The topological field theory approach makes the so-called "constrained instanton" configurations and the instanton measure arise in a natural way. | result 0.51 | 0.67 | 0.11 | asserted 1.00 |
| s5 | As a consequence, instanton-dominated Green's functions in N=2 Super Yang-Mills can be equivalently computed either using the constrained instanton method or making reference to the topological twisted version of the theory. | result 0.47 | 0.46 | 0.35 | asserted 0.97 |
| s6 | We explicitly compute the instanton measure and the contribution to $u=<\Tr \phi^2>$ for winding numbers one and two. | contribution 0.88 | 0.96 | 0.11 | asserted 1.00 |
| s7 | We then show that each non-perturbative contribution to the N=2 low-energy effective action can be written as the integral of a total derivative of a function of the instanton moduli. | result 0.89 | 0.90 | 0.35 | asserted 1.00 |
| s8 | Only instanton configurations of zero conformal size contribute to this result. | result 0.99 | 0.80 | 0.13 | asserted 1.00 |
| s9 | Finally, the 8k-dimensional instanton moduli space is built using the hyperkahler quotient procedure, which clarifies the geometrical meaning of our approach. | method 0.63 | 0.84 | 0.08 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- 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
The results obtained by Seiberg and Witten for the low-energy Wilsonian effective actions of N=2 supersymmetric theories with gauge group SU(2) are in agreement with instanton computations carried out for winding numbers one and two. This suggests that the instanton saddle point saturates the non-perturbative contribution to the functional integral. A natural framework in which corrections to this approximation are absent is given by the topological field theory built out of the N=2 Super Yang-Mills theory. After extending the standard construction of the Topological Yang-Mills theory to encompass the case of a non-vanishing vacuum expectation value for the scalar field, a BRST transformation is defined (as a supersymmetry plus a gauge variation), which on the instanton moduli space is the exterior derivative. The topological field theory approach makes the so-called "constrained instanton" configurations and the instanton measure arise in a natural way. As a consequence, instanton-dominated Green's functions in N=2 Super Yang-Mills can be equivalently computed either using the constrained instanton method or making reference to the topological twisted version of the theory. We explicitly compute the instanton measure and the contribution to $u=<\Tr \phi^2>$ for winding numbers one and two. We then show that each non-perturbative contribution to the N=2 low-energy effective action can be written as the integral of a total derivative of a function of the instanton moduli. Only instanton configurations of zero conformal size contribute to this result. Finally, the 8k-dimensional instanton moduli space is built using the hyperkahler quotient procedure, which clarifies the geometrical meaning of our approach.
Human review
References
How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers whose main result relates to this one's
States the same result 1 paper
-
In this letter we argue that instanton-dominated Green's functions in N=2 Super Yang-Mills theories can be equivalently computed either using the so-called constrained instanton method or making reference to the topological twisted version of the theory.
Multi-Instantons, Supersymmetry and Topological Field Theories · 0.99
Papers citing it · 1 sentence without a confident label
Cites it as background 1 paper
-
In particular its application to Seiberg-Witten (SW) theory [ref] allows one to reduce seemingly intractable instanton moduli integrals to essentially smaller submanifold of instantons invariant with respect to an Abelian subgroup of global gauge singled out by the adjoint scalar VEV [ref] .
A note on rank $\frac{3}{2}$ Liouville irregular block · Introduction · 0.84
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.