Abstract
We study the stability of some classical string worldsheet solutions employed for computing the potential energy between two static fundamental quarks in confining and non-confining gravity duals. We discuss the fixing of the diffeomorphism invariance of the string action, its relation with the fluctuation orientation and the interpretation of the quark mass substraction worldsheet needed for computing the potential energy in smooth (confining) gravity background. We consider various dual gravity backgrounds and show by a numerical analysis the existence of instabilities under linear fluctuations for classical string embedding solutions having positive length function derivative L′(r 0) > 0. Finally we make a brief discussion of ’t Hooft loops in non-conformal backgrounds.
Similar content being viewed by others
References
K.G. Wilson, Confinement of quarks, Phys. Rev. D 10 (1974) 2445 [SPIRES].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
A.M. Polyakov, String theory and quark confinement, Nucl. Phys. Proc. Suppl. 68 (1998) 1 [hep-th/9711002] [SPIRES].
A.M. Polyakov, The wall of the cave, Int. J. Mod. Phys. A 14 (1999) 645 [hep-th/9809057] [SPIRES].
S.J. Rey and J.T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and Anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [SPIRES].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [SPIRES].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [SPIRES].
G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B 72 (1974) 461 [SPIRES].
J. Sonnenschein, What does the string/gauge correspondence teach us about Wilson loops?, hep-th/0003032 [SPIRES].
Y. Kinar, E. Schreiber and J. Sonnenschein, Q anti-Q potential from strings in curved spacetime: classical results, Nucl. Phys. B 566 (2000) 103 [hep-th/9811192] [SPIRES].
D.J. Gross and H. Ooguri, Aspects of large-N gauge theory dynamics as seen by string theory, Phys. Rev. D 58 (1998) 106002 [hep-th/9805129] [SPIRES].
C.P. Herzog and I.R. Klebanov, On string tensions in supersymmetric SU(M) gauge theory, Phys. Lett. B 526 (2002) 388 [hep-th/0111078] [SPIRES].
J. Gomis and F. Passerini, Holographic Wilson loops, JHEP 08 (2006) 074 [hep-th/0604007] [SPIRES].
J. Gomis and F. Passerini, Wilson loops as D3-branes, JHEP 01 (2007) 097 [hep-th/0612022] [SPIRES].
S.S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [SPIRES].
I.R. Klebanov, J.M. Maldacena and C.B. Thorn, III, Dynamics of flux tubes in large-N gauge theories, JHEP 04 (2006) 024 [hep-th/0602255] [SPIRES].
J.J. Friess, S.S. Gubser, G. Michalogiorgakis and S.S. Pufu, Stability of strings binding heavy-quark mesons, JHEP 04 (2007) 079 [hep-th/0609137] [SPIRES].
S.D. Avramis, K. Sfetsos and K. Siampos, Stability of strings dual to flux tubes between static quarks in N = 4 SYM, Nucl. Phys. B 769 (2007) 44 [hep-th/0612139] [SPIRES].
S.D. Avramis, K. Sfetsos and K. Siampos, Stability of string configurations dual to quarkonium states in AdS/CFT, Nucl. Phys. B 793 (2008) 1 [arXiv:0706.2655] [SPIRES].
K. Sfetsos and K. Siampos, Stability issues with baryons in AdS/CFT, JHEP 08 (2008) 071 [arXiv:0807.0236] [SPIRES].
S.-J. Rey, S. Theisen and J.-T. Yee, Wilson-Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity, Nucl. Phys. B 527 (1998) 171 [hep-th/9803135] [SPIRES].
A. Brandhuber, N. Itzhaki, J. Sonnenschein and S. Yankielowicz, Wilson loops in the large-N limit at finite temperature, Phys. Lett. B 434 (1998) 36 [hep-th/9803137] [SPIRES].
C.G. Callan, Jr. and A. Guijosa, Undulating strings and gauge theory waves, Nucl. Phys. B 565 (2000) 157 [hep-th/9906153] [SPIRES].
Y. Kinar, E. Schreiber, J. Sonnenschein and N. Weiss, Quantum fluctuations of Wilson loops from string models, Nucl. Phys. B 583 (2000) 76 [hep-th/9911123] [SPIRES].
S. Förste, D. Ghoshal and S. Theisen, Stringy corrections to the Wilson loop in N = 4 super Yang-Mills theory, JHEP 08 (1999) 013 [hep-th/9903042] [SPIRES].
N. Drukker, D.J. Gross and A.A. Tseytlin, Green-Schwarz string in AdS 5 × S 5 : semiclassical partition function, JHEP 04 (2000) 021 [hep-th/0001204] [SPIRES].
P.C. Argyres, M. Edalati and J.F. Vazquez-Poritz, No-drag string configurations for steadily moving quark-antiquark pairs in a thermal bath, JHEP 01 (2007) 105 [hep-th/0608118] [SPIRES].
A. Brandhuber and K. Sfetsos, Wilson loops from multicentre and rotating branes, mass gaps and phase structure in gauge theories, Adv. Theor. Math. Phys. 3 (1999) 851 [hep-th/9906201] [SPIRES].
F. Bigazzi, A.L. Cotrone, C. Nunez and A. Paredes, Heavy quark potential with dynamical flavors: a first order transition, Phys. Rev. D 78 (2008) 114012 [arXiv:0806.1741] [SPIRES];
F. Bigazzi, A.L. Cotrone, A. Paredes and A.V. Ramallo, The Klebanov-Strassler model with massive dynamical flavors, JHEP 03 (2009) 153 [arXiv:0812.3399] [SPIRES].
C. Bachas, Convexity of the quarkonium potential, Phys. Rev. D 33 (1986) 2723 [SPIRES].
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].
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] [SPIRES].
A. Loewy and J. Sonnenschein, On the holographic duals of N = 1 gauge dynamics, JHEP 08 (2001) 007 [hep-th/0103163] [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].
C. Vafa, Superstrings and topological strings at large-N, J. Math. Phys. 42 (2001) 2798 [hep-th/0008142] [SPIRES].
M. Bertolini, Four lectures on the gauge/gravity correspondence, Int. J. Mod. Phys. A 18 (2003) 5647 [hep-th/0303160] [SPIRES].
E. Imeroni, The gauge/string correspondence towards realistic gauge theories, hep-th/0312070 [SPIRES].
A. Paredes, Supersymmetric solutions of supergravity from wrapped branes, hep-th/0407013 [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.H. Chamseddine and M.S. Volkov, Non-abelian solitons in N = 4 gauged supergravity and leading order string theory, Phys. Rev. D 57 (1998) 6242 [hep-th/9711181] [SPIRES].
C. Núñez, M. Piai and A. Rago, Wilson loops in string duals of walking and flavored systems, arXiv:0909.0748 [SPIRES].
M.J. Strassler, The duality cascade, hep-th/0505153 [SPIRES].
G. ’t Hooft, On the phase transition towards permanent quark confinement, Nucl. Phys. B 138 (1978) 1 [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].
C.P. Herzog, I.R. Klebanov and P. Ouyang, Remarks on the warped deformed conifold, hep-th/0108101 [SPIRES].
R.C. Brower, C.-I. Tan and C.B. Thorn, String/flux tube duality on the lightcone, Phys. Rev. D 73 (2006) 124037 [hep-th/0603256] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 0911.0662
Rights and permissions
About this article
Cite this article
Arias, R.E., Silva, G.A. Wilson loops stability in the gauge/string correspondence. J. High Energ. Phys. 2010, 23 (2010). https://doi.org/10.1007/JHEP01(2010)023
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2010)023