Abstract
We consider circular non-BPS Maldacena-Wilson loops in five-dimensional supersymmetric Yang-Mills theory (d = 5 SYM) both as macroscopic strings in the D4- brane geometry and directly in gauge theory. We find that in the Dp-brane geometries for increasing p, p = 4 is the last value for which the radius of the string worldsheet describing the Wilson loop is independent of the UV cut-off. It is also the last value for which the area of the worldsheet can be (at least partially) regularized by the standard Legendre transformation. The asymptotics of the string worldsheet allow the remaining divergence in the regularized area to be determined, and it is found to be logarithmic in the UV cut- off. We also consider the M2-brane in AdS7 × S 4 which is the M-theory lift of the Wilson loop, and dual to a “Wilson surface” in the (2,0), d = 6 CFT. We find that it has exactly the same logarithmic divergence in its regularized action. The origin of the divergence has been previously understood in terms of a conformal anomaly for surface observables in the CFT. Turning to the gauge theory, a similar picture is found in d = 5 SYM. The divergence and its coefficient can be recovered by summing the leading divergences in the analytic continuation of dimensional regularization of planar rainbow/ladder diagrams. These diagrams are finite in 5 − ϵ dimensions. The interpretation is that the Wilson loop is renormalized by a factor containing this leading divergence of six-dimensional origin, and also subleading divergences, and that the remaining part of the Wilson loop expectation value is a finite, scheme-dependent quantity. We substantiate this claim by showing that the interacting diagrams at one loop are finite in our regularization scheme in d = 5 dimensions, but not for d ≥ 6.
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References
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
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] [INSPIRE].
J. Erickson, G. Semenoff and K. Zarembo, Wilson loops in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 582 (2000) 155 [hep-th/0003055] [INSPIRE].
N. Drukker and D.J. Gross, An exact prediction of N = 4 SUSYM theory for string theory, J. Math. Phys. 42 (2001) 2896 [hep-th/0010274] [INSPIRE].
N. Drukker, J. Plefka and D. Young, Wilson loops in 3-dimensional N = 6 supersymmetric Chern-Simons theory and their string theory duals, JHEP 11 (2008) 019 [arXiv:0809.2787] [INSPIRE].
N. Drukker and D. Trancanelli, A supermatrix model for N = 6 super Chern-Simons-matter theory, JHEP 02 (2010) 058 [arXiv:0912.3006] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, arXiv:0712.2824 [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact results for Wilson loops in superconformal Chern-Simons theories with matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
M. Mariño and P. Putrov, Exact results in ABJM theory from topological strings, JHEP 06 (2010) 011 [arXiv:0912.3074] [INSPIRE].
N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys. 306 (2011) 511 [arXiv:1007.3837] [INSPIRE].
N. Drukker and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02 (2005) 010 [hep-th/0501109] [INSPIRE].
J. Gomis and F. Passerini, Holographic Wilson loops, JHEP 08 (2006) 074 [hep-th/0604007] [INSPIRE].
J. Gomis and F. Passerini, Wilson loops as D3-branes, JHEP 01 (2007) 097 [hep-th/0612022] [INSPIRE].
S.A. Hartnoll and S. Kumar, Higher rank Wilson loops from a matrix model, JHEP 08 (2006) 026 [hep-th/0605027] [INSPIRE].
S.A. Hartnoll, Two universal results for Wilson loops at strong coupling, Phys. Rev. D 74 (2006) 066006 [hep-th/0606178] [INSPIRE].
S. Yamaguchi, Wilson loops of anti-symmetric representation and D5-branes, JHEP 05 (2006) 037 [hep-th/0603208] [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Gravity duals of half-BPS Wilson loops, JHEP 06 (2007) 063 [arXiv:0705.1004] [INSPIRE].
S. Yamaguchi, Bubbling geometries for half BPS Wilson lines, Int. J. Mod. Phys. A 22 (2007) 1353 [hep-th/0601089] [INSPIRE].
O. Lunin, On gravitational description of Wilson lines, JHEP 06 (2006) 026 [hep-th/0604133] [INSPIRE].
N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].
