Journal of Holography Applications in Physics
Moore-Tachikawa Varieties: Beyond Duality
Document Type : Regular article
Author
Newnham College, Sidgwick Avenue, CB39DF, Cambridge, UK
Abstract
Abstract: We propose a generalisation of the Moore-Tachikawa varieties for the case in which the target category of the 2D TFT is a hyperkaehler quotient. The setup requires generalising the bordism operators of Moore and Segal to the case involving lack of reparametrisation-invariance on the Riemann surface, ultimately enabling to relate this to the issue of defining a Drinfeld center for composite class S theories.
Keywords
- Cochain level theories
- Symplectic varieties
- Topological field theories
- Categorical duality
- Quiver gauge theories
- Higher categories
- Relative QFTs
Main Subjects
Article PDF
[1] V. Pasquarella, Categorical Symmetries and Fiber Functors from Multiple Condensing Homomorphisms from 6D N = (2; 0) SCFTs, [arXiv:2305.18515 [hep-th]]. DOI: 10.48550/arXiv.2305.18515
[2] V. Pasquarella, Drinfeld Centers from Magnetic Quivers, [arXiv:2306.12471 [hep-th]]. DOI: 10.48550/arXiv.2306.12471
[3] E. Witten, Some comments on string dynamics, [arXiv:hep-th/9507121 [hep-th]]. DOI: 10.48550/arXiv.hep-th/9507121
[4] E. Witten, Geometric Langlands From Six Dimensions, [arXiv:0905.2720 [hep-th]]. DOI: 10.48550/arXiv.0905.2720
[5] D. Ben-Zvi, Theory X and Geometric Representation Theory, talks at Mathematical Aspects of Six-Dimensional Quantum Field Theories IHES 2014, notes by Qiaochu Yuan.
[6] E. Witten, Conformal Field Theory In Four And Six Dimensions, [arXiv:0712.0157 [math.RT]]. DOI: 10.48550/arXiv.0712.0157
[7] G. Moore, Applications of the six-dimensional (2,0) theories to Physical Mathematics, Felix Klein lectures Bonn (2012).
[8] V. Bashmakov, M. Del Zotto and A. Hasan, On the 6d Origin of Non-invertible Symmetries in 4d, JHEP 09, 161 (2023). DOI: 10.1007/JHEP09(2023)161
[9] V. Bashmakov, M. Del Zotto, A. Hasan and J. Kaidi, Non-invertible Symmetries of Class S Theories, JHEP 05, 225 (2023). DOI: 10.1007/JHEP05(2023)225
[10] J. Kaidi, K. Ohmori, Y. Zheng, Kramers-Wannier like Duality Defects in (3+1)D Gauge Theories, Phys. Rev. Lett. 128, 111601 (2022) . DOI: 10.1103/PhysRevLett.128.111601
[11] J. Kaidi, K. Ohmori and Y. Zheng, Kramers-Wannier-like Duality Defects in (3+1)D Gauge Theories, Phys. Rev. Lett. 128, no.11, 111601 (2022). DOI: 10.1103/PhysRevLett.128.111601
[12] Y. Choi, C. Cordova, P. S. Hsin, H. T. Lam and S. H. Shao, Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions, Commun.Math.Phys. 402 1, 489-542 (2023). DOI: 10.1007/s00220-023-04727-4
[13] Y. Choi, C. Cordova, P. S. Hsin, H. T. Lam and S. H. Shao, Noninvertible duality defects in 3+1 dimensions, Phys. Rev. D 105 no.12, 125016 (2022). DOI: 10.1103/PhysRevD.105.125016
[14] W. Ji and X. G. Wen, Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions, Phys. Rev. Research. 1, 033054 (2019). DOI: 10.1103/PhysRevResearch.1.033054
[15] O. Chacaltana, J. Distler and Y. Tachikawa, Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories, Int. J. Mod. Phys. A 28, 1340006 (2013). DOI: 10.1142/S0217751X1340006X
[16] Y. Tachikawa, On the 6d origin of discrete additional data of 4d gauge theories, JHEP 05, 020 (2014). DOI: 10.1007/JHEP05(2014)020
[17] G. W. Moore and G. Segal, D-branes and K-theory in 2D topological eld theory, [arXiv:hep-th/0609042 [hep-th]]. DOI: 10.48550/arXiv.hep-th/0609042
[18] G. W. Moore and Y. Tachikawa, On 2d TQFTs whose values are holomorphic symplectic varieties, Proc. Symp. Pure Math. 85, 191-208 (2012). DOI: 10.1090/pspum/085/1379
[19] O. Aharony, N. Seiberg and Y. Tachikawa, Reading between the lines of fourdimensional gauge theories, JHEP 08, 115 (2013). DOI: 10.1007/JHEP08(2013)115
[20] D. S. Freed and C. Teleman, Relative quantum eld theory, Commun. Math. Phys. 326, 459-476 (2014). DOI: 10.1007/s00220-013-1880-1
[21] D. S. Freed, G. W. Moore and C. Teleman, Topological symmetry in quantum eld theory, [arXiv:2209.07471 [hep-th]]. DOI: 10.48550/arXiv.2209.07471
[22] D. S. Freed, Introduction to topological symmetry in QFT, [arXiv:2212.00195 [hepth]]. DOI: 10.48550/arXiv.2212.00195
[23] T. Johnson-Freyd, Operators and higher categories in quantum eld theory, Lecture series.
[24] L. Kong, Anyon condensation and tensor categories, Nucl. Phys. B 886 436-482 (2014). DOI: 10.1016/j.nuclphysb.2014.07.003
[25] M. Yu, Gauging Categorical Symmetries in 3d Topological Orders and Bulk Reconstruction, [arXiv:2111.13697 [hep-th]]. DOI: 10.48550/arXiv.2111.13697
[26] V. Pasquarella, to appear.
