Holographic Normal Ordering and Multi-particle States in the AdS/CFT Correspondence

The general correlator of composite operators of N=4 supersymmetric gauge field theory is divergent. We introduce a means for renormalizing these correlators by adding a boundary theory on the AdS space correcting for the divergences. Such renormalizations are not equivalent to the standard normal ordering of current algebras in two dimensions. The correlators contain contact terms that contribute to the OPE; we relate them diagrammatically to correlation functions of compound composite operators dual to multi-particle states.Comment: 18 pages, one equation corr., further comments and refs. adde

Four-point Functions of Lowest Weight CPOs in N=4 SYM_4 in Supergravity Approximation

We show that the recently found quartic action for the scalars from the massless graviton multiplet of type IIB supergravity compactified on AdS_5\times S^5 background coincides with the relevant part of the action of the gauged N=8 5d supergravity on AdS_5. We then use this action to compute the 4-point function of the lowest weight chiral primary operators \tr(\phi^{(i}\phi^{j)}) in N=4 SYM_4 at large $N$ and at strong `t Hooft coupling.Comment: Latex, 21p, misprints are correcte

On the number of representations providing noiseless subsystems

This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and also has applications to the understanding of quantum decoherence. We prove that for Hilbert spaces of sufficiently high dimension, decoherence-free subspaces exist for almost all representations of the error algebra. For decoherence-free subsystems, we plot the function $f_d(n)$ which is the fraction of all $d$-dimensional quantum systems which preserve $n$ bits of information through DF subsystems, and note that this function fits an inverse beta distribution. The mathematical tools which arise include techniques from classical number theory.Comment: 17 pp, 4 figs, accepted for Physical Review

Topological Quantum Compiling

A method for compiling quantum algorithms into specific braiding patterns for non-Abelian quasiparticles described by the so-called Fibonacci anyon model is developed. The method is based on the observation that a universal set of quantum gates acting on qubits encoded using triplets of these quasiparticles can be built entirely out of three-stranded braids (three-braids). These three-braids can then be efficiently compiled and improved to any required accuracy using the Solovay-Kitaev algorithm.Comment: 20 pages, 20 figures, published versio

Protected gates for topological quantum field theories

We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators --- for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically-local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons; in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.Comment: 50 pages, many figures, v3: updated to match published versio

Conjecture on Hidden Superconformal Symmetry of N=4 Supergravity

We argue that the observed UV finiteness of the 3-loop extended supergravities may be a manifestation of a hidden local superconformal symmetry of supergravity. We focus on the SU(2,2|4) dimensionless superconformal model. In Poincare gauge where the compensators are fixed to phi^2= 6 M_P^2 this model becomes a pure classical N=4 Einstein supergravity. We argue that in N=4 the higher-derivative superconformal invariants like phi^{-4}W^2 \bar W^2 and the consistent local anomaly delta (ln phi W^2) are not available. This conjecture on hidden local N=4 superconformal symmetry of Poincare supergravity may be supported by subsequent loop computations.Comment: 14 p A discussion of half-maximal D=6 superconformal models is adde

Bosonic Quadratic Actions for 11D Supergravity on AdS_7/4 x S_4/7

We determine from 11D supergravity the quadratic bulk action for the physical bosonic fields relevant for the computation of correlation functions of normalized chiral operators in D=6, N=(0,2) and D=3, N=8 supersymmetric CFT in the large N limit, as dictated by the AdS/CFT duality conjecture.Comment: 16 pages, Plain TeX, no figures, requires AMS font files amssym.def and amssym.tex, a few typos correcte

Solution to the 3-loop Φ\Phi-derivable Approximation for Scalar Thermodynamics

We solve the 3-loop $\Phi$-derivable approximation to the thermodynamics of the massless $\phi^4$ field theory by reducing it to a 1-parameter variational problem. The thermodynamic potential is expanded in powers of $g^2$ and $m/T$, where $g$ is the coupling constant, $m$ is a variational mass parameter, and $T$ is the temperature. There are ultraviolet divergences beginning at 6th order in $g$ that cannot be removed by renormalization. However the finite thermodynamic potential obtained by truncating after terms of 5th order in $g$ and $m/T$ defines a stable approximation to the thermodynamic functions.Comment: 4 pages, 1 figur

Universal properties of superconformal OPEs for 1/2 BPS operators in 3≤D≤63\leq D \leq 6

We give a general analysis of OPEs of 1/2 BPS superfield operators for the $D=3,4,5,6$ superconformal algebras OSp(8/4,R), PSU(2,2), F${}_4$ and OSp($8^*/4$) which underlie maximal AdS supergravity in $4\leq D+1\leq 7$. \\ The corresponding three-point functions can be formally factorized in a way similar to the decomposition of a generic superconformal UIR into a product of supersingletons. This allows for a simple derivation of branching rules for primary superfields. The operators of protected conformal dimension which may appear in the OPE are classified and are shown to be either 1/2 or 1/4 BPS, or semishort. As an application, we discuss the "non-renormalization" of extremal $n$-point correlators.Comment: To be published in NJP Focus Issue: Supersymmetry in condensed matter and high energy physic