Journal of Holography Applications in Physics
Drinfeld Centers from Magnetic Quivers
Document Type : Regular article
Author
Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS), Shanghai 200433, China; Research Institute of Intelligent Complex Systems, Fudan University, Shanghai 200433, China; Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cam bridge, Wilberforce Road, CB3 0WA, Cambridge, UK
Abstract
The present work shows that magnetic quivers encode the necessary information for determining the Drinfeld center in the symmetry topological field theory constructions (SymTFT) associated with a given absolute theory. The crucial argument resides in their common aim of generalising homological mirror symmetry.
Keywords
- Symplectic Singularities
- Mirror Symmetry
- Representation Theory
- Supersymmetric Field Theories
- Higher Categories
- Quiver Gauge Theories
Main Subjects
Article PDF
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[2] D. Pomerleano, and C. Tteleman, ”Quantization commutes with reduction again: the quantum GIT conjecture I”, [arXiv:2405.20301 [math.SG]]
[3] V. Pasquarella, “Categorical Symmetries and Fiber Functors from Multiple Condensing Homomorphisms from 6D N = (2, 0) SCFTs,” [arXiv:2305.18515 [hep-th]].
[4] D. S. Freed, G. W. Moore and C. Teleman, “Topological symmetry in quantum field theory,” [arXiv:2209.07471 [hep-th]].
[5] V. Pasquarella, ”Advancements in Functorial Homological Mirror Symmetry”, [arXiv:2502.06951 [hep-th]], DOI: https://doi.org/10.22128/jhap.2025.3019.1130
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[7] A. Bourget, S. Cabrera, J. F. Grimminger, A. Hanany, M. Sperling, A. Zajac and Z. Zhong, “The Higgs mechanism — Hasse diagrams for symplectic singularities,” JHEP 01, 157 (2020). DOI: 10.1007/JHEP01(2020)157 [arXiv:1908.04245 [hep-th]].
[8] A. Bourget, J. F. Grimminger, A. Hanany, M. Sperling and Z. Zhong, “Branes, Quivers, and the Affne Grassmannian,” Adv. Stud. Pure Math. 88, 331 (2023). DOI: 10.2969/aspm/08810331 [arXiv:2102.06190 [hep-th]].
[9] A. Bourget, J. F. Grimminger, A. Hanany, R. Kalveks, M. Sperling and Z. Zhong, “A Tale of N Cones,” [arXiv:2303.16939 [hep-th]].
[10] A. Bourget, S. Cabrera, J. F. Grimminger, A. Hanany and Z. Zhong, “Brane Webs and Magnetic Quivers for SQCD,” JHEP 03, 176 (2020). DOI: 10.1007/JHEP03(2020)176 [arXiv:1909.00667 [hep-th]].
[11] G. Ferlito and A. Hanany, “A tale of two cones: the Higgs Branch of Sp(n) theories with 2n flavours,” [arXiv:1609.06724 [hep-th]].
[12] A. Hanany and R. Kalveks, “Quiver Theories and Hilbert Series of Classical Slodowy Intersections,” Nucl. Phys. B 952, 114939 (2020). DOI: 10.1016/j.nuclphysb.2020.114939 [arXiv:1909.12793 [hep-th]].
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[14] S. D’Alesio, “Derived representation schemes and Nakajima quiver varieties,” Selecta Math. 28(1), 20 (2022). DOI: 10.1007/s00029-021-00724-4
[15] A. Braverman, M. Finkelberg and H. Nakajima, “Coulomb branches of 3d N = 4 quiver gauge theories and slices in the affne Grassmannian,” Adv. Theor. Math. Phys. 23, 75 (2019). DOI: 10.4310/ATMP.2019.v23.n1.a3 [arXiv:1604.03625 [math.RT]].
[16] A. Braverman, M. Finkelberg and H. Nakajima, “Towards a mathematical definition of Coulomb branches of 3-dimensional N = 4 gauge theories, II,” Adv. Theor. Math. Phys. 22, 1071 (2018). DOI: 10.4310/ATMP.2018.v22.n5.a1 [arXiv:1601.03586 [math.RT]].
[17] M. F. Atiyah, N. J. Hitchin, V. G. Drinfeld and Y. I. Manin, “Construction of Instantons,” Phys. Lett. A 65, 185 (1978). DOI: 10.1016/0375-9601(78)90141-X.
