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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 10th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexI gave _[[Seiberg-Witten theory]]_ an Idea-paragraph, added the orinal reference and cross-linked with _[[N=2 D=4 super Yang-Mills theory]]_ and with _[[electric-magnetic duality]]_.

   I gave Seiberg-Witten theory an Idea-paragraph, added the orinal reference and cross-linked with N=2 D=4 super Yang-Mills theory and with electric-magnetic duality.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeJan 10th 2013
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI added a link to the well-known Matilde Marcolli's (quite old) lectures on the subject.

   I added a link to the well-known Matilde Marcolli’s (quite old) lectures on the subject.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 10th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks.

   Thanks.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeDec 31st 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded this reference on the relation between [[Rozansky-Witten invariants]] and [[Seiberg-Witten invariants]] of [[3-manifolds]]: * [[Matthias Blau]], George Thompson, _On the Relationship between the Rozansky-Witten and the 3-Dimensional Seiberg-Witten Invariants_, Adv. Theor. Math. Phys. 5 (2002) 483-498 ([arXiv:hep-th/0006244](https://arxiv.org/abs/hep-th/0006244)) <a href="https://ncatlab.org/nlab/revision/diff/Seiberg-Witten+theory/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/Seiberg-Witten+theory/15">v15</a>, <a href="https://ncatlab.org/nlab/show/Seiberg-Witten+theory">current</a>

   added this reference on the relation between Rozansky-Witten invariants and Seiberg-Witten invariants of 3-manifolds:

   • Matthias Blau, George Thompson, On the Relationship between the Rozansky-Witten and the 3-Dimensional Seiberg-Witten Invariants, Adv. Theor. Math. Phys. 5 (2002) 483-498 (arXiv:hep-th/0006244)

   diff, v15, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJan 8th 2024
   • (edited Jan 8th 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexam adding pointers on quantum SW curves, starting with this one: In relation to [[E-strings]] and [[D6-D8-brane bound states]]: * [[Jin Chen]], [[Babak Haghighat]], [[Hee-Cheol Kim]], [[Marcus Sperling]], [[Xin Wang]], *E-string Quantum Curve* &lbrack;[arXiv:2103.16996](https://arxiv.org/abs/2103.16996), [doi:10.1016/j.nuclphysb.2021.115602](https://doi.org/10.1016/j.nuclphysb.2021.115602)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Seiberg-Witten+theory/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/Seiberg-Witten+theory/18">v18</a>, <a href="https://ncatlab.org/nlab/show/Seiberg-Witten+theory">current</a>

   am adding pointers on quantum SW curves, starting with this one:

   In relation to E-strings and D6-D8-brane bound states:

   • Jin Chen, Babak Haghighat, Hee-Cheol Kim, Marcus Sperling, Xin Wang, E-string Quantum Curve [arXiv:2103.16996, doi:10.1016/j.nuclphysb.2021.115602]

   diff, v18, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJan 8th 2024
   • (edited Jan 8th 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexand this one: in relation to [[class S-theories]] and "[[M3]]"-[[defect branes]] inside [[M5-branes]]: * [[Jin Chen]], [[Babak Haghighat]], [[Hee-Cheol Kim]], [[Marcus Sperling]], *Elliptic Quantum Curves of Class $\mathcal{S}_k$*, J. High Energ. Phys. **2021** 28 (2021) &lbrack;[arXiv:2008.05155](https://arxiv.org/abs/2008.05155), <a href="https://doi.org/10.1007/JHEP03(2021)028">doi:10.1007/JHEP03(2021)028</a>&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Seiberg-Witten+theory/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/Seiberg-Witten+theory/18">v18</a>, <a href="https://ncatlab.org/nlab/show/Seiberg-Witten+theory">current</a>

   and this one:

   in relation to class S-theories and “M3”-defect branes inside M5-branes:

   • Jin Chen, Babak Haghighat, Hee-Cheol Kim, Marcus Sperling, Elliptic Quantum Curves of Class $\mathcal{S}_k$, J. High Energ. Phys. 2021 28 (2021) [arXiv:2008.05155, doi:10.1007/JHEP03(2021)028]

   diff, v18, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJan 9th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Alexander Gorsky]], [[Igor Krichever]], [[Andrei Marshakov]], [[Andrei Mironov]], [[Andrey Morozov]], *Integrability and Seiberg-Witten Exact Solution*, Phys. Lett. B **355** (1995) 466-474 &lbrack;[arXiv:hep-th/9505035](https://arxiv.org/abs/hep-th/9505035), <a href="https://doi.org/10.1016/0370-2693(95)00723-X">doi:10.1016/0370-2693(95)00723-X</a>&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Seiberg-Witten+theory/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/Seiberg-Witten+theory/20">v20</a>, <a href="https://ncatlab.org/nlab/show/Seiberg-Witten+theory">current</a>

   added pointer to:

   • Alexander Gorsky, Igor Krichever, Andrei Marshakov, Andrei Mironov, Andrey Morozov, Integrability and Seiberg-Witten Exact Solution, Phys. Lett. B 355 (1995) 466-474 [arXiv:hep-th/9505035, doi:10.1016/0370-2693(95)00723-X]

   diff, v20, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJan 9th 2024
   • (edited Jan 9th 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Taro Kimura]], *Seiberg–Witten Geometry*, Chapter 4 in: *Instanton Counting, Quantum Geometry and Algebra*, Mathematical Physics Studies, Springer (2021) &lbrack;[doi:10.1007/978-3-030-76190-5_4](https://doi.org/10.1007/978-3-030-76190-5_4)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Seiberg-Witten+theory/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/Seiberg-Witten+theory/21">v21</a>, <a href="https://ncatlab.org/nlab/show/Seiberg-Witten+theory">current</a>

   added pointer to:

   • Taro Kimura, Seiberg–Witten Geometry, Chapter 4 in: Instanton Counting, Quantum Geometry and Algebra, Mathematical Physics Studies, Springer (2021) [doi:10.1007/978-3-030-76190-5_4]

   diff, v21, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeJul 8th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * Shuhan Jiang, [[Jürgen Jost]]: *Cohomological field theories and generalized Seiberg-Witten equations* &lbrack;[arXiv:2407.04019](https://arxiv.org/abs/2407.04019)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Seiberg-Witten+theory/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/Seiberg-Witten+theory/26">v26</a>, <a href="https://ncatlab.org/nlab/show/Seiberg-Witten+theory">current</a>

   added pointer to:

   • Shuhan Jiang, Jürgen Jost: Cohomological field theories and generalized Seiberg-Witten equations [arXiv:2407.04019]

   diff, v26, current

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2024
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[Yuji Tachikawa]]: *$N=2$ supersymmetric dynamics for pedestrians*, Lecture Notes in Physics, Springer (2015) &lbrack;[doi:https://doi.org/10.1007/978-3-319-08822-8](https://doi.org/10.1007/978-3-319-08822-8)&rbrack; also: *$N=2$ supersymmetric dynamics for dummies*, lecture notes &lbrack;[pdf](https://member.ipmu.jp/yuji.tachikawa/lectures/dummies/dummies2.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Seiberg-Witten+theory/27">diff</a>, <a href="https://ncatlab.org/nlab/revision/Seiberg-Witten+theory/27">v27</a>, <a href="https://ncatlab.org/nlab/show/Seiberg-Witten+theory">current</a>

    added pointer to:

    • Yuji Tachikawa: $N=2$ supersymmetric dynamics for pedestrians, Lecture Notes in Physics, Springer (2015) [doi:https://doi.org/10.1007/978-3-319-08822-8]

      also: $N=2$ supersymmetric dynamics for dummies, lecture notes [pdf]

    diff, v27, current

11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeDec 10th 2024
    • (edited Dec 10th 2024)
    • PermaLink
    Author: Urs
    Format: MarkdownItexhave added more references for the Bauer-Furuta invariant in stable (co)homotopy and gave the list its own subsection, now [here](https://ncatlab.org/nlab/show/Seiberg-Witten+theory#ReferencesSeibergWittenInvariantsInStableHomotopy) Also changed the wording of the lead-in line a little: As far as I can see, the Bauer-Furuta invariant takes values in stable homotopy groups of spheres. While we can of course think of this as being stable *co*-homotopy of the point in negative degree, which some authors do, I am not sure that this is usefully descriptive? (Though I see that the long exact sequence in stable Cohomotopy is invoked in (3.15) [p. 26](https://adebray.github.io/lecture_notes/s19_furuta.pdf#page=26) of Debray's note.) But I notice that Furuta in his articles without Bauer does speak of "stable homotopy", instead (already in the early preprint [Furuta 1997](https://ncatlab.org/nlab/show/Seiberg-Witten+theory#Furuta97) but also more recently in [Furuta et al. 2007](https://ncatlab.org/nlab/show/Seiberg-Witten+theory#FurutaKametaniMatsueMinami07)). <a href="https://ncatlab.org/nlab/revision/diff/Seiberg-Witten+theory/28">diff</a>, <a href="https://ncatlab.org/nlab/revision/Seiberg-Witten+theory/28">v28</a>, <a href="https://ncatlab.org/nlab/show/Seiberg-Witten+theory">current</a>

    have added more references for the Bauer-Furuta invariant in stable (co)homotopy

    and gave the list its own subsection, now here

    Also changed the wording of the lead-in line a little: As far as I can see, the Bauer-Furuta invariant takes values in stable homotopy groups of spheres.

    While we can of course think of this as being stable co-homotopy of the point in negative degree, which some authors do, I am not sure that this is usefully descriptive? (Though I see that the long exact sequence in stable Cohomotopy is invoked in (3.15) p. 26 of Debray’s note.)

    But I notice that Furuta in his articles without Bauer does speak of “stable homotopy”, instead (already in the early preprint Furuta 1997 but also more recently in Furuta et al. 2007).

    diff, v28, current