, The corresponding magnetic gauge group (at position? := l j ) is abelian in the first four cases and nonabelian in the last two

, ? 1: the identity

, ? ? 3 (µ)I (1,0) : the SU (2) electric-flavour currents

, ? ? 3 (?)I (0,1) : the S U (2) magnetic-flavour currents

, ? ? 5 (µ)I (2,0) : products of two electric currents

, ? ? 5 (?)I (0,2) : products of two magnetic currents

. ?-?i, ,1) : the energy-momentum tensor multiplet A 2

, The bottom componentQpQ r of an electric-current multiplet is the product of an antifundamental and a fundamental chiral scalar (the F -term condition imposesQ 1 Q 1 +Q 2 Q 2 = 0)

, theory has no mixed marginal (or relevant) chiral operators. All exactly-marginal deformations are purely electric or purely magnetic superpotentials

O. Aharony, L. Berdichevsky, M. Berkooz, and I. Shamir, Near-horizon solutions for D3-branes ending on 5-branes, Phys. Rev, vol.84, p.126003, 2011.

O. Aharony, M. Berkooz, and B. Katz, Non-local effects of multi-trace deformations in the AdS/CFT correspondence, JHEP, vol.10, p.97, 2005.

O. Aharony, M. Berkooz, and E. Silverstein, Multiple trace operators and nonlocal string theories, JHEP, vol.08, p.6, 2001.

O. Aharony, A. B. Clark, and A. Karch, The CFT/AdS correspondence, massive gravitons and a connectivity index conjecture, Phys. Rev, vol.74, p.86006, 2006.

O. Aharony, O. Dewolfe, D. Z. Freedman, and A. Karch, Defect conformal field theory and locally localized gravity, JHEP, 2003.

O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept, vol.323, 2000.

O. Aharony, A. Hanany, K. A. Intriligator, N. Seiberg, and M. J. Strassler, Aspects of N=2 supersymmetric gauge theories in three-dimensions, Nucl. Phys, vol.499, pp.67-99, 1997.

F. Apruzzi, M. Fazzi, A. Passias, D. Rosa, and A. Tomasiello, AdS 6 solutions of type II supergravity, JHEP, vol.11, p.99, 2014.

F. Apruzzi, M. Fazzi, A. Passias, A. Rota, and A. Tomasiello, Six-Dimensional Superconformal Theories and their Compactifications from Type IIA Supergravity, Phys. Rev. Lett, vol.115, issue.6, p.61601, 2015.

N. Arkani-hamed, H. Georgi, and M. D. Schwartz, Effective field theory for massive gravitons and gravity in theory space, Annals Phys, vol.305, pp.96-118, 2003.

B. Assel, Ring Relations and Mirror Map from Branes, JHEP, vol.03, p.152, 2017.

B. Assel, C. Bachas, J. Estes, and J. Gomis, Holographic Duals of D=3 N=4 Superconformal Field Theories, JHEP, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00602444

B. Assel, C. Bachas, J. Estes, and J. Gomis, IIB Duals of D=3 N=4 Circular Quivers, JHEP, vol.12, p.44, 2012.
URL : https://hal.archives-ouvertes.fr/hal-02301280

B. Assel, J. Estes, and M. Yamazaki, Large N Free Energy of 3d N=4 SCFTs and AdS 4 /CF T 3, JHEP, vol.09, p.74, 2012.

C. Bachas, C. Bunster, and M. Henneaux, Dynamics of Charged Events, Phys. Rev. Lett, vol.103, p.91602, 2009.
URL : https://hal.archives-ouvertes.fr/hal-02301285

C. Bachas, M. R. Douglas, and C. Schweigert, Flux stabilization of D-branes, JHEP, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00012345

C. Bachas and P. M. Petropoulos, Topological models on the lattice and a remark on string theory cloning, Commun. Math. Phys, vol.152, pp.191-202, 1993.

C. Bachas, Massive AdS Supergravitons and Holography, JHEP, vol.06, p.73, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02144300

C. Bachas, M. Bianchi, and A. Hanany, N = 2 moduli of AdS 4 vacua: a fine-print study, JHEP, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01862055

C. Bachas and J. Estes, Spin-2 spectrum of defect theories, JHEP, vol.06, p.5, 2011.
URL : https://hal.archives-ouvertes.fr/hal-02301283

C. Bachas and I. Lavdas, Massive Anti-de Sitter Gravity from String Theory. JHEP, vol.11, p.3, 2018.

C. Bachas and I. Lavdas, Quantum Gates to other Universes, Fortsch. Phys, vol.66, issue.2, p.1700096, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01724929

C. Bachas, I. Lavdas, and B. L. Floch, Marginal Deformations of 3d N=4 Linear Quiver Theories, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02148058

