Thank you for visiting nature.

You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

After exactly half a century of Anderson localization 1the subject is more alive than ever. Direct observation of Anderson localization of electrons was always hampered by interactions and finite temperatures. Yet, many theoretical breakthroughs were made, highlighted by finite-size scaling 2the self-consistent theory 3 and the numerical solution of the Anderson tight-binding model 45.

Theoretical understanding is based on simplified models or approximations and comparison with experiment is crucial. Despite a wealth of new experimental data, with microwaves and light 6789101112ultrasound 13 and cold atoms 141516many questions remain, especially for three dimensions.

Here, we report the first observation of sound localization in a random three-dimensional elastic network. The data are well described by the self-consistent theory of localization.

The transmission reveals non-Gaussian statistics, consistent with theoretical predictions. Most text books on condensed matter explain that the electronic states in disordered conductors are extended plane or Bloch waves with finite lifetimes. This offers a mechanism to explain the widely observed metalâ€”insulator transitions Scaling theory proposes a single parameter, the Thouless conductance gto describe the anomalous length dependence of the resistance of a sample 2. Although these ideas were first proposed for electron localization, in the early s interest in classical-wave localization was raised 1819with the promise of avoiding the difficulties caused by interactions in electronic systems.

Here, we demonstrate Anderson localization of ultrasound in a three-dimensional 3D medium. Our samples are single-component random networks made by brazing aluminium beads together, see Fig. With ultrasound, we probe the vibrational excitations of the network in the intermediate frequency regime 0.

We use pulsed techniques to measure the amplitude transmission coefficient, shown in Fig. The transmission spectrum exhibits a succession of bandgaps and pass bands, due to the overlapping resonances of the aluminium beads Our study focuses on frequencies just below the first bandgap at 0. Around 0. The samples were made from 4. In previous reports on Anderson localization with classical waves, absorption has been a major obstacle to reaching unambiguous conclusions 781011 The following experiment is capable of probing Anderson localization without being blurred by absorption.

We measure the spatially and time-resolved transmitted intensity through our sample.We show that recently proposed free boundary conditions for AdS 3 are dual to two-dimensional quantum gravity in certain fixed gauges. In particular, we note that an appropriate identification of the generator of Virasoro transformations leads to a vanishing total central charge in agreement with the theory at the boundary.

We argue that this identification is necessary to match the bulk and boundary generators of Virasoro transformations and for consistency with the constraint equations.

N2 - We show that recently proposed free boundary conditions for AdS3 are dual to two-dimensional quantum gravity in certain fixed gauges. AB - We show that recently proposed free boundary conditions for AdS3 are dual to two-dimensional quantum gravity in certain fixed gauges. Luis Apolo, Massimo Porrati. Overview Fingerprint. Abstract We show that recently proposed free boundary conditions for AdS 3 are dual to two-dimensional quantum gravity in certain fixed gauges.

Access to Document Link to publication in Scopus. Link to citation list in Scopus. Journal of High Energy Physics3[]. Apolo L, Porrati M. Journal of High Energy Physics.

### Donate to arXiv

Apolo, Luis ; Porrati, Massimo. In: Journal of High Energy Physics.HEP Experiments. Learn more. Justin R. David Bangalore, Indian Inst. Published in: JHEP 03 DOI: Citations per year 2 7 5 1. Abstract: Springer.

Note: 28 pages. Chern-Simons Theories Conformal Field Theory Supersymmetric gauge theory space: noncompact field theory: conformal symmetry: conformal anti-de Sitter partition function supersymmetry: 2 localization. References Figures 0. Two-dimensional gauge theories revisited Edward Witten Princeton U. Seiberg-Witten prepotential from instanton counting Nikita A. Andrei Okounkov Princeton U.

Localization of gauge theory on a four-sphere and supersymmetric Wilson loops Vasily Pestun Princeton U. Maxim Zabzine Uppsala U. Tudor Dimofte Perimeter Inst. Thomas T. Dumitrescu Harvard U. A 50 44 Advanced Study.

Nathan Seiberg Princeton, Inst. JHEP 06 Exploring Curved Superspace Thomas T. Dumitrescu Princeton U. Guido Festuccia Princeton, Inst. JHEP 08 Alberto Zaffaroni Milan Bicocca U.Typically, the story is presented as follows. Now consider the action for a bulk scalardual to some primary operator in the CFT:.

The on-shell equations of motion yield the familiar Klein-Gordon equation. This is a second-order differential equation with two independent solutions, whose leading behaviour as one approaches the boundary at scale likewhere are given by. For compactness, we shall henceforth set the AdS radius. The general solution to the Klein-Gordon equation in the limit may therefore be expressed as a linear combination of these solutions, with coefficients and :.