[18] Y. Berest, G. Khachatryan, A. Ramadoss, “Derived representation schemes and cyclic homology,” Adv. Math. 245, 625 (2013).
[19] S. Cabrera and A. Hanany, “Quiver Subtractions,” JHEP 09, 008 (2018). DOI: 10.1007/JHEP09(2018)008 [arXiv:1803.11205 [hep-th]].
[20] C. Teleman, “The rôle of Coulomb branches in 2D gauge theory,” J. Eur. Math. Soc. 23(11), 3497 (2021). DOI: 10.4171/jems/1071 [arXiv:1801.10124 [math.AG]].
[21] C. Teleman. “The Quantization Conjecture Revisited.,” Annals of Mathematics 152(1), 1 (2000). DOI: 10.2307/2661378.
[22] E. Gonzalez, C. Y. Mak and D. Pomerleano, “Coulomb branch algebras via symplectic cohomology,” [arXiv:2305.04387 [math.SG]].
[23] N. Seiberg and E. Witten, “Gauge dynamics and compactification to three-dimensions,” [arXiv:hep-th/9607163 [hep-th]].
[24] A. Kapustin and L. Rozansky, “Three-dimensional topological field theory and symplectic algebraic geometry II,” Commun. Num. Theor. Phys. 4, 463 (2010). DOI: 10.4310/CNTP.2010.v4.n3.a1 [arXiv:0909.3643 [math.AG]].
[25] A. Kapustin, L. Rozansky and N. Saulina, “Three-dimensional topological field theory and symplectic algebraic geometry I,” Nucl. Phys. B 816, 295 (2009). DOI: 10.1016/j.nuclphysb.2009.01.027 [arXiv:0810.5415 [hep-th]].
[26] R. Bezrukavnikov, M. Finkelberg, and I. Mirkovíc, “Equivariant homology and K-theory of affne Grassmannians and Toda lattices,” Compos. Math. 141, 746 (2005).
[27] L. Bhardwaj, M. Bullimore, A. E. V. Ferrari and S. Schafer-Nameki, “Generalized Symmetries and Anomalies of 3d N=4 SCFTs,” [arXiv:2301.02249 [hep-th]].
[28] D. Gaiotto and J. Kulp, “Orbifold groupoids,” JHEP 02, 132 (2021). DOI: 10.1007/JHEP02(2021)132 [arXiv:2008.05960 [hep-th]].
[29] L. Kong, T. Lan, X. G. Wen, Z. H. Zhang and H. Zheng, “Algebraic higher symmetry and categorical symmetry – a holographic and entanglement view of symmetry,” Phys. Rev. Res. 2(4), 043086 (2020). DOI: 10.1103/PhysRevResearch.2.043086 [arXiv:2005.14178 [cond-mat.str-el]].
[30] L. Kong and Z. H. Zhang, “An invitation to topological orders and category theory,” [arXiv:2205.05565 [cond-mat.str-el]].
[31] L. Kong and H. Zheng, “A mathematical theory of gapless edges of 2d topological orders. Part I,” JHEP 02, 150 (2020). DOI: 10.1007/JHEP02(2020)150 [arXiv:1905.04924 [cond-mat.str-el]].
[32] L. Kong and H. Zheng, “A mathematical theory of gapless edges of 2d topological orders. Part II,” Nucl. Phys. B 966, 115384 (2021). DOI: 10.1016/j.nuclphysb.2021.115384 [arXiv:1912.01760 [cond-mat.str-el]].
[33] L. Kong and H. Zheng, “Categorical computation,” Front. Phys. 18(2), 21302 (2023). [arXiv:2102.04814v2[quant-ph]].
[34] D. Gaiotto and T. Johnson-Freyd, “Condensations in higher categories,” [arXiv:1905.09566 [math.CT]].
[35] T. Johnson-Freyd and M. Yu, “Topological Orders in (4+1)-Dimensions,” SciPost Phys. 13(3), 068 (2022). DOI: 10.21468/SciPostPhys.13.3.068 [arXiv:2104.04534 [hep-th]].
