Abstract
We examine the AdS-CFT dual of arbitrary (non)supersymmetric fermionic mass deformations of \( \mathcal{N} \) = 4 SYM, and investigate how the backreaction of the RR and NS-NS two-form potentials dual to the fermion masses contribute to Coulomb-branch potential of D3 branes, which we interpret as the bulk boson mass matrix. Using representation theory and supergravity arguments we show that the fermion masses completely determine the trace of this matrix, and that on the other hand its traceless components have to be turned on as non-normalizable modes. Our result resolves the tension between the belief that the AdS bulk dual of the trace of the boson mass matrix (which is not a chiral operator) is a stringy excitation with dimension of order (g s N )1/4 and the existence of non-stringy supergravity flows describing theories where this trace is nonzero, by showing that the stringy mode does not parameterize the sum of the squares of the boson masses but rather its departure from the trace of the square of the fermion mass matrix. Hence, asymptotically-AdS flows can only describe holographically theories where the sums of the squares of the bosonic and fermionic masses are equal, which is consistent with the weakly-coupled result that only such theories can have a conformal UV fixed point.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [INSPIRE].
R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].
R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys. B 460 (1996) 299 [hep-th/9510101] [INSPIRE].
D.Z. Freedman and J.A. Minahan, Finite temperature effects in the supergravity dual of the N = 1* gauge theory, JHEP 01 (2001) 036 [hep-th/0007250] [INSPIRE].
H.J. Kim, L.J. Romans and P. van Nieuwenhuizen, The mass spectrum of chiral N = 2 D = 10 supergravity on S 5, Phys. Rev. D 32 (1985) 389 [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Renormalization group flows from holography supersymmetry and a c theorem, Adv. Theor. Math. Phys. 3 (1999) 363 [hep-th/9904017] [INSPIRE].
L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, The supergravity dual of N = 1 super Yang-Mills theory, Nucl. Phys. B 569 (2000) 451 [hep-th/9909047] [INSPIRE].
K. Pilch and N.P. Warner, N = 2 supersymmetric RG flows and the IIB dilaton, Nucl. Phys. B 594 (2001) 209 [hep-th/0004063] [INSPIRE].
N.J. Evans and M. Petrini, AdS RG flow and the super Yang-Mills cascade, Nucl. Phys. B 592 (2001) 129 [hep-th/0006048] [INSPIRE].
K. Pilch and N.P. Warner, N = 1 supersymmetric renormalization group flows from IIB supergravity, Adv. Theor. Math. Phys. 4 (2002) 627 [hep-th/0006066] [INSPIRE].
A. Khavaev and N.P. Warner, A Class of N = 1 supersymmetric RG flows from five-dimensional N = 8 supergravity, Phys. Lett. B 495 (2000) 215 [hep-th/0009159] [INSPIRE].
F. Bigazzi, A.L. Cotrone, M. Petrini and A. Zaffaroni, Supergravity duals of supersymmetric four-dimensional gauge theories, Riv. Nuovo Cim. 25N12 (2002) 1 [hep-th/0303191] [INSPIRE].
R. Apreda, D.E. Crooks, N.J. Evans and M. Petrini, Confinement, glueballs and strings from deformed AdS, JHEP 05 (2004) 065 [hep-th/0308006] [INSPIRE].
C.N. Gowdigere and N.P. Warner, Holographic Coulomb branch flows with N = 1 supersymmetry, JHEP 03 (2006) 049 [hep-th/0505019] [INSPIRE].
A. Buchel and C. Pagnutti, Bulk viscosity of N = 2∗ plasma, Nucl. Phys. B 816 (2009) 62 [arXiv:0812.3623] [INSPIRE].
M. Taylor, Anomalies, counterterms and the N = 0 Polchinski-Strassler solutions, hep-th/0103162 [INSPIRE].
I. Bena, M. Graña, S. Kuperstein, P. Ntokos and M. Petrini, D3-brane model building and the supertrace rule, Phys. Rev. Lett. 116 (2016) 141601 [arXiv:1510.07039] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χ SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
C. Hoyos, S. Paik and L.G. Yaffe, Screening in strongly coupled N = 2∗ supersymmetric Yang-Mills plasma, JHEP 10 (2011) 062 [arXiv:1108.2053] [INSPIRE].
I. Bena, M. Graña, S. Kuperstein and S. Massai, Tachyonic anti-M 2 Branes, JHEP 06 (2014) 173 [arXiv:1402.2294] [INSPIRE].
I. Bena, M. Graña, S. Kuperstein and S. Massai, Giant tachyons in the landscape, JHEP 02 (2015) 146 [arXiv:1410.7776] [INSPIRE].
S. Kachru, J. Pearson and H.L. Verlinde, Brane/flux annihilation and the string dual of a nonsupersymmetric field theory, JHEP 06 (2002) 021 [hep-th/0112197] [INSPIRE].
I. Bena and S. Kuperstein, Brane polarization is no cure for tachyons, JHEP 09 (2015) 112 [arXiv:1504.00656] [INSPIRE].
R. Slansky, Group theory for unified model building, Phys. Rept. 79 (1981) 1 [INSPIRE].
M. Graña and J. Polchinski, Supersymmetric three form flux perturbations on AdS 5, Phys. Rev. D 63 (2001) 026001 [hep-th/0009211] [INSPIRE].
F. Zamora, Nonsupersymmetric SO(3) invariant deformations of N = 1∗ vacua and their dual string theory description, JHEP 12 (2000) 021 [hep-th/0007082] [INSPIRE].
S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
M. Graña, T.W. Grimm, H. Jockers and J. Louis, Soft supersymmetry breaking in Calabi-Yau orientifolds with D-branes and fluxes, Nucl. Phys. B 690 (2004) 21 [hep-th/0312232] [INSPIRE].
M. Graña, D3-brane action in a supergravity background: the fermionic story, Phys. Rev. D 66 (2002) 045014 [hep-th/0202118] [INSPIRE].
I. Bena, J. Blabäck and D. Turton, Brane effective actions for anti-D3 branes in Klabanov-Strassler, to appear.
I. Jack and D.R.T. Jones, Nonstandard soft supersymmetry breaking, Phys. Lett. B 457 (1999) 101 [hep-ph/9903365] [INSPIRE].
S.P. Martin and M.T. Vaughn, Two loop renormalization group equations for soft supersymmetry breaking couplings, Phys. Rev. D 50 (1994) 2282 [Erratum ibid. D 78 (2008) 039903] [hep-ph/9311340] [INSPIRE].
I. Jack and D.R.T. Jones, Soft supersymmetry breaking and finiteness, Phys. Lett. B 333 (1994) 372 [hep-ph/9405233] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1512.00011
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Bena, I., Graña, M., Kuperstein, S. et al. Fermionic and bosonic mass deformations of \( \mathcal{N} \) = 4 SYM and their bulk supergravity dual. J. High Energ. Phys. 2016, 149 (2016). https://doi.org/10.1007/JHEP05(2016)149
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2016)149