Spectrum of the planar AdS/CFT correspondence
Objective
Field of Science
string theory
Funding Scheme
MCIOF  International Outgoing Fellowships (IOF)
Coordinator
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Address
Rue Michel Ange 3
75794 Paris
France
Activity type
Research Organisations
EU Contribution
€ 229 056,80
Administrative Contact
Ludovic Hamon (Mr.)
Project information
Spectrum of AdS/CFT
Grant agreement ID: 273854
Status
Closed project

Start date
1 October 2011

End date
30 September 2014
Funded under:
FP7PEOPLE

Overall budget:
€ 229 056,80

EU contribution
€ 229 056,80
Relating quantum field and gravity theories
INDUSTRIAL TECHNOLOGIES
Juan Maldacena proposed in 1997 a duality between superstring theory in the AdS background space and quantum field theories in four dimensions. This socalled antide Sitter/conformal field theory (AdS/CFT) correspondence is one of the most significant results in string theory. This relationship still has no formal mathematical proof, but in certain limits calculations are vastly simplified. Extensive checks carried out within the EUfunded project 'Spectrum of the planar AdS/CFT correspondence' (SPECTRUM OF ADS/CFT) involved calculations of observable quantities related by a specific dictionary – the dictionary that translates between the two theories. The energies of strings in the AdS5xS5space were conjectured by Maldacena to correspond to scaling dimensions of the 4D super YangMills gauge theory (CFT4). Recently, these quantities were proposed to be solutions to certain set of equations. These equations follow from the Thermodynamic Bethe Ansatz, which is wellknown in the field of integrable models. Integrable models are manybody systems that can be reduced to a combination of twobody systems rendering the equations solvable. SPECTRUM OF ADS/CFT scientists put this set of spectral equations to nonperturbative tests. The underlying idea is to look at the Thermodynamic Bethe Ansatz equations for excited states given a dynamic background. Such a background for the AdS5/CFT4 correspondence is furnished by the Gubser, Klebanov and Polyakov (GKP) solution. Next, a considerable amount of research was devoted to generalising this methodology to theories with less supersymmetry, such as AdS4/CFT3 and AdS3/CFT2.SPECTRUM OF ADS/CFT scientists gathered evidence in favour of these conjectured correspondences, as both theories of these dualities were shown to be solvable. A better understanding was offered on how physical quantities in each theory should be matched. These ideas of duality explored within the SPECTRUM OF ADS/CFT project have also been applied to lowenergy systems, such as superconductors. The hope is that such dualities can soon be tested experimentally in laboratories, with exciting implications for other areas of condensed matter physics.
Keywords
Quantum field, gravity, condensed matter, AdS/CFT, string theory
Project information
Spectrum of AdS/CFT
Grant agreement ID: 273854
Status
Closed project

