We show that the large-N limits of certainconformal field theories in various dimensions includein their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds. This is shown bytaking some branes in the full M/string theory and thentaking a low-energy limit where the field theory on thebrane decouples from the bulk. We observe that, in this limit, we can still trust thenear-horizon geometry for large N. The enhancedsupersymmetries of the near-horizon geometry correspondto the extra supersymmetry generators present in thesuperconformal group (as opposed to just the super-Poincaregroup). The 't Hooft limit of 3 + 1 N = 4 super-Yang–Mills at the conformal pointis shown to contain strings: they are IIB strings. Weconjecture that compactifications of M/string theory on various anti-de Sitterspacetimes is dual to various conformal field theories.This leads to a new proposal for a definition ofM-theory which could be extended to include fivenoncompact dimensions.

https://www.intlpress.com/site/pub/files/_fulltext/journals/atmp/1998/0002/0002/ATMP-1998-0002-0002-a001.pdf

The Large N limit of superconformal field theories and supergravity

Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of ${\cal N}=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the ${\cal N}=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

/pdf/anti-de-sitter-space-and-holography-58a7vi1qn6.pdf

Anti De Sitter Space And Holography

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of $\N=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the $\N=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

Anti de sitter space and holography

http://inspirehep.net/record/499969/files/arXiv:hep-th_9905111.pdf

Large N Field Theories, String Theory and Gravity

https://dspace.library.uu.nl/bitstream/handle/1874/15996/dewit_88_quantummechanics.pdf;sequence=1

On the quantum mechanics of supermembranes

http://cds.cern.ch/record/138066/files/198207015.pdf

N = 8 supergravity

A formal ``small tension'' expansion of $D=11$ supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite-dimensional coset space ${E}_{10}/K({E}_{10})$, where $K({E}_{10})$ is the maximal compact subgroup of the hyperbolic Kac-Moody group ${E}_{10}(\mathbb{R})$. For the proof we make use of a novel decomposition of ${E}_{10}$ into irreducible representations of its $\mathrm{S}\mathrm{L}(10,\mathbb{R})$ subgroup. We explicitly show how to identify the first four rungs of the ${E}_{10}$ coset fields with the values of geometric quantities constructed from $D=11$ supergravity fields and their spatial gradients taken at some comoving spatial point.

E10 and a Small Tension Expansion of M Theory

https://pure.mpg.de/pubman/item/item_153467_1/component/file_153466/353871.pdf

Hermann Nicolai

Papers

On the quantum mechanics of supermembranes

N = 8 supergravity

E10 and a Small Tension Expansion of M Theory

The consistency of the S7 truncation in d=11 supergravity

Conformal symmetry and the Standard Model