Edge Dynamics in Quantum Hall Bilayers II: Exact Results with Disorder and Parallel Fields

We study edge dynamics in the presence of interlayer tunneling, parallel magnetic field, and various types of disorder for two infinite sequences of quantum Hall states in symmetric bilayers. These sequences begin with the 110 and 331 Halperin states and include their fractional descendants at lower filling factors; the former is easily realized experimentally while the latter is a candidate for the experimentally observed quantum Hall state at a total filling factor of 1/2 in bilayers. We discuss the experimentally interesting observables that involve just one chiral edge of the sample and the correlation functions needed for computing them. We present several methods for obtaining exact results in the presence of interactions and disorder which rely on the chiral character of the system. Of particular interest are our results on the 331 state which suggest that a time-resolved measurement at the edge can be used to discriminate between the 331 and Pfaffian scenarios for the observed quantum Hall state at filling factor 1/2 in realistic double-layer systems.Comment: revtex+epsf; two-up postscript at http://www.sns.ias.edu/~leonid/ntwoup.p

N=4 SYM to Two Loops: Compact Expressions for the Non-Compact Symmetry Algebra of the su(1,1|2) Sector

We begin a study of higher-loop corrections to the dilatation generator of N=4 SYM in non-compact sectors. In these sectors, the dilatation generator contains infinitely many interactions, and therefore one expects very complicated higher-loop corrections. Remarkably, we find a short and simple expression for the two-loop dilatation generator. Our solution for the non-compact su(1,1|2) sector consists of nested commutators of four O(g) generators and one simple auxiliary generator. Moreover, the solution does not require the planar limit; we conjecture that it is valid for any gauge group. To obtain the two-loop dilatation generator, we find the complete O(g^3) symmetry algebra for this sector, which is also given by concise expressions. We check our solution using published results of direct field theory calculations. By applying the expression for the two-loop dilatation generator to compute selected anomalous dimensions and the bosonic sl(2) sector internal S-matrix, we confirm recent conjectures of the higher-loop Bethe ansatz of hep-th/0412188.Comment: 28 pages, v2: additional checks against direct field theory calculations, references added, minor corrections, v3: additional minor correction

Dual Spikes; New Spiky String Solutions

We find a new class of spiky solutions for closed strings in flat, $AdS_3\subset AdS_5$ and $R\times S^2(\subset S^5)$ backgrounds. In the flat case the new solutions turn out to be T-dual configurations of spiky strings found by Kruczenski hep-th/0410226. In the case of solutions living in $AdS$, we make a semi classical analysis by taking the large angular momentum limit. The anomalous dimension for these dual spikes is similar to that for rotating and pulsating circular strings in AdS with angular momentum playing the role of the level number. This replaces the well known logarithmic dependence for spinning strings. For the dual spikes living on sphere we find that no large angular momentum limit exists.Comment: Added reference

The algebra of flat currents for the string on AdS_5 x S^5 in the light-cone gauge

We continue the program initiated in hep-th/0411200 and calculate the algebra of the flat currents for the string on AdS_5 x S^5 background in the light-cone gauge with kappa-symmetry fixed. We find that the algebra has a closed form and that the non-ultralocal terms come with a weight factor e^{\phi} that depends on the radial AdS_5 coordinate. Based on results in two-dimensional sigma models coupled to gravity via the dilaton field, this suggests that the algebra of transition matrices in the present case is likely to be unambigous.Comment: 27 pages, references added, version published in JHE

Integrable twists in AdS/CFT

A class of marginal deformations of four-dimensional N=4 super Yang-Mills theory has been found to correspond to a set of smooth, multiparameter deformations of the S^5 target subspace in the holographic dual on AdS_5 x S^5. We present here an analogous set of deformations that act on global toroidal isometries in the AdS_5 subspace. Remarkably, certain sectors of the string theory remain classically integrable in this larger class of so-called gamma-deformed AdS_5 x S^5 backgrounds. Relying on studies of deformed su(2)_gamma models, we formulate a local sl(2)_gamma Lax representation that admits a classical, thermodynamic Bethe equation (based on the Riemann-Hilbert interpretation of Bethe's ansatz) encoding the spectrum in the deformed AdS_5 geometry. This result is extended to a set of discretized, asymptotic Bethe equations for the twisted string theory. Near-pp-wave energy spectra within sl(2)_gamma and su(2)_gamma sectors provide a useful and stringent test of such equations, demonstrating the reliability of this technology in a wider class of string backgrounds. In addition, we study a twisted Hubbard model that yields certain predictions of the dual beta-deformed gauge theory.Comment: v2: references and clarifications added, 46 page

Is string theory a theory of quantum gravity?