A. Agarwal and D. Young, Supersymmetric Wilson loops in diverse dimensions, JHEP 06 (2009) 063 [arXiv:0904.0455] [INSPIRE].
K. Zarembo, Supersymmetric Wilson loops, Nucl. Phys. B 643 (2002) 157 [hep-th/0205160] [INSPIRE].
N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev. D 60 (1999) 125006 [hep-th/9904191] [INSPIRE].
N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, M5-branes, D4-branes and quantum 5D super-Yang-Mills, JHEP 01 (2011) 083 [arXiv:1012.2882] [INSPIRE].
M.R. Douglas, On D = 5 super Yang-Mills theory and (2, 0) theory, JHEP 02 (2011) 011 [arXiv:1012.2880] [INSPIRE].
C. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence, Nucl. Phys. B 546 (1999) 52 [hep-th/9901021] [INSPIRE].
M. Henningson and K. Skenderis, Weyl anomaly for Wilson surfaces, JHEP 06 (1999) 012 [hep-th/9905163] [INSPIRE].
A. Gustavsson, On the Weyl anomaly of Wilson surfaces, JHEP 12 (2003) 059 [hep-th/0310037] [INSPIRE].
A. Gustavsson, Conformal anomaly of Wilson surface observables: a field theoretical computation, JHEP 07 (2004) 074 [hep-th/0404150] [INSPIRE].
S. Bolognesi and K. Lee, Instanton partons in 5-dim SU(N ) gauge theory, Phys. Rev. D 84 (2011) 106001 [arXiv:1106.3664] [INSPIRE].
S. Bolognesi and K. Lee, 1/4 BPS string junctions and N 3 problem in 6-dim (2, 0) superconformal theories, Phys. Rev. D 84 (2011) 126018 [arXiv:1105.5073] [INSPIRE].
A. Gustavsson, A preliminary test of Abelian D4-M5 duality, Phys. Lett. B 706 (2011) 225 [arXiv:1111.6339] [INSPIRE].
A. Jevicki, Y. Kazama and T. Yoneya, Generalized conformal symmetry in D-brane matrix models, Phys. Rev. D 59 (1999) 066001 [hep-th/9810146] [INSPIRE].
J. Frenkel and J. Taylor, NonAbelian eikonal exponentiation, Nucl. Phys. B 246 (1984) 231 [INSPIRE].
J. Gatheral, Exponentiation of eikonal cross-sections in nonAbelian gauge theories, Phys. Lett. B 133 (1983) 90 [INSPIRE].
R.A. Brandt, F. Neri and M.-a. Sato, Renormalization of loop functions for all loops, Phys. Rev. D 24 (1981) 879 [INSPIRE].
A.M. Polyakov, Gauge fields as rings of glue, Nucl. Phys. B 164 (1980) 171 [INSPIRE].
R. Corrado, B. Florea and R. McNees, Correlation functions of operators and Wilson surfaces in the D = 6, (0, 2) theory in the large-N limit, Phys. Rev. D 60 (1999) 085011 [hep-th/9902153] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [INSPIRE].
T. Wiseman and B. Withers, Holographic renormalization for coincident Dp-branes, JHEP 10 (2008) 037 [arXiv:0807.0755] [INSPIRE].
C.-S. Chu and D. Giataganas, UV-divergences of Wilson loops for gauge/gravity duality, JHEP 12 (2008) 103 [arXiv:0810.5729] [INSPIRE].
D.E. Berenstein, R. Corrado, W. Fischler and J.M. Maldacena, The operator product expansion for Wilson loops and surfaces in the large-N limit, Phys. Rev. D 59 (1999) 105023 [hep-th/9809188] [INSPIRE].
D. Young, BPS Wilson loops on S 2 at higher loops, JHEP 05 (2008) 077 [arXiv:0804.4098] [INSPIRE].
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ArXiv ePrint: 1112.3309
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Young, D. Wilson loops in five-dimensional Super-Yang-Mills. J. High Energ. Phys. 2012, 52 (2012). https://doi.org/10.1007/JHEP02(2012)052
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DOI: https://doi.org/10.1007/JHEP02(2012)052