C. P. Bachas, On the Symmetries of Classical String Theory, Quantum Mechanics of Fundamental Systems: The Quest for Beauty and Simplicity: Claudio Bunster Festschrift, pp.17-26, 2009.
URL : https://hal.archives-ouvertes.fr/hal-02301286

C. Beem, T. Dimofte, and S. Pasquetti, Holomorphic Blocks in Three Dimensions, JHEP, vol.12, p.177, 2014.

B. Bellazzini, F. Riva, J. Serra, and F. Sgarlata, Beyond Positivity Bounds and the Fate of Massive Gravity, Phys. Rev. Lett, vol.120, issue.16, p.161101, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01793209

F. Benini and S. Cremonesi, Partition Functions of N = (2, 2) Gauge Theories on S 2 and Vortices, Commun. Math. Phys, vol.334, issue.3, pp.1483-1527, 2015.

S. Benvenuti and S. Pasquetti, 3D-partition functions on the sphere: exact evaluation and mirror symmetry, JHEP, vol.05, p.99, 2012.

M. Berkooz, A. Sever, and A. Shomer, Double trace' deformations, boundary conditions and space-time singularities, JHEP, 2002.

J. Bhattacharya, S. Bhattacharyya, S. Minwalla, and S. Raju, Indices for Superconformal Field Theories in 3,5 and 6 Dimensions, JHEP, vol.02, p.64, 2008.

V. Borokhov, Monopole operators in three-dimensional N=4 SYM and mirror symmetry, JHEP, 2004.

V. Borokhov, A. Kapustin, and X. Wu, Topological disorder operators in three-dimensional conformal field theory, JHEP, vol.11, p.49, 2002.

D. G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev, vol.6, pp.3368-3382, 1972.

F. Carta and H. Hayashi, Hilbert series and mixed branches of, JHEP, vol.02, p.37, 2017.

H. Ali, V. Chamseddine, and . Mukhanov, Hidden Ghost in Massive gravity, JHEP, 2013.

H. Ali, V. Chamseddine, and . Mukhanov, Mimetic Massive Gravity: Beyond Linear Approximation, JHEP, 2018.

T. Clifton, P. G. Ferreira, A. Padilla, and C. Skordis, Modified Gravity and Cosmology. Phys. Rept, vol.513, pp.1-189, 2012.

C. Cordova, T. T. Dumitrescu, and K. Intriligator, Deformations of Superconformal Theories, JHEP, vol.11, p.135, 2016.

C. Cordova, T. T. Dumitrescu, and K. Intriligator, Multiplets of Superconformal Symmetry in Diverse Dimensions, JHEP, vol.03, p.163, 2019.

E. Cremmer, B. Julia, and J. Scherk, Supergravity Theory in Eleven-Dimensions, Phys. Lett, vol.76, pp.409-412, 1978.

S. Cremonesi, 3d supersymmetric gauge theories and Hilbert series, Proc. Symp. Pure Math, vol.98, pp.21-48, 2018.

S. Cremonesi, A. Hanany, N. Mekareeya, and A. Zaffaroni, Coulomb branch Hilbert series and Hall-Littlewood polynomials, JHEP, vol.09, p.178, 2014.

S. Cremonesi, N. Mekareeya, and A. Zaffaroni, The moduli spaces of 3d N ? 2 Chern-Simons gauge theories and their Hilbert series, JHEP, vol.10, p.46, 2016.

J. Senarath-de-alwis, L. Louis, H. Mcallister, A. Triendl, and . Westphal, Moduli spaces in AdS 4 supergravity, JHEP, 2014.

J. De-boer, K. Hori, H. Ooguri, Y. Oz, and Z. Yin, Mirror symmetry in three-dimensional theories, SL(2,Z) and D-brane moduli spaces, Nucl. Phys, vol.493, pp.148-176, 1997.

J. De-boer, K. Hori, and Y. Oz, Dynamics of N=2 supersymmetric gauge theories in three-dimensions, Nucl. Phys, vol.500, pp.163-191, 1997.

, Claudia de Rham. Massive Gravity. Living Rev. Rel, vol.17, p.7, 2014.

C. De-rham, G. Gabadadze, and A. J. Tolley, Resummation of Massive Gravity, Phys. Rev. Lett, vol.106, p.231101, 2011.

C. De-rham, S. Melville, A. J. Tolley, and S. Zhou, Positivity Bounds for Massive Spin-1 and Spin-2 Fields, JHEP, 2019.

C. Deffayet, G. R. Dvali, and G. Gabadadze, Accelerated universe from gravity leaking to extra dimensions, Phys. Rev, vol.65, p.44023, 2002.

