Abstract
We study new supergravity solutions related to large-N c \( \mathcal{N} = 1 \) supersymmetric gauge field theories with a large number N f of massive flavors. We use a recently proposed framework based on configurations with N c color D5 branes and a distribution of N f flavor D5 branes, governed by a function N f S(r). Although the system admits many solutions, under plausible physical assumptions the relevant solution is uniquely determined for each value of x ≡ N f /N c . In the IR region, the solution smoothly approaches the deformed Maldacena-Núñez solution. In the UV region it approaches a linear dilaton solution. For x < 2 the gauge coupling β g function computed holographically is negative definite, in the UV approaching the NSVZ β function with anomalous dimension γ 0 = −1/2 (approaching − 3/(32π 2)(2N c − N f )g 3)), and with β g → −∞ in the IR. For x = 2, β g has a UV fixed point at strong coupling, suggesting the existence of an IR fixed point at a lower value of the coupling. We argue that the solutions with x > 2 describe a “Seiberg dual” picture where N f − 2N c flips sign.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena and C.Núñez, Towards the large-N limit of pure N = 1 super Yang-Mills, Phys. Rev. Lett. 86 (2001) 588 [hep-th/0008001] [SPIRES].
A.H. Chamseddine and M.S. Volkov, Non-abelian BPS monopoles in N = 4 gauged supergravity, Phys. Rev. Lett. 79 (1997) 3343 [hep-th/9707176] [SPIRES].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [SPIRES].
R. Casero, C. Núñez and A. Paredes, Towards the string dual of N = 1 SQCD-like theories, Phys. Rev. D 73 (2006) 086005 [hep-th/0602027] [SPIRES].
R. Casero, C. Núñez and A. Paredes, Elaborations on the string dual to N = 1 SQCD, Phys. Rev. D 77 (2008) 046003 [arXiv:0709.3421] [SPIRES].
C. Hoyos-Badajoz, C. Núñez and I. Papadimitriou, Comments on the string dual to N = 1 SQCD, Phys. Rev. D 78 (2008) 086005 [arXiv:0807.3039] [SPIRES].
A. Paredes, On unquenched N = 2 holographic flavor, JHEP 12 (2006) 032 [hep-th/0610270] [SPIRES].
G. Bertoldi, F. Bigazzi, A.L. Cotrone and J.D. Edelstein, Holography and unquenched quark-gluon plasmas, Phys. Rev. D 76 (2007) 065007 [hep-th/0702225] [SPIRES].
E. Caceres, R. Flauger, M. Ihl and T. Wrase, New supergravity backgrounds dual to N = 1 SQCD-like theories with N f = 2N c , JHEP 03 (2008) 020 [arXiv:0711.4878] [SPIRES].
E. Conde, J. Gaillard and A.V. Ramallo, On the holographic dual of N = 1 SQCD with massive flavors, arXiv:1107.3803 [SPIRES].
T. Appelquist, K.D. Lane and U. Mahanta, On the ladder approximation for spontaneous chiral symmetry breaking, Phys. Rev. Lett. 61 (1988) 1553 [SPIRES].
T. Appelquist, A.G. Cohen and M. Schmaltz, A new constraint on strongly coupled field theories, Phys. Rev. D 60 (1999) 045003 [hep-th/9901109] [SPIRES].
J. Braun and H. Gies, Chiral phase boundary of QCD at finite temperature, JHEP 06 (2006) 024 [hep-ph/0602226] [SPIRES].
J. Braun and H. Gies, Scaling laws near the conformal window of many-flavor QCD, JHEP 05 (2010) 060 [arXiv:0912.4168] [SPIRES].
T.A. Ryttov and F. Sannino, Supersymmetry inspired QCD β-function, Phys. Rev. D 78 (2008) 065001 [arXiv:0711.3745] [SPIRES].