[36] T. Johnson-Freyd, “On the Classification of Topological Orders,” Commun. Math. Phys. 393(2), 989 (2022). DOI: 10.1007/s00220-022-04380-3 [arXiv:2003.06663 [math.CT]].
[37] T. D. Décoppet and M. Yu, “Gauging noninvertible defects: a 2-categorical perspective,” Lett. Math. Phys. 113(2), 36 (2023). DOI: 10.1007/s11005-023-01655-1 [arXiv:2211.08436 [math.CT]].[38] D. S. Freed and C. Teleman, “Relative quantum field theory,” Commun. Math. Phys. 326, 459 (2014). DOI: 10.1007/s00220-013-1880-1 [arXiv:1212.1692 [hep-th]].
[39] T. Johnson-Freyd, “Operators and higher categories in quantum field theory,” Lecture series.
[40] K. Hori and C. Vafa, “Mirror symmetry,” [arXiv:hep-th/0002222 [hep-th]].
[41] A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. P. Warner, “Selfdual strings and N=2 supersymmetric field theory,” Nucl. Phys. B 477, 746 (1996). DOI: 10.1016/0550- 3213(96)00353-7 [arXiv:hep-th/9604034 [hep-th]].
[42] M. Kontsevich, “Homological Algebra of Mirror Symmetry,” [arXiv:alg-geom/9411018 [math.AG]].
[43] D. Gaiotto and E. Witten, “S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory,” Adv. Theor. Math. Phys. 13(3), 721 (2009). DOI: 10.4310/ATMP.2009.v13.n3.a5 [arXiv:0807.3720 [hep-th]].
[44] C. Teleman, conference talk, Gauge Theory, Mirror Symmetry, and Langlands Duality.
[45] W. Crawley-Boevey, “Geometry of the moment map for representations of quivers,” Compositio Math. 126(3), 257 (2001).
[46] H. Kraft, C. Procesi, “Minimal singularities inGL n,” Invent. Math. 62, 503 (1980). DOI: https://doi.org/10.1007/BF01394257.
[47] H. Kraft, C. Procesi, “On the geometry of conjugacy classes in classical groups,” Comment. Math. Helv. 57, 539 (1982). DOI: 10.1007/BF02565876.
[2] D. Pomerleano, and C. Tteleman, ”Quantization commutes with reduction again: the quantum GIT conjecture I”, [arXiv:2405.20301 [math.SG]]
[3] V. Pasquarella, “Categorical Symmetries and Fiber Functors from Multiple Condensing Homomorphisms from 6D N = (2, 0) SCFTs,” [arXiv:2305.18515 [hep-th]].
[4] D. S. Freed, G. W. Moore and C. Teleman, “Topological symmetry in quantum field theory,” [arXiv:2209.07471 [hep-th]].
[5] V. Pasquarella, ”Advancements in Functorial Homological Mirror Symmetry”, [arXiv:2502.06951 [hep-th]], DOI: https://doi.org/10.22128/jhap.2025.3019.1130
[6] S. Cabrera, A. Hanany and M. Sperling, “Magnetic quivers, Higgs branches, and 6d N=(1,0) theories,” JHEP 06, 071 (2019). DOI: 10.1007/JHEP06(2019)071 [arXiv:1904.12293 [hep-th]].
[7] A. Bourget, S. Cabrera, J. F. Grimminger, A. Hanany, M. Sperling, A. Zajac and Z. Zhong, “The Higgs mechanism — Hasse diagrams for symplectic singularities,” JHEP 01, 157 (2020). DOI: 10.1007/JHEP01(2020)157 [arXiv:1908.04245 [hep-th]].
[8] A. Bourget, J. F. Grimminger, A. Hanany, M. Sperling and Z. Zhong, “Branes, Quivers, and the Affne Grassmannian,” Adv. Stud. Pure Math. 88, 331 (2023). DOI: 10.2969/aspm/08810331 [arXiv:2102.06190 [hep-th]].
[9] A. Bourget, J. F. Grimminger, A. Hanany, R. Kalveks, M. Sperling and Z. Zhong, “A Tale of N Cones,” [arXiv:2303.16939 [hep-th]].
