AdS-CFT Research Articles

Three-Point Functions of Aging Dynamics and the AdS-CFT Correspondence

Aging can be realized as a subalgebra of Schrödinger algebra by discarding the time-translation generator. While the two-point functions of the age algebra have been known for some time, little else was known about the higher n-point correlators. In this Letter, we present novel three-point correlators of scalar primary operators. We find that the aging correlators are distinct from the Schrödinger correlators by more than certain dressings with time-dependent factors, as was the case with two-point functions. In the existing literature, the holographic geometry of aging is obtained by performing certain general coordinate transformations on the holographic dual of the Schrödinger theory. Consequently, the aging two-point functions derived from holography look as the Schrödinger two-point functions dressed by time-dependent factors. However, since the three-point functions obtained in this Letter are not merely dressed Schrödinger correlators and instead, depend on an additional time-translation breaking variable, we conclude that the most general holographic realization of aging is yet to be found. We also comment on various extensions of the Schrödinger and aging algebras.

Local unit invariance, back-reacting tractors and the cosmological constant problem

When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of fields necessary to keep local unit invariance manifest). The relationship between these weights and masses is through the scalar curvature. As a consequence mass terms are spacetime dependent for off-shell gravitational backgrounds, but happily constant for physical, Einstein manifolds. Unfortunately this introduces a naturalness problem because the scalar curvature is proportional to the cosmological constant. By writing down tractor stress tensors (multiplets built from the standard stress tensor and its first and second derivatives), we show how back-reaction solves this naturalness problem. We also show that classical back-reaction generates an interesting potential for scalar fields. We speculate that a proper description of how physical systems couple to scale, could improve our understanding of naturalness problems caused by the disparity between the particle physics and observed, cosmological constants. We further give some ideas how an ambient description of tractor calculus could lead to a Ricci-flat/CFT correspondence which generalizes the AdS side of Maldacena's duality to a Ricci-flat space of one higher dimension.

De Broglie Deterministic Dice and emerging Relativistic Quantum Mechanics

Generalizing the de Broglie hypothesis of intrinsically periodic matter fields, it can be shown that the basic quantum behavior of ordinary field theory can be retrieved in a semi-classical and geometrical way. The geometrodynamical description of interactions that arises in this theory provides an intuitive interpretation of the Maldacena's conjecture and it turns out to be of the same type of the one prescribed by general relativity.

Perturbations of blackp-branes

We consider black $p$-brane solutions of the low energy string action, computing scalar perturbations. Using standard methods, we derive the wave equations obeyed by the perturbations and treat them analytically and numerically. We have found that tensorial perturbations obtained via a gauge-invariant formalism leads to the same results as scalar perturbations. No instability has been found. Asymptotically, these solutions typically reduce to a $AdS_{(p+2)}\times S^{(8-p)}$ space, which, in the framework of Maldacena's conjecture, can be regarded as a gravitational dual to a conformal field theory defined in a $(p+1)$-dimensional flat space-time. The results presented open the possibility of a better understanding the AdS/CFT correspondence, as originally formulated in terms of the relation among brane structures and gauge theories.

HOLOGRAPHY, GAUGE-GRAVITY CONNECTION AND BLACK HOLE ENTROPY

The issues of holography and possible links with gauge theories in spacetime physics is discussed, in an approach quite distinct from the more restricted AdS-CFT correspondence. A particular notion of holography in the context of black hole thermodynamics is derived (rather than conjectured) from rather elementary considerations, which also leads to a criterion of thermal stability of radiant black holes, without resorting to specific classical metrics. For black holes that obey this criterion, the canonical entropy is expressed in terms of the microcanonical entropy of an Isolated Horizon which is essentially a local generalization of the very global event horizon and is a null inner boundary of spacetime, with marginal outer trapping. It is argued why degrees of freedom on this horizon must be described by a topological gauge theory. Quantizing this boundary theory leads to the microcanonical entropy of the horizon expressed in terms of an infinite series asymptotic in the cross-sectional area, with the leading 'area-law' term followed by finite, unambiguously calculable corrections arising from quantum spacetime fluctuations.

