TY - JOUR

T1 - AdS/CFT correspondence and symmetry breaking

AU - Klebanov, Igor R.

AU - Witten, Edward

N1 - Funding Information:
We are grateful to A. Ceresole, G. Dall'Agata, D. Freedman, S. Gubser, E Kraus, E Larsen, V. Periwal and L. Rastelli for useful comments. The work of I.R.K. was supported in part by the NSF grant PHY-9802484 and by the James S. McDonnell Foundation Grant No. 91-48. The work of E.W. is supported in part by NSF grant PHY-9513835.

PY - 1999/9/6

Y1 - 1999/9/6

N2 - We study, using the dual AdS description, the vacua of field theories where some of the gauge symmetry is broken by expectation values of scalar fields. In such vacua, operators built out of the scalar fields acquire expectation values, and we show how to calculate them from the behavior of perturbations to the AdS background near the boundary. Specific examples include the N = 4 SYM theory, and theories on D3-branes placed on orbifolds and conifolds. We also clarify some subtleties of the AdS/CFT correspondence that arise in this analysis. In particular, we explain how scalar fields in AdS space of sufficiently negative mass-squared can be associated with CFT operators of two possible dimensions. All dimensions are bounded from below by (d - 2)/2; this is the unitarity bound for scalar operators in d-dimensional field theory. We further argue that the generating functional for correlators in the theory with one choice of operator dimension is a Legendre transform of the generating functional in the theory with the other choice.

AB - We study, using the dual AdS description, the vacua of field theories where some of the gauge symmetry is broken by expectation values of scalar fields. In such vacua, operators built out of the scalar fields acquire expectation values, and we show how to calculate them from the behavior of perturbations to the AdS background near the boundary. Specific examples include the N = 4 SYM theory, and theories on D3-branes placed on orbifolds and conifolds. We also clarify some subtleties of the AdS/CFT correspondence that arise in this analysis. In particular, we explain how scalar fields in AdS space of sufficiently negative mass-squared can be associated with CFT operators of two possible dimensions. All dimensions are bounded from below by (d - 2)/2; this is the unitarity bound for scalar operators in d-dimensional field theory. We further argue that the generating functional for correlators in the theory with one choice of operator dimension is a Legendre transform of the generating functional in the theory with the other choice.

KW - Anti-de sitter space

KW - Conical singularities

KW - Infrared fixed points

KW - String theory

KW - Supersymmetric Yang-Mills theory

KW - Threebranes

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U2 - 10.1016/S0550-3213(99)00387-9

DO - 10.1016/S0550-3213(99)00387-9

M3 - Article

AN - SCOPUS:0033530062

SN - 0550-3213

VL - 556

SP - 89

EP - 114

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 1-2

ER -