AdS Dual of the Critical O(N) Vector Model

AdS Dual of the Critical O(N) Vector Model

October 2002 | I. R. Klebanov and A. M. Polyakov
This paper proposes a duality between large N conformal field theories in d dimensions containing N-component vector fields and theories of infinite number of higher-spin massless gauge fields in AdS_{d+1}. Specifically, it suggests that the singlet sector of the critical 3-d O(N) model with the (ϕ^aϕ^a)^2 interaction is dual, in the large N limit, to the minimal bosonic theory in AdS_4 containing massless gauge fields of even spin. The authors argue that the correspondence between free CFTs of matrix-valued fields and higher-spin massless gauge theories is a remarkable conjecture, and they use a similar statement for free vector-valued fields in Section 2. They note that theories of Fradkin-Vasiliev type do contain enough fields to be dual to large N field theories where elementary fields are in the fundamental rather than adjoint representation. In this case, the only possible class of “single-trace” operators are ϕ^a∂^lϕ^a whose number does not grow with the dimension. This roughly matches the number of fields found in theories of Fradkin-Vasiliev type. Therefore, a massless higher-spin gauge theory in AdS_{d+1} may capture the dynamics of such singlet currents. The authors also discuss the operator products at large N and the correspondence between the 3-d O(N) model and the AdS_4 theory. They show that the correlation functions of the singlet currents in the free 3-d theory may be obtained from the bulk action in AdS_4 through the usual AdS/CFT prescription. They also discuss the implications of this duality for the 4-point function and the role of higher-spin currents in reproducing the OPE of the critical O(N) vector model. The paper concludes with a discussion of possible extensions of the duality and the implications for higher-spin theories in AdS space.This paper proposes a duality between large N conformal field theories in d dimensions containing N-component vector fields and theories of infinite number of higher-spin massless gauge fields in AdS_{d+1}. Specifically, it suggests that the singlet sector of the critical 3-d O(N) model with the (ϕ^aϕ^a)^2 interaction is dual, in the large N limit, to the minimal bosonic theory in AdS_4 containing massless gauge fields of even spin. The authors argue that the correspondence between free CFTs of matrix-valued fields and higher-spin massless gauge theories is a remarkable conjecture, and they use a similar statement for free vector-valued fields in Section 2. They note that theories of Fradkin-Vasiliev type do contain enough fields to be dual to large N field theories where elementary fields are in the fundamental rather than adjoint representation. In this case, the only possible class of “single-trace” operators are ϕ^a∂^lϕ^a whose number does not grow with the dimension. This roughly matches the number of fields found in theories of Fradkin-Vasiliev type. Therefore, a massless higher-spin gauge theory in AdS_{d+1} may capture the dynamics of such singlet currents. The authors also discuss the operator products at large N and the correspondence between the 3-d O(N) model and the AdS_4 theory. They show that the correlation functions of the singlet currents in the free 3-d theory may be obtained from the bulk action in AdS_4 through the usual AdS/CFT prescription. They also discuss the implications of this duality for the 4-point function and the role of higher-spin currents in reproducing the OPE of the critical O(N) vector model. The paper concludes with a discussion of possible extensions of the duality and the implications for higher-spin theories in AdS space.
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