[10] A. Bourget, S. Cabrera, J. F. Grimminger, A. Hanany and Z. Zhong, “Brane Webs and Magnetic Quivers for SQCD,” JHEP 03, 176 (2020). DOI: 10.1007/JHEP03(2020)176 [arXiv:1909.00667 [hep-th]].
[11] G. Ferlito and A. Hanany, “A tale of two cones: the Higgs Branch of Sp(n) theories with 2n flavours,” [arXiv:1609.06724 [hep-th]].
[12] A. Hanany and R. Kalveks, “Quiver Theories and Hilbert Series of Classical Slodowy Intersections,” Nucl. Phys. B 952, 114939 (2020). DOI: 10.1016/j.nuclphysb.2020.114939 [arXiv:1909.12793 [hep-th]].
[13] L. Rozansky and E. Witten, “HyperKahler geometry and invariants of three manifolds,” Selecta Math. 3, 401 (1997). DOI: 10.1007/s000290050016 [arXiv:hep-th/9612216 [hepth]].
[14] S. D’Alesio, “Derived representation schemes and Nakajima quiver varieties,” Selecta Math. 28(1), 20 (2022). DOI: 10.1007/s00029-021-00724-4
[15] A. Braverman, M. Finkelberg and H. Nakajima, “Coulomb branches of 3d N = 4 quiver gauge theories and slices in the affne Grassmannian,” Adv. Theor. Math. Phys. 23, 75 (2019). DOI: 10.4310/ATMP.2019.v23.n1.a3 [arXiv:1604.03625 [math.RT]].
[16] A. Braverman, M. Finkelberg and H. Nakajima, “Towards a mathematical definition of Coulomb branches of 3-dimensional N = 4 gauge theories, II,” Adv. Theor. Math. Phys. 22, 1071 (2018). DOI: 10.4310/ATMP.2018.v22.n5.a1 [arXiv:1601.03586 [math.RT]].
[17] M. F. Atiyah, N. J. Hitchin, V. G. Drinfeld and Y. I. Manin, “Construction of Instantons,” Phys. Lett. A 65, 185 (1978). DOI: 10.1016/0375-9601(78)90141-X.
[18] Y. Berest, G. Khachatryan, A. Ramadoss, “Derived representation schemes and cyclic homology,” Adv. Math. 245, 625 (2013).
[19] S. Cabrera and A. Hanany, “Quiver Subtractions,” JHEP 09, 008 (2018). DOI: 10.1007/JHEP09(2018)008 [arXiv:1803.11205 [hep-th]].
[20] C. Teleman, “The rôle of Coulomb branches in 2D gauge theory,” J. Eur. Math. Soc. 23(11), 3497 (2021). DOI: 10.4171/jems/1071 [arXiv:1801.10124 [math.AG]].
[21] C. Teleman. “The Quantization Conjecture Revisited.,” Annals of Mathematics 152(1), 1 (2000). DOI: 10.2307/2661378.
[22] E. Gonzalez, C. Y. Mak and D. Pomerleano, “Coulomb branch algebras via symplectic cohomology,” [arXiv:2305.04387 [math.SG]].
[23] N. Seiberg and E. Witten, “Gauge dynamics and compactification to three-dimensions,” [arXiv:hep-th/9607163 [hep-th]].
[24] A. Kapustin and L. Rozansky, “Three-dimensional topological field theory and symplectic algebraic geometry II,” Commun. Num. Theor. Phys. 4, 463 (2010). DOI: 10.4310/CNTP.2010.v4.n3.a1 [arXiv:0909.3643 [math.AG]].
[25] A. Kapustin, L. Rozansky and N. Saulina, “Three-dimensional topological field theory and symplectic algebraic geometry I,” Nucl. Phys. B 816, 295 (2009). DOI: 10.1016/j.nuclphysb.2009.01.027 [arXiv:0810.5415 [hep-th]].
[26] R. Bezrukavnikov, M. Finkelberg, and I. Mirkovíc, “Equivariant homology and K-theory of affne Grassmannians and Toda lattices,” Compos. Math. 141, 746 (2005).
[27] L. Bhardwaj, M. Bullimore, A. E. V. Ferrari and S. Schafer-Nameki, “Generalized Symmetries and Anomalies of 3d N=4 SCFTs,” [arXiv:2301.02249 [hep-th]].