Some problems in finding a complete quantum theory incorporating gravity are discussed. One is that of giving a consistent unitary description of high-energy scattering. Another is that of giving a consistent quantum description of cosmology, with appropriate observables. While string theory addresses some problems of quantum gravity, its ability to resolve these remains unclear. Answers may require new mechanisms and constructs, whether within string theory, or in another framework.Comment: Invited contribution for "Forty Years of String Theory: Reflecting on the Foundations," a special issue of Found. Phys., ed. by G 't Hooft, E. Verlinde, D. Dieks, S. de Haro. 32 pages, 5 figs., harvmac. v2: final version to appear in journal (small revisions

Critical behavior of weakly-disordered anisotropic systems in two dimensions

The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the so-called generalized Ashkin-Teller model (GATM) is studied. In the critical region this model is shown to be described by a multifermion field theory similar to the Gross-Neveu model with a few independent quartic coupling constants. Renormalization group calculations are used to obtain the temperature dependence near the critical point of some thermodynamic quantities and the large distance behavior of the two-spin correlation function. The equation of state at criticality is also obtained in this framework. We find that random models described by the GATM belong to the same universality class as that of the two-dimensional Ising model. The critical exponent $\nu$ of the correlation length for the 3- and 4-state random-bond Potts models is also calculated in a 3-loop approximation. We show that this exponent is given by an apparently convergent series in $\epsilon=c-\frac{1}{2}$ (with $c$ the central charge of the Potts model) and that the numerical values of $\nu$ are very close to that of the 2D Ising model. This work therefore supports the conjecture (valid only approximately for the 3- and 4-state Potts models) of a superuniversality for the 2D disordered models with discrete symmetries.Comment: REVTeX, 24 pages, to appear in Phys.Rev.

On Physical Equivalence between Nonlinear Gravity Theories

We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical. We explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system.Comment: 37 pp., TO-JLL-P 3/93 Dec 199

On the Feasibility of Unstructured Peer-to-Peer Information Retrieval

Abstract. We consider the feasibility of web-scale search in an unstructured peer-to-peer network. Since the network is unstructured, any such search is probabilistic in nature. We therefore adopt a probably approximately correct (PAC) search framework. The accuracy of such a search is defined by the overlap between the set of documents retrieved by a PAC search and the set of documents retrieved by an exhaustive (deterministic) search of the network. For an accuracy of 90%, we theoretically determine the number of nodes each query must be sent to for three distributions of documents in the network, namely uniform, proportional and square root. We assume that the query distribution follows a power law and investigate how performance is affected by the scale factor. For various configurations, we estimate the global and local network traffic induced by the search. For a network of 1 million nodes, a query rate of 1000 queries per second, and assuming each node is capable of indexing 0.1 % of the collection, our analysis indicates that the network traffic is less that 0.07 % of global internet traffic.

Cosmological production of charged black hole pairs

We investigate the pair creation of charged black holes in a background with a positive cosmological constant. We consider $C$ metrics with a cosmological constant, and show that the conical singularities in the metric only disappear when it reduces to the Reissner-Nordstr\"om de Sitter metric. We construct an instanton describing the pair production of extreme black holes and an instanton describing the pair production of non-extreme black holes from the Reissner-Nordstr\"om de Sitter metric, and calculate their actions. There are a number of striking similarities between these instantons and the Ernst instantons, which describe pair production in a background electromagnetic field. We also observe that the type I instanton in the ordinary $C$ metric with zero cosmological constant is actually the Reissner-Nordstr\"om solution.Comment: 29 pages, latex, 3 figures in a seperate uuencoded compressed file. Discussion of the significance of the instantons enlarged, and minor emendation