Deviation from Alday–Maldacena duality for wavy circle

Alday–Maldacena conjecture is stated in this paper that the area A Π of the minimal surface in AdS 5 space with a boundary Π, located in Euclidean space at infinity of AdS 5 , coincides with a double integral D Π along Π, the Abelian Wilson average in an auxiliary dual model. This comes from Alday and Maldacena's original proposal and the BDS conjecture on the extrapolation of the MHV amplitudes. The boundary Π is a polygon formed by momenta of n external light-like particles in N = 4 SYM theory, and in a certain n = ∞ limit it can be substituted by an arbitrary smooth curve (wavy circle). The Alday–Maldacena conjecture is known to be violated for n > 5 , when it fails to be supported by the peculiar global dual conformal invariance, however, the structure of deviations remains obscure. The case of wavy lines can appear more convenient for analysis of these deviations due to the systematic method developed in [H. Itoyama, A. Mironov, A. Morozov, Anomaly in n = ∞ Alday–Maldacena duality for wavy circle, JHEP 0807 (2008) 024, arXiv:0803.1547] for (perturbative) evaluation of minimal areas, which is not yet available in the presence of angles at finite n. We correct a mistake in that paper and explicitly evaluate the h 2 h ¯ 2 terms, where the first deviation from the Alday–Maldacena duality arises for the wavy circle.

Negative energy, instability, and AdS–CFT This paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

We consider a freely orbifolded AdS5 × S5 and demonstrate that standard boundary conditions allow states of arbitrarily negative energy. These states describe bubbles that are regular up to singularities due to smeared D3-branes. We discuss the evolution of this data and point out that if the usual boundary conditions are enforced such bubbles may never reach infinity.

Black hole thermodynamics from simulations of lattice Yang-Mills theory

We report on lattice simulations of 16 supercharge $SU(N)$ Yang-Mills quantum mechanics in the 't Hooft limit. Maldacena duality conjectures that in this limit the theory is dual to IIA string theory, and, in particular, that the behavior of the thermal theory at low temperature is equivalent to that of certain black holes in IIA supergravity. Our simulations probe the low temperature regime for $N\ensuremath{\le}5$ and the intermediate and high temperature regimes for $N\ensuremath{\le}12$. We observe 't Hooft scaling, and at low temperatures our results are consistent with the dual black hole prediction. The intermediate temperature range is dual to the Horowitz-Polchinski correspondence region, and our results are consistent with continuous behavior there. We include the Pfaffian phase arising from the fermions in our calculations where appropriate.

Plumbing the abyss: black ring microstates

We construct the first smooth, horizonless ``microstate geometries'' that have the same charges, dipole charges and angular momenta as a BPS black ring whose horizon is macroscopic. These solutions have exactly the same geometry as black rings, except that the usual infinite throat is smoothly capped off at a very large depth. If the solutions preserve a U(1)x U(1) isometry, then this depth is limited by flux quantization but if this symmetry is broken then the throat can be made arbitrarily deep by tuning classical, geometric moduli. Interpreting these ``abysses'' (smooth microstate geometries of arbitrary depth) from the point of view of the AdS-CFT correspondence suggests two remarkable alternatives: either stringy effects can eliminate very large regions of a smooth low-curvature supergravity solution, or the D1-D5-P CFT has quantum critical points. The existence of solutions whose depth depends on moduli also enables us to define ``entropy elevators,'' and these provide a new tool for studying the entropy of BPS and near-BPS black holes.

