Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence
By E. Witten. 2001
388 citations recorded by the source corpus.
We argue that multi-trace interactions in quantum eld theory on the boundary of AdS space can be incorporated in the AdS/CFT correspondence by using a more general boundary condition for the bulk elds than has been considered hitherto. We illustrate the procedure for a renormalizable four-dimensional eld theory with a (Tr 2 ) 2 interaction. In this example, we show how the AdS elds with the appropriate boundary condition reproduce the renormalization group eects found in the boundary eld theory. We also construct in related examples a line of xed points with a nonperturbative duality and a flow between two methods of quantization.
Subfields: Astronomy and Astrophysics, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/418f120077f115e4970bc16a61129f322b29ea69
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Citations in the corpus
- Boundary conditions and dualities: vector fields in AdS/CFT (2006, background): “However, in this case the β = 0 theory is not precisely conformal [7].”
- Clean Time-Dependent String Backgrounds from Bubble Baths (2002, methodology): “The appearance of worldsheet non-locality here (and its connection to a boundary action) is very similar to its appearance in the discussion of multi-trace operators, related to multi-particle states in AdS, in [13] (and its interpretation in supergravity on AdS in terms of a boundary action [ 37 ])”
- `Double-trace' deformations, boundary conditions and spacetime singularities (2001, methodology): “Boundary conditions in AdS/CF T correspondence where recently discussed in [8]. In [ 9 ]”
- Integrating out geometry: holographic Wilsonian RG and the membrane paradigm (2010, background): “When we switch this operator on the fixed point corresponding to CFT d flows to the the CFT d in the IR [57].”
- Microscopic formulation of black holes in string theory (2002, background): “Multi-trace operators in the AdS/CFT correspondence has been discussed in [123, 124].”
- Semi-holographic Fermi liquids (2010, background): “the planar limit the RG flows induced by multi-trace operators (functions of gauge-singlet operators) are rather tame [25, 26, 27, 28].”
- Black holes with scalar hair and asymptotics in N = 8 supergravity (2004, background): “In particular, Witten has argued [32] they correspond to the addition of a term W [O′], so that after formally replacing O′ by its expectation value β in W one has”
- Holography in 4D (super) higher spin theories and a test via cubic scalar couplings (2003, background): “sentation, with the θ-expansion W= ϕ+iθψ¯ + θθ¯ 2i f, (4.11) and the constant c1 = 23/2πis chosen such that hOOi has unit strength. The N = 1 supersymmetric extension of the arguments given by Witten [18] suggests that the Bλ boundary condition corresponds to adding the double-trace deformation λ 2 ”
- SL(2;Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry (2003, background): “(This flow is described by the more general boundary condition α = fβ [22,23], where f is the coefficient of the relevant perturbation.”
- Holographic description of AdS cosmologies (2005, background): “In general, imposing nontrivial boundary conditions β(α) in the bulk corresponds to adding a multi-trace interaction ∫ W (O) to the CFT action, such that after formally replacing O by its expectation value α one has [21, 23] β = δW δα (3.”