S. Deser, K. Izumi, Y. C. Ong, and A. Waldron, Problems of massive gravities, Mod. Phys. Lett, vol.30, p.1540006, 2015.

D. Eric, J. Hoker, M. Estes, and . Gutperle, Exact half-BPS Type IIB interface solutions. I. Local solution and supersymmetric Janus, JHEP, vol.06, p.21, 2007.

D. Eric, J. Hoker, M. Estes, and . Gutperle, Exact half-BPS Type IIB interface solutions. I. Local solution and supersymmetric Janus, JHEP, vol.06, p.21, 2007.

D. Eric, J. Hoker, M. Estes, and . Gutperle, Exact half-BPS Type IIB interface solutions. II. Flux solutions and multi-Janus, JHEP, 2007.

D. Eric, J. Hoker, M. Estes, and . Gutperle, Exact half-BPS Type IIB interface solutions. II. Flux solutions and multi-Janus, JHEP, 2007.

D. Eric, M. Hoker, A. Gutperle, C. F. Karch, and . Uhlemann, Warped AdS 6 × S 2 in Type IIB supergravity I: Local solutions, JHEP, vol.08, p.46, 2016.

D. Eric, M. Hoker, C. F. Gutperle, and . Uhlemann, Warped AdS 6 × S 2 in Type IIB supergravity II: Global solutions and five-brane webs, JHEP, p.131, 2017.

P. D. Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory. Graduate Texts in Contemporary Physics, 1997.

F. A. Dolan, On Superconformal Characters and Partition Functions in Three Dimensions, J. Math. Phys, vol.51, p.22301, 2010.

N. Doroud, J. Gomis, B. L. Floch, and S. Lee, Exact Results in D=2 Supersymmetric Gauge Theories, JHEP, 2013.

M. J. Duff, J. T. Liu, and H. Sati, Complementarity of the Maldacena and Karch-Randall pictures, Phys. Rev, vol.69, p.85012, 2004.

S. Ferrara, A. Kehagias, and D. Lüst, Aspects of Weyl Supergravity. JHEP, vol.08, p.197, 2018.

M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond, vol.173, pp.211-232, 1939.

D. Gaiotto and J. Maldacena, The Gravity duals of N=2 superconformal field theories, JHEP, vol.10, p.189, 2012.

D. Gaiotto and E. Witten, S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory, Adv. Theor. Math. Phys, vol.13, issue.3, pp.721-896, 2009.

P. Gao, D. L. Jafferis, and A. Wall, Traversable Wormholes via a Double Trace Deformation, JHEP, vol.12, p.151, 2017.

F. F. Gautason, M. Schillo, T. Van-riet, and M. Williams, Remarks on scale separation in flux vacua, JHEP, 2016.

G. W. Gibbons, M. B. Green, and M. J. Perry, Instantons and seven-branes in type IIB superstring theory, Phys. Lett, vol.370, pp.37-44, 1996.

S. Giombi and I. R. Klebanov, Interpolating between a and F, JHEP, vol.03, p.117, 2015.

J. Gomis and S. Lee, Exact Kahler Potential from Gauge Theory and Mirror Symmetry, JHEP, vol.04, p.19, 2013.

D. Green, Z. Komargodski, N. Seiberg, Y. Tachikawa, and B. Wecht, Exactly Marginal Deformations and Global Symmetries, JHEP, vol.06, p.106, 2010.

A. Hanany and N. Mekareeya, Complete Intersection Moduli Spaces in N=4 Gauge Theories in Three Dimensions, JHEP, vol.01, p.79, 2012.

A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and threedimensional gauge dynamics, Nucl. Phys, vol.492, pp.152-190, 1997.

S. F. Hassan and R. A. Rosen, Resolving the Ghost Problem in non-Linear Massive Gravity, Phys. Rev. Lett, vol.108, p.41101, 2012.

A. Higuchi, Forbidden Mass Range for Spin-2 Field Theory in De Sitter Space-time, Nucl. Phys, vol.282, pp.397-436, 1987.

K. Hinterbichler, Theoretical Aspects of Massive Gravity, Rev. Mod. Phys, vol.84, pp.671-710, 2012.

Y. Imamura and S. Yokoyama, Index for three dimensional superconformal field theories with general R-charge assignments, JHEP, vol.04, p.7, 2011.

A. Kenneth, N. Intriligator, and . Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett, vol.387, pp.513-519, 1996.

A. Kapustin, B. Willett, and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP, 2010.

A. Karch, E. Katz, and L. Randall, Absence of a VVDZ discontinuity in AdS(AdS), JHEP, vol.12, p.16, 2001.

A. Karch and L. Randall, Localized gravity in string theory, Phys. Rev. Lett, vol.87, p.61601, 2001.

A. Karch and L. Randall, Locally localized gravity, JHEP, p.140, 2000.

H. Kim, S. Kim, and K. Lee, 5-dim Superconformal Index with Enhanced En Global Symmetry, JHEP, vol.10, p.142, 2012.

J. Kinney, J. M. Maldacena, S. Minwalla, and S. Raju, An Index for 4 dimensional super conformal theories, Commun. Math. Phys, vol.275, pp.209-254, 2007.