## On the Boundary Conditions in Deformed Quantum Mechanics with Minimal Length Uncertainty

Note that the condition imposes a limit on the allowed mass of the bulk field, namely that. This is known as the Breitenlohner-Freedman BF bound. Furthermore, if one integrates the action 2 from to the cutoff atthe result will be finite fori. Thus is a solution for all masses above the BF bound. Forthe situation is slightly more subtle. One can show that the boundary term obtained by integrating 2 by parts is non-zero only if ; i. And in this case, the bulk integral up to the cutoff is finite only forwhich corresponds to the restricted mass range.

The upper limit is called the unitarity bound, since the limit corresponds to the constraint, from unitarity, on the representation of conformal field theories.

Hence for masses below the unitarity bound but above the BF bound, of courseone may choose either orwhich implies two different bulk theories for the same CFT. More on this below. Slightly more technical details can be found in section 5. This appears to be based on the observation that, since by definition, the second term dominates in the limit, which requires that one set in order that the solution be normalizableâ€”though as remarked above, this is clearly not the full story in the mass range 6.

Sometimes, an attempt is made to justify this identification by the observation that one can multiply through bywhereupon one sees that. In accordance with the extrapolate dictionary, this indeed suggests that sources the bulk field. But it does not explain why should be identified as the boundary dual of this bulk field; that is, it does not explain why and should be related in the CFT action as.

Furthermore, it does not follow from the fact that the bulk coefficient has the correct conformal dimension as the boundary source field and that both will be set to zero on-shell that the two must be identified: this may be aesthetically suggestive, but it is by no means logically necessary.

Some clarification is found in the classic paper by Klebanov and Witten [2]. They observe that the extrapolate dictionary â€” or what one would identify, in more modern language, as the HKLL prescription for bulk reconstruction â€” can be written.

Choosing then implies that in order to be consistent with 5we must identifyand. We then recognize the position-space Green functionwhence.

**Can AdS/CFT See the Black Hole Interior? - Joe Polchinski**

That is, recall that the generating function can be written in terms of the Feynman propagator as. Of course, setting causes the one-point function to vanish on-shell. The fact that we set the sources to zero resolves the apparent tension between setting for normalizability, and simultaneously having it appear in 12 : the expansion 5 was obtained by solving the equations of motion, so we only have on-shell.

Thus we see that the bulk-boundary correspondence in the form 9 provides the extra constraint needed to relate the coefficients and in the expansion 5 as vev of operator and source, respectively, and that choosing the alternative boundary condition simply interchanges these roles.

It is an interesting and under-appreciated fact that any holographic CFT therefore admits two different bulk duals, i. The above essentially summarizes the basic story for the usual case, i. However, the question I encountered during my research that actually motivated this post is what happens to these boundary conditions in the presence of a double-trace deformation.

If the coupling is irrelevantthen the deformation does not change the effective field theory, since it only plays a role in high-energy correlators. However, if the coupling is relevantthen the perturbation induces a flow into the IR.

And it turns out that the boundary conditions change from in the UV to in the IR as a result.We investigate the properties of the background gauge field configurations that act as disorder for the Anderson localization mechanism in the Dirac spectrum of QCD at high temperatures.

The dependence of these observations on the boundary conditions of the valence operator is studied. We also investigate the spatial overlap of the left-handed and right-handed projected eigenmodes in correlation with the localization and the corresponding eigenvalue. We discuss an interpretation of the results in terms of monopole-instanton structures. Download to read the full article text. Aoki, G. Endrodi, Z. Fodor, S. Katz and K. Banks and A. Pittler, Anderson Localization in quark-gluon PlasmaPhys.

D 86 [ arXiv Giordano, T. Verbaarschot and T. Bruckmann, T. Kovacs and S. Schierenberg, Anderson localization through Polyakov loops: lattice evidence and Random matrix modelPhys. D 84 [ arXiv Katz, T. Giordano and F. Garcia-Garcia and J. Osborn, Chiral phase transition and anderson localization in the instanton liquid model for QCDNucl. Kovacs and F. Aoki and Y. Taniguchi, Chiral properties of domain wall fermions from eigenvalues of four-dimensional Wilson-Dirac operatorPhys.

Golterman and Y. Bilgici et al. Prasad and C. Bogomolny, Stability of Classical SolutionsSov. Brower, H. Neff and K. Orginos, Mobius fermionsNucl. Morningstar and M. Hashimoto et al. Cossu et al. D 93 [ arXiv Ujfalusi, M. Giordano, F. Pittler, T. Varga, Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperaturePhys.July 9, feature.

A team of researchers at the University of Maryland has recently explored the potential of this theoretical construct in cosmology studies. Antonini and his colleague Brian Swingle asked themselves whether it was possible to describe the evolution of a cosmological universe using this theoretical construct, which had so far primarily been applied to other research topics. The researchers' study builds on ideas proposed in a previous paper by Swingle and other researchers, published in Springer Link's Journal of High Energy Physics.

