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On 1-loop diagrams in AdS space and the random disorder problem
High Energy Physics - Theory · Submitted 15 Jul 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Applying our methods to compute the effects of a time-dependent impurity to the conductivities using the replica trick in AdS/CFT, we find that generally an IR-relevant disorder reduces the conductivity and that in the extreme low frequency limit the correction due to the impurities overwhelms the planar CFT result even though it is supposedly $1/N^2$ suppressed.
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The abstract, sentence by sentence
We study the complex scalar loop corrections to the boundary-boundary gauge two point function in pure AdS space in Poincare coordinates, in the presence of a boundary quadratic perturbation to the scalar. These perturbations correspond to double trace perturbations in the dual CFT and modify the boundary conditions of the bulk scalars in AdS. We find that, in addition to the usual UV divergences, the 1-loop calculation suffers from a divergence originating in the limit as the loop vertices approach the AdS horizon. We show that this type of divergence is independent of the boundary coupling, and making use of which we extract the finite relative variation of the imaginary part of the loop via Cutkosky rules as the boundary perturbation varies. Applying our methods to compute the effects of a time-dependent impurity to the conductivities using the replica trick in AdS/CFT, we find that generally an IR-relevant disorder reduces the conductivity and that in the extreme low frequency limit the correction due to the impurities overwhelms the planar CFT result even though it is supposedly $1/N^2$ suppressed. Comments on the effect of time-independent impurity in such a system are presented.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the complex scalar loop corrections to the boundary-boundary gauge two point function in pure AdS space in Poincare coordinates, in the presence of a boundary quadratic perturbation to the scalar. | contribution 1.00 | 0.91 | 0.04 | asserted 0.86 |
| s1 | These perturbations correspond to double trace perturbations in the dual CFT and modify the boundary conditions of the bulk scalars in AdS. | background 0.64 | 0.19 | 0.04 | asserted 1.00 |
| s2 | We find that, in addition to the usual UV divergences, the 1-loop calculation suffers from a divergence originating in the limit as the loop vertices approach the AdS horizon. | result 1.00 | 0.96 | 0.16 | asserted 1.00 |
| s3 | We show that this type of divergence is independent of the boundary coupling, and making use of which we extract the finite relative variation of the imaginary part of the loop via Cutkosky rules as the boundary perturbation varies. | method 0.38 | 0.95 | 0.14 | asserted 1.00 |
| s4 | Applying our methods to compute the effects of a time-dependent impurity to the conductivities using the replica trick in AdS/CFT, we find that generally an IR-relevant disorder reduces the conductivity and that in the extreme low frequency limit the correction due to the impurities overwhelms the planar CFT result even though it is supposedly $1/N^2$ suppressed. | result 0.99 | 0.95 | 0.54 | asserted 1.00 |
| s5 | Comments on the effect of time-independent impurity in such a system are presented. | contribution 0.78 | 0.50 | 0.03 | unclear 0.92 |
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The paper
Original abstract
We study the complex scalar loop corrections to the boundary-boundary gauge two point function in pure AdS space in Poincare coordinates, in the presence of a boundary quadratic perturbation to the scalar. These perturbations correspond to double trace perturbations in the dual CFT and modify the boundary conditions of the bulk scalars in AdS. We find that, in addition to the usual UV divergences, the 1-loop calculation suffers from a divergence originating in the limit as the loop vertices approach the AdS horizon. We show that this type of divergence is independent of the boundary coupling, and making use of which we extract the finite relative variation of the imaginary part of the loop via Cutkosky rules as the boundary perturbation varies. Applying our methods to compute the effects of a time-dependent impurity to the conductivities using the replica trick in AdS/CFT, we find that generally an IR-relevant disorder reduces the conductivity and that in the extreme low frequency limit the correction due to the impurities overwhelms the planar CFT result even though it is supposedly $1/N^2$ suppressed. Comments on the effect of time-independent impurity in such a system are presented.
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How the literature uses it
5 arXiv papers cite this in 9 sentences
Papers citing it · 6 sentences without a confident label
Uses its method or tool 1 paper
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Another way to see this is to proceed as in [ref] by using the analytic continuation of the series expansion of the Bessel functions
Deep inelastic scattering off scalar mesons in the 1/N expansion from the D3D7-brane system · Integrals of products of Bessel functions · 0.98
Compares with it 1 paper
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Some of the diagrams shown in Fig. [ref] are similar to the 1-loop diagrams considered in [ref] , but milder since only one of the vertices of the “loop” needs to be integrated throughout the AdS bulk.
Correlation functions in the holographic replica method · The sub-leading contributions and a new holographic replica method? · 0.99
Cites it as background 1 paper
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Another motivation of this setup is a possibility of constructing a holographic dual of a system with impurities (for earlier works from different viewpoints see [ref] ).
Probing AdS Wormholes by Entanglement Entropy · Holographic Conductivity · 0.80
What it cites · 40 sentences without a confident label
Uses the method or tool of 2 papers
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Using the folding trick that treats these replicated bosons as if they live in the same AdS space [ref] we can thus apply techniques discussed in the previous sections to compute the conductivities in the presence of random disorder.
The CFT/AdS correspondence, massive gravitons and a connectivity index conjecture · The replica trick and the conductivities · 0.98
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While we concentrated our effort toward studying the imaginary part of the diagrams, which is of particular interest physically and can be readily extracted via a simple generalization of Cutkosky rules [ref] , we found that in Poincare coordinates these loops suffer from extra divergences shared by both the real and imaginary parts of the diagram, arising when the vertices of the diagrams are pushed toward the AdS horizon simultaneously and the geodesic distance between them shrinks to zero.
The large $N_c$ limit of four-point functions in N=4 super-Yang-Mills theory from anti-de Sitter Supergravity · Conclusion and discussion · 0.84
Compares with 1 paper
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One could check, as we demonstrate in Appendix [ref], that this representation agrees with the bulk-to-bulk propagator in [ref] obtained in the Euclidean signature, which simply means $k^2$ is positive in ([ref]).
Double-trace operators and one-loop vacuum energy in AdS/CFT · Scalar propagators of mixed boundary conditions · 0.98
Cites as background 11 papers
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AdS/CFT correspondence [ref] has proven itself an extremely powerful tool in extending our understanding of strongly coupled quantum field theories, stretching its influence into many different realms of physics.
Anti De Sitter Space And Holography · Introduction · 1.00
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AdS/CFT correspondence [ref] has proven itself an extremely powerful tool in extending our understanding of strongly coupled quantum field theories, stretching its influence into many different realms of physics.
The Large N Limit of Superconformal Field Theories and Supergravity · Introduction · 1.00
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AdS/CFT correspondence [ref] has proven itself an extremely powerful tool in extending our understanding of strongly coupled quantum field theories, stretching its influence into many different realms of physics.
Gauge Theory Correlators from Non-Critical String Theory · Introduction · 1.00
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