Start date
1 October 2011

End date
30 September 2014
Funded under:
FP7PEOPLE

Overall budget:
€ 229 056,80

EU contribution
€ 229 056,80
Discover other articles in the same domain of application
Final Report Summary  SPECTRUM OF ADS/CFT (Spectrum of the planar AdS/CFT correspondence)
Although Maldacena’s duality has become a vital ingredient of modern theoretical physics and it was successfully tested in some cases, only recently progress has been made towards proving it. The main obstacles are the complications arising while quantizing both constituent theories. No nonperturbative quantization of the N = 4 SYM theory is known and the full quantization of string theory on curved backgrounds is currently also beyond reach. In the planar limit, i.e. when the rank of the symmetry group goes to infinity, these constituent theories become much simpler, as suggested by ‘t Hooft. This is due to the fact that only planar Feynman diagrams need to be taken into account on the gauge theory side, while the string theory reduces to a supersymmetric nonlinear sigma model.
Remarkably, the simplification of the dynamics is much more farreaching than expected. Rich structures emerge for different “observables” of the planar string/gauge correspondence: spectral problem, scattering amplitudes, correlation functions, etc.
Arguably, the best studied aspect is the spectrum of the duality. The dilatation operator of the planar N = 4 gauge theory, which “measures” the scaling dimensions of the operators, has been found to be asymptotically integrable. This implies that the computation of scaling dimensions of long operators is reduced to computing the energies of states of the corresponding integrable spin chain. On the other hand, the scattering processes in integrable spin chains are known to factorize into sequences of twobody scattering and the solution to the spectral problem is provided by a closed set of algebraic equations, the Bethe equations. Consequently, the computation of the scaling dimensions of long operators boils down to solving a set of coupled algebraic equations, termed asymptotic Bethe equations (ABA). A significant simplification occurs also on the string theory side. The classical supersymmetric sigmamodel on the AdS5×S5 product space is integrable and there are indications that this remains true also at the quantum level.
Short strings/operators are unfortunately not accessible by these techniques due to the so called wrapping diagrams, which typically have to be included at the order O(g^2L). These extra diagrams correspond to highly nonlocal interactions from the spin chain point of view. Recently, there has been a breakthrough in computing anomalous dimensions of composite operator of arbitrary length. Different groups have conjectured the Thermodynamic Bethe Ansatz (TBA) for the ground state (BPS state) and the sl(2) subsector of the theory. If supplemented with additional analytic information, these equations might be used to compute nonperturbatively the energy/dimension of any string state/composite operator of the correspondence thus accounting for the neglected wrapping diagrams. Very recently this infinite set of coupled integral equations has been written in a very compact form, raising hopes that they may be derived from the first principles on both sides of the correspondence.
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The objectives of this project revolve around the following aspects:
1) Testing the veracity of the proposed TBA equations
2) Extracting from them insights into nonperturbative dynamics of AdS/CFT correspondence.
3) The leading order (LO) and nexttoleading (NLO) BFKL equations and their origins in AdS/CFT correspondence
4) Application of the integrability methods to cousin theories : AdS4/CFT3 and AdS3/CFT2.
The objectives 1),2) and 4) have been fully met and encouraging partial results towards fulfillment of 2) have been obtained. The experienced researcher has published two long (50+ pages), comprehensive and already wellcited papers in Nuclear Physics B. Both articles are interdisciplinary with crossconnections between the aforementioned objectives. With these two articles a new conceptual framework has been created that allows for a nonperturbative test of spectral equations for strong/weak coupling dualities. The underlying idea is to look at the dynamics of excitations on top of a dynamic background. Such a background for AdS/CFT is furnished by the GKP solution (this includes all currently known cases: AdS5/CFT4, AdS4/CFT3 and AdS3/CFT2!). It corresponds to long twisttwo operators on the gauge theory side. It turns out that the physics of the lowenergy excitations on this “vacuum state” is described by a sigma model, which is a consistent truncation of the string theory sigma model. This approach allowed to conduct nonperturbative tests of spectral equations for AdS5/CFT4 and AdS4/CFT3. This included a nonperturbative test of the dressing factor for AdS4/CFT3, which was not extensively tested so far. Furthermore, the framework developed allows to analyze how the interpolation between weak and strongcoupling limit works in practice! Finally, the Smatrix constructed in one of these papers has found an important application in the nonperturbative computation of scattering amplitudes for AdS5/CFT4 (see arXiv:1303.1396 and followup articles). Thus, the results obtained during this fellowship have significantly contributed to the advancement of AdS/CFT correspondence.
Project information
Spectrum of AdS/CFT
Grant agreement ID: 273854
Status
Closed project

Start date
1 October 2011

End date
30 September 2014
Funded under:
FP7PEOPLE

Overall budget:
€ 229 056,80

EU contribution
€ 229 056,80
Deliverables
Deliverables not available
Publications
Project information
Spectrum of AdS/CFT
Grant agreement ID: 273854
Status
Closed project

Start date
1 October 2011

End date
30 September 2014
Funded under:
FP7PEOPLE

Overall budget:
€ 229 056,80

EU contribution
€ 229 056,80
Project information
Spectrum of AdS/CFT
Grant agreement ID: 273854
Status
Closed project

Start date
1 October 2011

End date
30 September 2014
Funded under:
FP7PEOPLE

Overall budget:
€ 229 056,80

EU contribution
€ 229 056,80