E. Kiritsis, Product CFTs, gravitational cloning, massive gravitons and the space of gravitational duals, JHEP, vol.11, p.49, 2006.

E. Kiritsis and V. Niarchos, Interacting String Multi-verses and Holographic Instabilities of Massive Gravity, Nucl. Phys, vol.812, pp.488-524, 2009.
URL : https://hal.archives-ouvertes.fr/in2p3-00714909

I. I. Kogan, The m -¿ 0 limit for massive graviton in dS(4) and AdS(4): How to circumvent the van Dam-Veltman-Zakharov discontinuity, Stavros Mouslopoulos, and Antonios Papazoglou, vol.503, pp.173-180, 2001.

H. Tom and . Koornwinder, q-special functions, a tutorial. arXiv preprint math/9403216, 1994.

G. Robert, M. J. Leigh, and . Strassler, Exactly marginal operators and duality in four-dimensional N=1 supersymmetric gauge theory, Nucl. Phys, vol.447, pp.95-136, 1995.

J. Louis and H. Triendl, Maximally supersymmetric AdS 4 vacua in N = 4 supergravity, JHEP, vol.10, p.7, 2014.

Y. Lozano, N. T. Macpherson, J. Montero, and C. Nunez, Threedimensional N = 4 linear quivers and non-Abelian T-duals, JHEP, vol.11, p.133, 2016.

J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys, vol.61, pp.781-811, 2013.

J. Martin-maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys, vol.38, p.231, 1998.

J. Martin-maldacena and A. Strominger, AdS(3) black holes and a stringy exclusion principle, JHEP, vol.12, p.5, 1998.

J. Mcgreevy, L. Susskind, and N. Toumbas, Invasion of the giant gravitons from Anti-de Sitter space, JHEP, 2000.

N. A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys, vol.7, issue.5, pp.831-864, 2003.

T. Nishioka, Y. Tachikawa, and M. Yamazaki, 3d Partition Function as Overlap of Wavefunctions, JHEP, 2011.

S. Pasquetti, Factorisation of N = 2 Theories on the Squashed 3-Sphere, JHEP, vol.04, p.120, 2012.

V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys, vol.313, pp.71-129, 2012.

M. Porrati, No van Dam-Veltman-Zakharov discontinuity in AdS space, Phys. Lett, vol.498, pp.92-96, 2001.

M. Porrati, Higgs phenomenon for 4-D gravity in anti-de Sitter space, JHEP, vol.04, p.58, 2002.

M. Porrati, Higgs phenomenon for the graviton in ADS space, Mod. Phys. Lett, vol.18, pp.1793-1802, 2003.

L. Rastelli and S. S. Razamat, The Superconformal Index of Theories of Class S, New Dualities of Supersymmetric Gauge Theories, pp.261-305, 2016.

S. S. Razamat and B. Willett, Down the rabbit hole with theories of class S, JHEP, vol.10, p.99, 2014.

A. Schmidt, -. , and M. V. Strauss, Recent developments in bimetric theory, J. Phys, vol.49, issue.18, p.183001, 2016.

N. Seiberg and E. Witten, Gauge dynamics and compactification to threedimensions, The mathematical beauty of physics: A memorial volume for Claude Itzykson. Proceedings, Conference, pp.333-366, 1996.

I. Tamm, Die verallgemeinerten Kugelfunktionen und die Wellenfunktionen eines Elektrons im Felde eines Magnetpoles, Z. Phys, vol.71, issue.3-4, pp.141-150, 1931.

D. Tsimpis, Supersymmetric AdS vacua and separation of scales, JHEP, vol.08, p.142, 2012.
URL : https://hal.archives-ouvertes.fr/in2p3-00712412

A. I. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett, vol.39, pp.393-394, 1972.

R. Van-breukelen and K. Papadodimas, Quantum teleportation through time-shifted AdS wormholes, JHEP, vol.08, p.142, 2018.

H. Van-dam and M. J. Veltman, Massive and massless Yang-Mills and gravitational fields, Nucl. Phys, vol.22, pp.397-411, 1970.

S. Weinberg, The Cosmological Constant Problem, Rev. Mod. Phys, vol.61, pp.1-23, 1988.

B. Willett, Localization on three-dimensional manifolds, J. Phys, vol.50, issue.44, p.443006, 2017.

E. Witten, Topological Quantum Field Theory, Commun. Math. Phys, vol.117, p.353, 1988.

E. Witten, Multitrace operators, boundary conditions, and AdS / CFT correspondence, 2001.