Towards a worldsheet derivation of the Maldacena conjecture

A U(2, 2|4)-invariant A-model constructed from fermionic superfields has recently been proposed as a sigma model for the superstring on AdS5 × S5. After explaining the relation of this A-model with the pure spinor formalism, the A-model action is expressed as a gauged linear sigma model. In the zero radius limit, the Coulomb branch of this sigma model is interpreted as D-brane holes which are related to gauge-invariant = 4 d = 4 super-Yang-Mills operators. As in the worldsheet derivation of open-closed duality for Chern-Simons theory, this construction may lead to a worldsheet derivation of the Maldacena conjecture. Intriguing connections to the twistorial formulation of = 4 Yang-Mills are also noted.

A new limit of theAdS5×S5sigma model

Using the pure spinor formalism, a quantizable sigma model has been constructed for the superstring in an AdS_5 x S^5 background with manifest PSU(2,2|4) invariance. The PSU(2,2|4) metric g_{AB} has both vector components g_{ab} and spinor components g_{alpha beta}, and in the limit where the spinor components g_{alpha beta} are taken to infinity, the AdS_5 x S^5 sigma model reduces to the worldsheet action in a flat background. In this paper, we instead consider the limit where the vector components g_{ab} are taken to infinity. In this limit, the AdS_5 x S^5 sigma model simplifies to a topological A-model constructed from fermionic N=2 superfields whose bosonic components transform like twistor variables. Just as d=3 Chern-Simons theory can be described by the open string sector of a topological A-model, the open string sector of this topological A-model describes d=4 N=4 super-Yang-Mills. These results might be useful for constructing a worldsheet proof of the Maldacena conjecture analogous to the Gopakumar-Vafa-Ooguri worldsheet proof of Chern-Simons/conifold duality.

Numerical evidence for the Maldacena conjecture in two-dimensional super Yang–Mills theory

The N=(8,8) super Yang-Mills theory in 1+1 dimensions is solved at strong coupling to directly confirm the predictions of supergravity at weak coupling. The calculations are done in the large-N_c approximation using Supersymmetric Discrete Light-Cone Quantization. The stress-energy correlator is obtained as a function of the separation r; for intermediate values of r, the correlator behaves in a manner consistent with the 1/r^5 behavior predicted by weak-coupling supergravity.

LargeNreductions and holography

The large $N$ reductions in gauge theories are identified with dimensional reductions with homogeneous distribution of the eigenvalues of the gauge fields, and it is used to identify the corresponding closed string descriptions in the Maldacena duality. When one does not take the zero-radii limit, the large $N$ reductions are naturally extended to the equivalences between the gauge theories and the ``generalized'' reduced models, which naturally contain the notion of $T$-dual equivalence. In the dual gravitational description, $T$-duality relates two type IIB supergravity solutions, the near horizon geometry of $D3$-branes, and the near horizon geometry of $D$-instantons distributed densely and homogeneously on the dual torus. This is the holographic description of the generalized large $N$ reductions.

Energy radiated from a fluctuating selfdual string

We compute the energy that is radiated from a fluctuating selfdual string in the large $N$ limit of $A_{N-1}$ theory using the AdS-CFT correspondence. We find that the radiated energy is given by a non-local expression integrated over the string world-sheet. We also make the corresponding computation for a charged string in six-dimensional classical electrodynamics, thereby generalizing the Larmor formula for the radiated energy from an accelerated point particle.

From the QCD vacuum to (strongly coupled) quark-gluon plasma

I start with brief discussion of the role of topological objects in the QCD vacuum, reminding why instantons play a special role in chiral symmetry breaking and hadronic physics. Then I move to high temperature T > T c domain, describing briefly some experimental discoveries made at RHIC such as robust collective flow phenomena. They are well described by ideal hydrodynamics, with the Equation of State (EoS) in good agreement with that predicted by lattice simulations. However for hydro to work the transport properties of QGP should be quite remarkable. These and other theoretical developments, especially based on lattice simulations, indicate that matter produced at RHIC is a strongly coupled liquid, sQGP for short. Existence of “new spectroscopy” of states, most of them colored, is expected. We also briefly discuss two other “strongly coupled systems”, (i) the strongly coupled supersymmetric theories studied via Maldacena duality; (ii) trapped ultra-cold atoms with very large scattering length.

