Abstract
Four-dimensional \( \mathcal{N} \) = 4 super Yang-Mills, with a codimension-one defect breaking half of the supersymmetry, arises as the field theory description of the D3/D5 intersection in the holographic limit. This is one of the earliest, most extensively studied, and commonly used systems in holography. In this note we give the full R-symmetry-covariant supersymmetry variations for this system. We also provide the supercurrents and compute the algebra of the corresponding supercharges, obtaining the full set of central charges. We show that magnetically charged finite-energy field configurations preserving half of the supersymmetry are solutions to a new form of the extended Bogomolny equations, in which the defect fields play the role of jumping data for the Nahm-like part of the equations. In the appendices, we explain the connection between our results and the superspace-based formulations in the literature.
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References
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
S.A. Cherkis and A. Kapustin, Singular monopoles and supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 525 (1998) 215 [hep-th/9711145] [INSPIRE].
A. Karch and L. Randall, Open and closed string interpretation of SUSY CFT’s on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132] [INSPIRE].
O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev. D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].
J. Erdmenger, Z. Guralnik and I. Kirsch, Four-dimensional superconformal theories with interacting boundaries or defects, Phys. Rev. D 66 (2002) 025020 [hep-th/0203020] [INSPIRE].
M. de Leeuw, C. Kristjansen and K. Zarembo, One-point functions in defect CFT and integrability, JHEP 08 (2015) 098 [arXiv:1506.06958] [INSPIRE].
M. De Leeuw, C. Kristjansen and G. Linardopoulos, Scalar one-point functions and matrix product states of AdS/dCFT, Phys. Lett. B 781 (2018) 238 [arXiv:1802.01598] [INSPIRE].
S. Komatsu and Y. Wang, Non-perturbative defect one-point functions in planar N = 4 super-Yang-Mills, Nucl. Phys. B 958 (2020) 115120 [arXiv:2004.09514] [INSPIRE].
D. Gaiotto and E. Witten, Supersymmetric boundary conditions in N = 4 super Yang-Mills theory, J. Statist. Phys. 135 (2009) 789 [arXiv:0804.2902] [INSPIRE].
K. Jensen, A. Karch, D.T. Son and E.G. Thompson, Holographic Berezinskii-Kosterlitz-Thouless transitions, Phys. Rev. Lett. 105 (2010) 041601 [arXiv:1002.3159] [INSPIRE].
E. Witten, Topological quantum field theory, Commun. Math. Phys. 117 (1988) 353 [INSPIRE].
S.A. Cherkis, C. O’Hara and C. Sämann, Super Yang-Mills theory with impurity walls and instanton moduli spaces, Phys. Rev. D 83 (2011) 126009 [arXiv:1103.0042] [INSPIRE].
E. Witten and D.I. Olive, Supersymmetry algebras that include topological charges, Phys. Lett. B 78 (1978) 97 [INSPIRE].
A. Kapustin and E. Witten, Electric-magnetic duality and the geometric Langlands program, Commun. Num. Theor. Phys. 1 (2007) 1 [hep-th/0604151] [INSPIRE].
E. Witten, Fivebranes and knots, Quantum Topol. 3 (2012) 1 [arXiv:1101.3216] [INSPIRE].
D. Gaiotto and E. Witten, Knot invariants from four-dimensional gauge theory, Adv. Theor. Math. Phys. 16 (2012) 935 [arXiv:1106.4789] [INSPIRE].
S.K. Domokos and A.B. Royston, Holography for field theory solitons, JHEP 07 (2017) 065 [arXiv:1706.00425] [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton, NJ, U.S.A. (1992).
S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace or one thousand and one lessons in supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].
D. Gaiotto and E. Witten, Janus configurations, Chern-Simons couplings, and the theta-angle in N = 4 super Yang-Mills theory, JHEP 06 (2010) 097 [arXiv:0804.2907] [INSPIRE].
M.F. Sohnius, Introducing supersymmetry, Phys. Rept. 128 (1985) 39 [INSPIRE].
S. Sethi, The matrix formulation of type IIB five-branes, Nucl. Phys. B 523 (1998) 158 [hep-th/9710005] [INSPIRE].
A. Kapustin and S. Sethi, The Higgs branch of impurity theories, Adv. Theor. Math. Phys. 2 (1998) 571 [hep-th/9804027] [INSPIRE].
R. Mazzeo and E. Witten, The Nahm pole boundary condition, in The influence of Solomon Lefschetz in geometry and topology, Contemp. Math. 621 (2014) 171 [arXiv:1311.3167] [INSPIRE].
R. Mazzeo and E. Witten, The KW equations and the Nahm pole boundary condition with knots, Commun. Anal. Geom. 28 (2020) 871 [arXiv:1712.00835] [INSPIRE].
S. He and R. Mazzeo, The extended Bogomolny equations and generalized Nahm pole boundary condition, Geom. Topol. 23 (2019) 2475 [arXiv:1710.10645] [INSPIRE].
S. He and R. Mazzeo, The extended Bogomolny equations with generalized Nahm pole boundary conditions, II, Duke Math. J. 169 (2020) 2281 [arXiv:1806.06314] [INSPIRE].
G.W. Moore, A.B. Royston and D. Van den Bleeken, Semiclassical framed BPS states, JHEP 07 (2016) 071 [arXiv:1512.08924] [INSPIRE].
G.W. Moore, A.B. Royston and D. Van den Bleeken, L2-kernels of Dirac-type operators on monopole moduli spaces, Proc. Symp. Pure Math. (2015) 169 [arXiv:1512.08923] [INSPIRE].
T.D. Brennan and G.W. Moore, A note on the semiclassical formulation of BPS states in four-dimensional N = 2 theories, PTEP 2016 (2016) 12C110 [arXiv:1610.00697] [INSPIRE].
T.D. Brennan, G.W. Moore and A.B. Royston, Wall crossing from Dirac zeromodes, JHEP 09 (2018) 038 [arXiv:1805.08783] [INSPIRE].
D. Gaiotto, A. Kahn, G. Moore and F. Yan, 2d categorical wall-crossing with twisted masses, and an application to knot invariants, presented by Gregory Moore at Number theory, strings, and quantum physics at IPMU, University of Tokyo, Tokyo, Japan, 2 June 2021.
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Domokos, S.K., Royston, A.B. Supersymmetry of the D3/D5 defect field theory. J. High Energ. Phys. 2022, 40 (2022). https://doi.org/10.1007/JHEP12(2022)040
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DOI: https://doi.org/10.1007/JHEP12(2022)040