This past study explored the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a particular structure that terminated at an end-of-the-world ETW brane. In string theory and other related physics theories, a brane is a dynamical object that can propagate through spacetime in accordance with quantum mechanics laws.

In the presence of a large black hole, however, this 'gravity localization' phenomenon is particularly troublesome to obtain. The model proposed by Antonini and his colleagues suggests that under appropriate conditions and for part of its evolution process, a brane sits far away from a black hole horizon and moves slowly.

The researchers showed that in this particular regime, a gravitational perturbation remains locally bound to the brane. This is because the perturbation is 'trapped' by a negative delta potential, which arises from the Neumann boundary conditions in the place where the brane is positioned. In other words, in this regime a hypothetical 4-D observer would interpret gravity to be 4-dimensional, as long as they do not try to probe very large spatial scales.

Secondly, we found that gravity is, indeed, locally localized on such brane-worlds. The ideas presented by Antonini and Swingle could ultimately open up new possibilities for describing quantum cosmology phenomena and simulating these on quantum computers. Explore further. More from Other Physics Topics. Your feedback will go directly to Science X editors. Thank you for taking your time to send in your valued opinion to Science X editors.

You can be assured our editors closely monitor every feedback sent and will take appropriate actions. Your opinions are important to us. We do not guarantee individual replies due to extremely high volume of correspondence.

## Researchers apply the anti-de Sitter/conformal field theory to cosmology

Learn more Your name Note Your email address is used only to let the recipient know who sent the email. Neither your address nor the recipient's address will be used for any other purpose.

The information you enter will appear in your e-mail message and is not retained by Phys. You can unsubscribe at any time and we'll never share your details to third parties. More information Privacy policy.

This site uses cookies to assist with navigation, analyse your use of our services, and provide content from third parties. By using our site, you acknowledge that you have read and understand our Privacy Policy and Terms of Use.We find the coordinate space wave functions, maximal localization states, and quasiposition wave functions in a GUP framework that implies a minimal length uncertainty using a formally self-adjoint representation. We show how the boundary conditions in quasiposition space can be exactly determined from the boundary conditions in coordinate space.

This idea in the context of the Generalized Gravitational Uncertainty Principle GUP has attracted much attention in recent years and many papers have appeared in the literature to address the effects of this minimal length on various quantum mechanical systems [ 1 â€” 14 ]. In fact, since the increase of the energies to probe small distances considerably disturbs the spacetime structure because of the gravitational effects, the spatial uncertainty eventually increases at energy scales as large as the Planck scale.

This minimal length can be considered as a fundamental property of quantum spacetime, a natural UV regulator, and a solution for the trans-Planckian problem. Since the string theory with large or warped extra dimensions can lower the Planck scale into the TeV range, this fundamental length scale also moved into the reach of the Large Hadron Collider. The thought experiments that support the minimal length proposal include the Heisenberg microscope with Newtonian gravity and its relativistic counterpart [ 15 ], limit to distance measurements [ 16 ], limit to clock synchronization, and limit to the measurement of the blackhole horizon [ 4 ].

Moreover, different approaches to quantum gravity such as string theory, loop quantum gravity, and loop quantum cosmology, quantized conformal fluctuations [ 1718 ], asymptotically safe gravity [ 19 ], and noncommutative geometry all indicate a fundamental limit to the resolution of structure.

As Adler and Santiago observed this GUP is invariant under and therefore has a momentum inversion symmetry. Because of the universality of the gravity, this correction modifies all Hamiltonians for the quantum systems near the Planck scale. Recently, an experimental scheme is suggested by Pikovski et al. They used quantum optical control and optical interferometric techniques for direct measurement of the canonical commutator deformations of a massive object.

This experiment does not need the Planck-scale accuracy of position measurement and can be reached by the current technology. Some attempts have been also made to test possible quantum gravitational phenomena using astronomical observations [ 2223 ]. In this paper, we consider a GUP that implies a minimal length uncertainty proportional to the Planck length. We find the exact coordinate space wave functions and quasiposition space wave functions using a formally self-adjoint representation.

We first obtain the eigenfunctions of the position operator and the maximal localization states. Then we discuss how the boundary conditions can be imposed consistently in both coordinate space and quasiposition space.

### Twisting and localization in supergravity: equivariant cohomology of BPS black holes

Consider the following one-dimensional deformed commutation relation [ 13 ]: where for we recover the well-known commutation relation in ordinary quantum mechanics and. Since cannot be made arbitrarily small, the absolutely smallest uncertainty in positions for this GUP is. To proceed further, consider the following representation [ 11 ]: which exactly satisfies 2.

This representation is formally self-adjoint subject to the inner product: and preserves the ordinary nature of the position operator. The operator with dense domain is self-adjoint if and. However, for the position operator in the momentum space, we have where vanishes at and takes arbitrary values at the boundaries.

## Boundary conditions and localization on ads