Dynamics of a wavy plane Wilson surface observable from AdS-CFT correspondence

Guided by the paper hep-th/0002106 by Polyakov and Rychkov, we compute the second variational derivative of a wavy plane Wilson surface observable, to find that a necessary condition for a proposed surface equation to be satisfied in the large $N$ limit is that we are in the critical dimension D=6.

What RHIC experiments and theory tell us about properties of quark–gluon plasma?

This brief review summarizes the main experimental discoveries made at RHIC and then discusses their implications. The robust collective flow phenomena are well described by ideal hydrodynamics, with the equation of state (EoS) predicted by lattice simulations. However the transport properties turned out to be unexpected, with rescattering cross section one-to-two orders of magnitude larger than expected from perturbative QCD. These and other theoretical developments indicate that quark–gluon plasma (QGP) produced at RHIC, and probably in a wider temperature region T c < T < 4 T c , is not at all a weakly coupled quasiparticle gas, but is rather in a strongly coupled regime, sQGP for short. After reviewing two other “strongly coupled systems”, (i) the strongly coupled supersymmetric theories studied via Maldacena duality; (ii) trapped ultra-cold atoms with very large scattering length, we return to sQGP and show that there should exist literally hundreds of bound states in it in the RHIC domain, most them colored. We then discuss recent ideas of their effect on the EoS, viscosity and jet quenching.

Higher impurity AdS/CFT correspondence in the near-BMN limit

The pp-wave/BMN limit of the AdS/CFT correspondence has exposed the Maldacena conjecture to a new regimen of direct tests. In one line of pursuit, finite-radius curvature corrections to the Penrose limit (which appear in inverse powers of the string angular momentum J) have been found to induce a complicated system of interaction perturbations to string theory on the pp-wave; these have been successfully matched to corresponding corrections to the BMN dimensions of N = 4 super-Yang–Mills (SYM) operators to two loops in the 't Hooft coupling λ. This result is tempered by a well-established breakdown in the correspondence at three loops. Notwithstanding the third-order mismatch, we proceed with this line of investigation by subjecting the string and gauge theories to new and significantly more rigorous tests. Specifically, we extend our earlier results at O ( 1 / J ) in the curvature expansion to include string states and SYM operators with three worldsheet or R-charge impurities. In accordance with the two-impurity problem, we find a perfect and intricate agreement between both sides of the correspondence to two-loop order in λ and, once again, the string and gauge theory predictions fail to agree at third order.

Conformal anomaly of Wilson surface observables - a field theoretical computation

We make an exact field theoretical computation of the conformal anomaly for two-dimensional submanifold observables. By including a scalar field in the definition for the Wilson surface, as appropriate for a spontaneously broken A_1 theory, we get a conformal anomaly which is such that N times it is equal to the anomaly that was computed in hep-th/9901021 in the large N limit and which relied on the AdS-CFT correspondence. We also show how the spherical surface observable can be expressed as a conformal anomaly.

A strongly coupled quark–gluon plasma

Successful description of robust collective flow phenomena at RHIC by ideal hydrodynamics, recent observations of bound states on the lattice, and other theoretical developments indicate that QGP produced at RHIC, and probably in a wider temperature region Tc < T < 4Tc, is not a weakly coupled quasiparticle gas as believed previously. We discuss how strong the interaction is and why it seems to generate hundreds of binary channels with bound states, surviving well inside the QGP phase. We in particular discuss their effect on pressure and viscosity. We conclude by reviewing the similar phenomena for other ‘strongly coupled systems’, such as (i) strongly coupled supersymmetric theories studied via Maldacena duality; (ii) trapped ultra-cold atoms with very large scattering length, tuned to Feschbach resonances.