A toy model for the AdS/CFT correspondence

By D. Berenstein. 2004

459 citations recorded by the source corpus.

We study the large-N gauged quantum mecchanics for a single hermitean matrix in the Harmonic oscillator potential well as a toy model for the AdS/CFT correspondence. We argue that the dual geometry should be a string in two dimensions with a curvature of stringy size. Even though the dual geometry is not weakly curved, one can still gain knowledge of the system from a detailed study of the open-closed string duality. We give a mapping between the basis of states made of traces (closed strings) and the eigenvalues of the matrix (D-brane picture) in terms of Schur polynomials. This is interpreted as an exact open-closed duality. We connect this model with a decoupling limit of = 4 SYM and the study of giant gravitons in AdS5 ? S5. We show that the two giant gravitons that expand along AdS5 and S5 can be interpreted in the matrix model as taking an eigenvalue from the Fermi sea and exciting it very much, or as making a hole in the Fermi sea respectively. This is similar to recent studies of the c = 1 string. This connection gives new insight on how to perform calculations for giant gravitons.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/136c3d65a962983bd923239deeb000f8e54531d7

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Citations in the corpus

BUBBLING GEOMETRIES FOR HALF-BPS WILSON LINES (2006, unknown): “This picture is consistent with the dynamics of eigenvalues of the Gaussian matrix quantum mechanics proposed by [5, 6, 7].”
The AdS/CFT correspondence (2014, background): “N ( ) 2  excitation in the field theory in terms of the bulk geometry is in general very difficult, one can in fact retain full control over certain special, but nevertheless rather rich, classes of supersymmetric states, describable by free fermions [61, 63].”
On gravitational description of Wilson lines (2006, background): “While all our metrics have AdS5 × S5 asymptotics, they generically have nontrivial topologies, which can be uniquely specified by a set of non–contractible three– and five–spheres.”
SUPERCONFORMAL FIELD THEORIES (2005, unknown): “Recently there has been a lot of progress in understanding the AdS-CFT correspondence [1, 2, 3, 4].”
ABJM theory as a Fermi gas (2011, unknown): “Finally, there might be a connection between the Fermi gas of this paper and two other pictures for string/M-theory based on fermions: the droplet picture proposed in [67, 68] to analyze 1/2 BPS operators in N = 4 SYM theory and the Fermi liquid picture of non-critical M-theory proposed in [69].”
Black holes as effective geometries (2008, background): “The Hilbert space of 1/2-BPS states in N = 4 U(N) super Yang–Mills is isomorphic to the Hilbert space of N fermions in a harmonic oscillator potential as shown in [48, 49].”
Branes, anti-branes and Brauer algebras in gauge-gravity duality (2007, unknown): “1y.kimura@qmul.ac.uk 2s.ramgoolam@qmul.ac.uk”
Supersymmetric states of N=4 Yang-Mills from giant gravitons (2006, background): “Half BPS giant gravitons have been studied extensively, see for instance [27, 28, 29, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63].”
The library of Babel: on the origin of gravitational thermodynamics (2005, background): “24”
LSZ in LST (2004, unknown): “It was further argued in [37-41] (by examining various correlation functions of”
Counting 1/8-BPS Dual-Giants (2006, background): “Further in the half-BPS sector the duality between giants and dual-giants follows form a unified description of the system [23, 24] in terms of N fermions in a harmonic oscillator potential.”
Giant Gravitons - with Strings Attached (III) (2007, background): “3.1 Dynamical emergence of Chan-Paton factors 14 3.2 Physical basis 16”
Three-dimensional N=6 SCFT's and their membrane dynamics (2008, background): “The set of such half-BPS operators in N = 4 SYM can be described by free fermions [47, 48], and it is convenient to think of these systems as an integer quantum Hall droplet.”
The dilatation operator of conformal N=4 super-Yang–Mills theory (2003, background): “Operators on the gauge theory side that are dual to giant gravitons were proposed to be Schur polynomials in [9; 10].”
Large N BPS states and emergent quantum gravity (2005, background): “4.1 Description of the quantum states of the matrix model 36”
D-branes in Yang-Mills theory and emergent gauge symmetry (2004, unknown): “The matrix model is studied most efficiently in terms of the free fermionic description of the eigenvalues [8], and it turns out that the two types of giant gravitons can be understood either as the fermions themselves, or as hole wavefunctions.”
Diagonal free field matrix correlators, global symmetries and giant gravitons (2008, background): “The systematic study of the correlation functions of gauge invariant multi-trace local operators in the half-BPS sector has been fruitful in identifying CFT duals [7, 8, 9] of giant gravitons, strings attached to them [10, 11, 12] as well as bulk geometries resulting from their back-reaction on spac”