[27] A. Braverman, M. Finkelberg and H. Nakajima, Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan), [arXiv:1706.02112 [math.RT]]. DOI: 10.48550/arXiv.1706.02112
[28] F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3d Sicilian theories, JHEP 09, 063 (2010). DOI: 10.1007/JHEP09(2010)063
[2] V. Pasquarella, Drinfeld Centers from Magnetic Quivers, [arXiv:2306.12471 [hep-th]]. DOI: 10.48550/arXiv.2306.12471
[3] E. Witten, Some comments on string dynamics, [arXiv:hep-th/9507121 [hep-th]]. DOI: 10.48550/arXiv.hep-th/9507121
[4] E. Witten, Geometric Langlands From Six Dimensions, [arXiv:0905.2720 [hep-th]]. DOI: 10.48550/arXiv.0905.2720
[5] D. Ben-Zvi, Theory X and Geometric Representation Theory, talks at Mathematical Aspects of Six-Dimensional Quantum Field Theories IHES 2014, notes by Qiaochu Yuan.
[6] E. Witten, Conformal Field Theory In Four And Six Dimensions, [arXiv:0712.0157 [math.RT]]. DOI: 10.48550/arXiv.0712.0157
[7] G. Moore, Applications of the six-dimensional (2,0) theories to Physical Mathematics, Felix Klein lectures Bonn (2012).
[8] V. Bashmakov, M. Del Zotto and A. Hasan, On the 6d Origin of Non-invertible Symmetries in 4d, JHEP 09, 161 (2023). DOI: 10.1007/JHEP09(2023)161
[9] V. Bashmakov, M. Del Zotto, A. Hasan and J. Kaidi, Non-invertible Symmetries of Class S Theories, JHEP 05, 225 (2023). DOI: 10.1007/JHEP05(2023)225
[10] J. Kaidi, K. Ohmori, Y. Zheng, Kramers-Wannier like Duality Defects in (3+1)D Gauge Theories, Phys. Rev. Lett. 128, 111601 (2022) . DOI: 10.1103/PhysRevLett.128.111601
[11] J. Kaidi, K. Ohmori and Y. Zheng, Kramers-Wannier-like Duality Defects in (3+1)D Gauge Theories, Phys. Rev. Lett. 128, no.11, 111601 (2022). DOI: 10.1103/PhysRevLett.128.111601
[12] Y. Choi, C. Cordova, P. S. Hsin, H. T. Lam and S. H. Shao, Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions, Commun.Math.Phys. 402 1, 489-542 (2023). DOI: 10.1007/s00220-023-04727-4
[13] Y. Choi, C. Cordova, P. S. Hsin, H. T. Lam and S. H. Shao, Noninvertible duality defects in 3+1 dimensions, Phys. Rev. D 105 no.12, 125016 (2022). DOI: 10.1103/PhysRevD.105.125016
[14] W. Ji and X. G. Wen, Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions, Phys. Rev. Research. 1, 033054 (2019). DOI: 10.1103/PhysRevResearch.1.033054
[15] O. Chacaltana, J. Distler and Y. Tachikawa, Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories, Int. J. Mod. Phys. A 28, 1340006 (2013). DOI: 10.1142/S0217751X1340006X
[16] Y. Tachikawa, On the 6d origin of discrete additional data of 4d gauge theories, JHEP 05, 020 (2014). DOI: 10.1007/JHEP05(2014)020
[17] G. W. Moore and G. Segal, D-branes and K-theory in 2D topological eld theory, [arXiv:hep-th/0609042 [hep-th]]. DOI: 10.48550/arXiv.hep-th/0609042
[18] G. W. Moore and Y. Tachikawa, On 2d TQFTs whose values are holomorphic symplectic varieties, Proc. Symp. Pure Math. 85, 191-208 (2012). DOI: 10.1090/pspum/085/1379
[19] O. Aharony, N. Seiberg and Y. Tachikawa, Reading between the lines of fourdimensional gauge theories, JHEP 08, 115 (2013). DOI: 10.1007/JHEP08(2013)115
[20] D. S. Freed and C. Teleman, Relative quantum eld theory, Commun. Math. Phys. 326, 459-476 (2014). DOI: 10.1007/s00220-013-1880-1
[21] D. S. Freed, G. W. Moore and C. Teleman, Topological symmetry in quantum eld theory, [arXiv:2209.07471 [hep-th]]. DOI: 10.48550/arXiv.2209.07471
[22] D. S. Freed, Introduction to topological symmetry in QFT, [arXiv:2212.00195 [hepth]]. DOI: 10.48550/arXiv.2212.00195
[23] T. Johnson-Freyd, Operators and higher categories in quantum eld theory, Lecture series.
[24] L. Kong, Anyon condensation and tensor categories, Nucl. Phys. B 886 436-482 (2014). DOI: 10.1016/j.nuclphysb.2014.07.003
[25] M. Yu, Gauging Categorical Symmetries in 3d Topological Orders and Bulk Reconstruction, [arXiv:2111.13697 [hep-th]]. DOI: 10.48550/arXiv.2111.13697
[26] V. Pasquarella, to appear.
[27] A. Braverman, M. Finkelberg and H. Nakajima, Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan), [arXiv:1706.02112 [math.RT]]. DOI: 10.48550/arXiv.1706.02112
[28] F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3d Sicilian theories, JHEP 09, 063 (2010). DOI: 10.1007/JHEP09(2010)063
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Volume 3, Issue 4
November 2023Pages 39-56
- Receive Date: 04 October 2023
- Revise Date: 30 October 2023
- Accept Date: 04 November 2023