On Vafa–Witten equations over Kähler manifolds

References

[1] L. Álvarez Cónsul and O. García-Prada, Hitchin–Kobayashi correspondence, quivers, and vortices, Comm. Math. Phys. 238 (2003), no. 1–2, 1–33. 10.1007/s00220-003-0853-1Search in Google Scholar

[2] S. Bando and Y.-T. Siu, Stable sheaves and Einstein–Hermitian metrics, Geometry and analysis on complex manifolds, World Scientific, River Edge (1994), 39–50. 10.1142/9789814350112_0002Search in Google Scholar

[3] A. S. Besicovitch, On sufficient conditions for a function to be analytic, and on behaviour of analytic functions in the neighbourhood of non-isolated singular points, Proc. Lond. Math. Soc. (2) 32 (1931), no. 1, 1–9. 10.1112/plms/s2-32.1.1Search in Google Scholar

[4] X. Chen and S. Sun, Reflexive sheaves, Hermitian–Yang–Mills connections, and tangent cones, Invent. Math. 225 (2021), no. 1, 73–129. 10.1007/s00222-020-01027-9Search in Google Scholar

[5] S. K. Donaldson, Infinite determinants, stable bundles and curvature, Duke Math. J. 54 (1987), no. 1, 231–247. 10.1215/S0012-7094-87-05414-7Search in Google Scholar

[6] S. K. Donaldson and P. B. Kronheimer, The geometry of four-manifolds, Oxford Math. Monogr., The Clarendon Press, New York 1990. 10.1093/oso/9780198535539.001.0001Search in Google Scholar

[7] S. K. Donaldson and R. P. Thomas, Gauge theory in higher dimensions, The geometric universe (Oxford 1996), Oxford University, Oxford (1998), 31–47. 10.1093/oso/9780198500599.003.0003Search in Google Scholar

[8] D. Greb, B. Sibley, M. Toma and R. Wentworth, Complex algebraic compactifications of the moduli space of Hermitian Yang–Mills connections on a projective manifold, Geom. Topol. 25 (2021), no. 4, 1719–1818. 10.2140/gt.2021.25.1719Search in Google Scholar

[9] S. He, The behavior of sequences of solutions to the Hitchin–Simpson equations, arXiv, preprint (2020), https://arxiv.org/abs/2002.08109. Search in Google Scholar

[10] N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. Lond. Math. Soc. (3) 55 (1987), no. 1, 59–126. 10.1112/plms/s3-55.1.59Search in Google Scholar

[11] M.-C. Hong and G. Tian, Asymptotical behaviour of the Yang–Mills flow and singular Yang–Mills connections, Math. Ann. 330 (2004), no. 3, 441–472. 10.1007/s00208-004-0539-9Search in Google Scholar

[12] S. Kobayashi, Differential geometry of complex vector bundles, Princeton University, Princeton 1987. 10.1515/9781400858682Search in Google Scholar

[13] T.-R. Lin, The Hermitian–Yang–Mills metrics and stability for holomorphic vector bundles with Higgs fields over compact Kaehler manifolds, University of California, San Diego 1989. Search in Google Scholar

[14] M. Lübke and A. Teleman, The Kobayashi–Hitchin correspondence, World Scientific, River Edge 1995. 10.1142/2660Search in Google Scholar

[15] M. Lübke and A. Teleman, The universal Kobayashi–Hitchin correspondence on Hermitian manifolds, Mem. Amer. Math. Soc. 183 (2006), no. 863, 1–97. 10.1090/memo/0863Search in Google Scholar

[16] F. Marchesano, R. Moraru and R. Savelli, A vanishing theorem for T-branes, J. High Energy Phys. 2020 (2020), no. 11, 1–32. 10.1007/JHEP11(2020)002Search in Google Scholar

[17] B. A. Mares, Jr, Some analytic aspects of Vafa–Witten twisted N = 4 supersymmetric Yang–Mills theory, Ph.D. Thesis, Massachusetts Institute of Technology, 2010. Search in Google Scholar

[18] R. Mazzeo, J. Swoboda, H. Weiss and F. Witt, Ends of the moduli space of Higgs bundles, Duke Math. J. 165 (2016), no. 12, 2227–2271. 10.1215/00127094-3476914Search in Google Scholar

[19] T. Mochizuki, Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces, J. Topol. 9 (2016), no. 4, 1021–1073. 10.1112/jtopol/jtw018Search in Google Scholar

[20] H. Nakajima, Compactness of the moduli space of Yang–Mills connections in higher dimensions, J. Math. Soc. Japan 40 (1988), no. 3, 383–392. 10.2969/jmsj/04030383Search in Google Scholar

[21] C. T. Simpson, Harmonic bundles on noncompact curves, J. Amer. Math. Soc. 3 (1990), no. 3, 713–770. 10.1090/S0894-0347-1990-1040197-8Search in Google Scholar

[22] C. T. Simpson, Higgs bundles and local systems, Publ. Math. Inst. Hautes Études Sci. 75 (1992), 5–95. 10.1007/BF02699491Search in Google Scholar

[23] Y. Tanaka, A weak compactness theorem of the Donaldson–Thomas instantons on compact Kähler threefolds, J. Math. Anal. Appl. 408 (2013), no. 1, 27–34. 10.1016/j.jmaa.2013.05.059Search in Google Scholar

[24] Y. Tanaka and R. P. Thomas, Vafa–Witten invariants for projective surfaces II: Semistable case, Pure Appl. Math. Q. 13 (2017), no. 3, 517–562. 10.4310/PAMQ.2017.v13.n3.a6Search in Google Scholar

[25] Y. Tanaka and R. P. Thomas, Vafa-Witten invariants for projective surfaces I: Stable case, J. Algebraic Geom. 29 (2020), no. 4, 603–668. 10.1090/jag/738Search in Google Scholar

[26] C. H. Taubes, The behavior of sequences of solutions to the Vafa–Witten equations, preprint (2017), https://arxiv.org/abs/1702.04610. Search in Google Scholar

[27] G. Tian, Gauge theory and calibrated geometry. I, Ann. of Math. (2) 151 (2000), no. 1, 193–268. 10.2307/121116Search in Google Scholar

[28] K. Uhlenbeck, A priori estimates for Yang–Mills fields, unpublished manuscript. Search in Google Scholar

[29] K. Uhlenbeck and S.-T. Yau, On the existence of Hermitian–Yang–Mills connections in stable vector bundles, Comm. Pure Appl. Math. 39 (1986), no. 2, S257–S293. 10.1002/cpa.3160390714Search in Google Scholar

[30] K. K. Uhlenbeck, Connections with L p bounds on curvature, Comm. Math. Phys. 83 (1982), no. 1, 31–42. 10.1007/BF01947069Search in Google Scholar

[31] C. Vafa and E. Witten, A strong coupling test of 𝑆-duality, Nuclear Phys. B 431 (1994), no. 1–2, 3–77. 10.1016/0550-3213(94)90097-3Search in Google Scholar