algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
A multi trace observable in a gauge theory is a polynomial in single trace operators (see there for more background).
Under the AdS/CFT correspondence, single trace observables in the gauge theory correspond to single particle/string excitations on the gravity-side, while multi-trace observables correspond to multi-particle/string excitations (Liu 98, p. 6 (7 of 39), Andrianapoli-Ferrara 99, p. 13, Chalmers-Schalm 00, Section 7, Aharony-Gubser-Maldacena-Ooguri-Oz 99, p. 75)
The asymptotic boundary conditions for fields on the AdS-side
that correspond to multi-trace observables have coefficients given by the derivative of the multi-trace polynomial by its single-trace variables :
The supersymmetric states of the BMN matrix model are temporally constant complex matrices which are complex metric Lie representations of su(2) (interpreted as fuzzy 2-sphere noncommutative geometries of giant gravitons or equivalently as fuzzy funnels of D0-D2 brane bound states).
A fuzzy 2-sphere-rotation invariant multi-trace observable on these supersymmetric states is hence an expression of the following form:
(from Sati-Schreiber 19c)
Here we are showing the corresponding string diagram/Penrose notation for metric Lie representations, which makes manifest that
these multi-trace observables are encoded by Sullivan chord diagrams
their value on the supersymmetric states is the evaluation of the corresponding Lie algebra weight system on .
Or equivalently, if is a horizontal chord diagram whose -permuted closure is (see here) then the values of the invariant multi-trace observables on the supersymmetric states of the BMN matrix model are the evaluation of on , as shown here:
(from Sati-Schreiber 19c)
But since all horizontal weight systems are partitioned Lie algebra weight systems this way, this identifies supersymmetric states of the BMN matrix model as seen by invariant multi-trace observables as horizontal chord diagrams evaluated in Lie algebra weight systems.
Discussion of multi-trace operators in super Yang-Mills theory and of their AdS-CFT dual gravity/string theory incarnation:
Tom Banks, Michael Douglas, Gary Horowitz, Emil Martinec, AdS Dynamics from Conformal Field Theory (arXiv:hep-th/9808016, spire:474214)
Hong Liu, Scattering in Anti-de Sitter Space and Operator Product Expansion, Phys. Rev. D 60, 106005 (1999) (arXiv:hep-th/9811152)
Laura Andrianopoli, Sergio Ferrara, On short and long multiplets in the AdS/CFT correspondence, Lett. Math.Phys. 48 (1999) 145-161 (arXiv:hep-th/9812067)
Gordon Chalmers, Koenraad Schalm, Holographic Normal Ordering and Multi-particle States in the AdS/CFT Correspondence, Phys. Rev. D61:046001, 2000 (arXiv:hep-th/9901144)
Ofer Aharony, Steven Gubser, Juan Maldacena, Hirosi Ooguri, Yaron Oz, Large Field Theories, String Theory and Gravity, Phys. Rept. 323:183-386, 2000 (arXiv:hep-th/9905111)
Massimo Bianchi, Stefano Kovacs, Giancarlo Rossi, Yassen S. Stanev, On the logarithmic behaviour in SYM theory, JHEP 9908 (1999) 020 (arXiv:hep-th/9906188)
Witold Skiba, Correlators of Short Multi-Trace Operators in Supersymmetric Yang-Mills, Phys. Rev. D 60, 105038 (1999) (arXiv:hep-th/9907088)
Eric D'Hoker, Daniel Freedman, Samir Mathur, A. Matusis, Leonardo Rastelli, Extremal Correlators in the AdS/CFT Correspondence, in: The many faces of the superworld (arXiv:hep-th/9908160)
Gleb Arutyunov, Sergey Frolov, A. C. Petkou, Perturbative and instanton corrections to the OPE of CPOs in , Nucl. Phys. B602:238-260, 2001; Erratum-ibid. B609:540, 2001 (arXiv:hep-th/0010137)
Ofer Aharony, Micha Berkooz, Eva Silverstein, Multiple-Trace Operators and Non-Local String Theories, JHEP 0108:006, 2001 (arXiv:hep-th/0105309)
Ofer Aharony, Micha Berkooz, Eva Silverstein, Non-local string theories on times and stable non-supersymmetric backgrounds, Phys. Rev. D65:106007, 2002 (arXiv:hep-th/0112178)
L. Hoffmann, L. Mesref, A. Meziane, W. Rühl, Multi-trace quasi-primary fields of from AdS -point functions, Nucl. Phys. B641 (2002) 188-222 (arXiv:hep-th/0112191)
Edward Witten, Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence (arXiv:hep-th/0112258)
Steven Gubser, Indrajit Mitra, Double-trace operators and one-loop vacuum energy in AdS/CFT, Phys. Rev. D67 (2003) 064018 (arXiv:hep-th/0210093)
Vijay Balasubramanian, Jan de Boer, Bo Feng, Yang-Hui He, Min-xin Huang, Vishnu Jejjala, Asad Naqvi, Multi-Trace Superpotentials vs. Matrix Models, Commun. Math. Phys. 242:361-392, 2003 (arXiv:hep-th/0212082)
Steven Gubser, Igor Klebanov, A universal result on central charges in the presence of double-trace deformations, Nucl. Phys. B656 (2003) 23-36 (arXiv:hep-th/0212138)
P. J. Heslop, Paul Howe, Aspects of =4 SYM, JHEP 0401 (2004) 058 (arXiv:hep-th/0307210)
Thomas Hartman, Leonardo Rastelli, Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT, JHEP 0801:019, 2008 (arXiv:hep-th/0602106)
Textbook account:
Sean Hartnoll, Andrew Lucas, Subir Sachdev, Section 1.7.3 of: Holographic quantum matter, MIT Press 2018 (arXiv:1612.07324, publisher)
(with an eye towards AdS/CFT in condensed matter physics)
Last revised on February 5, 2020 at 10:44:50. See the history of this page for a list of all contributions to it.