E. Poppitz and M. Ünsal, Conformality or confinement (II): one-flavor CFTs and mixed-representation QCD, JHEP 12 (2009) 011 [arXiv:0910.1245] [SPIRES].
T. Appelquist, G.T. Fleming and E.T. Neil, Lattice study of the conformal Window in QCD-like Theories, Phys. Rev. Lett. 100 (2008) 171607 [Erratum ibid. 102 (2009) 149902] [arXiv:0712.0609].
T. Appelquist, G.T. Fleming and E.T. Neil, Lattice study of conformal behavior in SU(3) Yang-Mills theories, Phys. Rev. D 79 (2009) 076010 [arXiv:0901.3766] [SPIRES].
A. Hasenfratz, Scaling properties of many-fermion systems from MCRG studies, PoS(LAT2009)052 [arXiv:0911.0646] [SPIRES].
A. Hasenfratz, Investigating the critical properties of beyond-QCD theories using Monte Carlo Renormalization Group matching, Phys. Rev. D 80 (2009) 034505 [arXiv:0907.0919] [SPIRES].
A. Hasenfratz, Investigating the critical properties of beyond-QCD theories using Monte Carlo Renormalization Group matching, Phys. Rev. D 80 (2009) 034505 [arXiv:0907.0919] [SPIRES].
A. Hasenfratz, Scaling properties of many-fermion systems from MCRG studies, PoS(LAT2009)052 [arXiv:0911.0646] [SPIRES].
A. Deuzeman, M.P. Lombardo and E. Pallante, Evidence for a conformal phase in SU(N) gauge theories, Phys. Rev. D 82 (2010) 074503 [arXiv:0904.4662] [SPIRES].
A. Deuzeman, M.P. Lombardo and E. Pallante, The physics of eight flavours, Phys. Lett. B 670 (2008) 41 [arXiv:0804.2905] [SPIRES].
Z. Fodor, K. Holland, J. Kuti, D. Nogradi and C. Schroeder, Twelve massless flavors and three colors below the conformal window, Phys. Lett. B 703 (2011) 348 [arXiv:1104.3124] [SPIRES].
A. Armoni, The conformal window from the worldline formalism, Nucl. Phys. B 826 (2010) 328 [arXiv:0907.4091] [SPIRES].
V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Exact Gell-Mann-Low function of supersymmetric Yang-Mills theories from instanton calculus, Nucl. Phys. B 229 (1983) 381 [SPIRES].
P. Di Vecchia, A. Lerda and P. Merlatti, N = 1 and N = 2 super Yang-Mills theories from wrapped branes, Nucl. Phys. B 646 (2002) 43 [hep-th/0205204] [SPIRES].
M. Bertolini and P. Merlatti, A note on the dual of N = 1 super Yang-Mills theory, Phys. Lett. B 556 (2003) 80 [hep-th/0211142] [SPIRES].
A.G. Cohen and H. Georgi, Walking beyond the rainbow, Nucl. Phys. B 314 (1989) 7 [SPIRES].
T. Banks and A. Zaks, On the phase structure of vector-like gauge theories with massless fermions, Nucl. Phys. B 196 (1982) 189 [SPIRES].
D.B. Kaplan, J.-W. Lee, D.T. Son and M.A. Stephanov, Conformality lost, Phys. Rev. D 80 (2009) 125005 [arXiv:0905.4752] [SPIRES].
P. Koerber and D. Tsimpis, Supersymmetric sources, integrability and generalized-structure compactifications, JHEP 08 (2007) 082 [arXiv:0706.1244] [SPIRES].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [SPIRES].
M.J. Strassler, The duality cascade, hep-th/0505153 [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1107.4002
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Barranco, A., Pallante, E. & Russo, J.G. \( \mathcal{N} = 1 \) SQCD-like theories with N f massive flavors from AdS/CFT and β functions. J. High Energ. Phys. 2011, 86 (2011). https://doi.org/10.1007/JHEP09(2011)086
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2011)086