[28] D. Gaiotto and J. Kulp, “Orbifold groupoids,” JHEP 02, 132 (2021). DOI: 10.1007/JHEP02(2021)132 [arXiv:2008.05960 [hep-th]].
[29] L. Kong, T. Lan, X. G. Wen, Z. H. Zhang and H. Zheng, “Algebraic higher symmetry and categorical symmetry – a holographic and entanglement view of symmetry,” Phys. Rev. Res. 2(4), 043086 (2020). DOI: 10.1103/PhysRevResearch.2.043086 [arXiv:2005.14178 [cond-mat.str-el]].
[30] L. Kong and Z. H. Zhang, “An invitation to topological orders and category theory,” [arXiv:2205.05565 [cond-mat.str-el]].
[31] L. Kong and H. Zheng, “A mathematical theory of gapless edges of 2d topological orders. Part I,” JHEP 02, 150 (2020). DOI: 10.1007/JHEP02(2020)150 [arXiv:1905.04924 [cond-mat.str-el]].
[32] L. Kong and H. Zheng, “A mathematical theory of gapless edges of 2d topological orders. Part II,” Nucl. Phys. B 966, 115384 (2021). DOI: 10.1016/j.nuclphysb.2021.115384 [arXiv:1912.01760 [cond-mat.str-el]].
[33] L. Kong and H. Zheng, “Categorical computation,” Front. Phys. 18(2), 21302 (2023). [arXiv:2102.04814v2[quant-ph]].
[34] D. Gaiotto and T. Johnson-Freyd, “Condensations in higher categories,” [arXiv:1905.09566 [math.CT]].
[35] T. Johnson-Freyd and M. Yu, “Topological Orders in (4+1)-Dimensions,” SciPost Phys. 13(3), 068 (2022). DOI: 10.21468/SciPostPhys.13.3.068 [arXiv:2104.04534 [hep-th]].
[36] T. Johnson-Freyd, “On the Classification of Topological Orders,” Commun. Math. Phys. 393(2), 989 (2022). DOI: 10.1007/s00220-022-04380-3 [arXiv:2003.06663 [math.CT]].
[37] T. D. Décoppet and M. Yu, “Gauging noninvertible defects: a 2-categorical perspective,” Lett. Math. Phys. 113(2), 36 (2023). DOI: 10.1007/s11005-023-01655-1 [arXiv:2211.08436 [math.CT]].[38] D. S. Freed and C. Teleman, “Relative quantum field theory,” Commun. Math. Phys. 326, 459 (2014). DOI: 10.1007/s00220-013-1880-1 [arXiv:1212.1692 [hep-th]].
[39] T. Johnson-Freyd, “Operators and higher categories in quantum field theory,” Lecture series.
[40] K. Hori and C. Vafa, “Mirror symmetry,” [arXiv:hep-th/0002222 [hep-th]].
[41] A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. P. Warner, “Selfdual strings and N=2 supersymmetric field theory,” Nucl. Phys. B 477, 746 (1996). DOI: 10.1016/0550- 3213(96)00353-7 [arXiv:hep-th/9604034 [hep-th]].
[42] M. Kontsevich, “Homological Algebra of Mirror Symmetry,” [arXiv:alg-geom/9411018 [math.AG]].
[43] D. Gaiotto and E. Witten, “S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory,” Adv. Theor. Math. Phys. 13(3), 721 (2009). DOI: 10.4310/ATMP.2009.v13.n3.a5 [arXiv:0807.3720 [hep-th]].
[44] C. Teleman, conference talk, Gauge Theory, Mirror Symmetry, and Langlands Duality.
[45] W. Crawley-Boevey, “Geometry of the moment map for representations of quivers,” Compositio Math. 126(3), 257 (2001).
[46] H. Kraft, C. Procesi, “Minimal singularities inGL n,” Invent. Math. 62, 503 (1980). DOI: https://doi.org/10.1007/BF01394257.
[47] H. Kraft, C. Procesi, “On the geometry of conjugacy classes in classical groups,” Comment. Math. Helv. 57, 539 (1982). DOI: 10.1007/BF02565876.
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Volume 6, Issue 2
January 2026Pages 1-34
- Receive Date: 28 October 2025
- Revise Date: 30 January 2026
- Accept Date: 11 December 2025