Multiple-Trace Operators and Non-Local String Theories

By O. Aharony, M. Berkooz, E. Silverstein. 2001

168 citations recorded by the source corpus.

We propose that a novel deformation of string perturbation theory, involving non-local interactions between strings, is required to describe the gravity duals of field theories deformed by multiple-trace operators. The new perturbative expansion involves a new parameter, which is neither the string coupling nor the coefficient of a vertex operator on the worldsheet. We explore some of the properties of this deformation, focusing on a special case where the deformation in the field theory is exactly marginal.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a6af186221820b88a5275f6e26129e68c42a2421

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. E. Witten
2. I. Klebanov
3. J. Polchinski
4. D. Marolf
5. S. Gubser
6. D. Harlow
7. S. Hartnoll
8. J. Maldacena

In Nuclear and High Energy Physics

1. E. Witten
2. J. Maldacena
3. Marcos Mariño
4. I. Klebanov
5. D. Harlow
6. C. Vafa
7. S. Raju
8. J. Polchinski

Citations in the corpus

• First order deconfinement transition in large N Yang-Mills theory on a small S 3 (2005, unknown): “10 See, for instance, [10,11] for recent discussions of how double-trace terms can contribute at leading order in the large N limit.”
• Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence (2001, methodology): “elds, are based on single-trace actions. Theories with multi-trace interactions have, however, also been considered in matrix models of two-dimensional gravity [3,6] and in the AdS/CFT correspondence [7]. The purpose of the present paper is to make a general proposal for how multi-trace interactions”
• Supersymmetric gauge theories and the AdS / CFT correspondence (2002, background): “ike charges forms a static solution of the BPS equations and therefore form a threshold bound state. Very recently, a direct coupling of double-trace operators to AdS supergravity has been studied in [50]. To identify the contents of irreducible representations of SU(2,2|4) on the AdS side, we descr”
• AdS dual of the critical O(N) vector model (2002, methodology): “This is a vector model analogue of the trace-squared terms which have been recently studied in the AdS/CFT setting [25, 26, 27, 28].”
• SL(2;Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry (2003, result): “This work was supported in part by NSF Grant PHY-0070928.”
• Matrix model as a mirror of Chern-Simons theory (2002, background): “These kinds of operators have been recently considered in the context of the AdS/CFT correspondence, see for example [38,39].”
• Boundary conditions and dualities: vector fields in AdS/CFT (2006, background): “Since a double-trace operator corresponds to a multiparticle state, the double-trace deformations in the CFT have also been related to worldsheet non-locality in the bulk string theory [12, 13].”
• An AdS_3 Dual for Minimal Model CFTs (2010, background): “Thus the perturbation is indeed by a ‘double trace’ operator [42].”
• `Double-trace' deformations, boundary conditions and spacetime singularities (2001, background): “(3.5) The product of delta functions for each point on the boundary can be represented by an integral on an additional boundary field β(~x) as follows: Zd.t.gr [ρ] = ∫ D[φ]D[λ]D[β]e−S[φ,λ,β;ρ,h̃] , (3.6) where now λ, φ, β are independent and we denoted: S[φ, λ, β; ρ, h̃] = (3.7) = 1 2 ∫ Bulk…”
• Holography from Conformal Field Theory (2009, background): “(9)A large-N expansion usually implies that the Hamiltonian is itself a single-trace operator, and we make this assumption explicit in order to exclude known exceptions in which a CFT is coupled to itself or to an otherwise-decoupled CFT through multi-trace interactions [18].”
• Double-trace operators and one-loop vacuum energy in AdS/CFT (2002, background): “Earlier work describing the same gauge theory deformations in terms of non-local terms in the string worldsheet action appeared in [8, 9].”
• The Search for a Holographic Dual to AdS(3)xS(3)xS(3)xS(1) (2004, background): “24 It is the analogue of a double-trace operator in the N = 4 SYM/AdS5 × S(5) correspondence [57].”
• Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields (2006, methodology): “δbi for some L. This is in line with the AdS-CFT correspondence where such functional relationships (defining “Lagrangian submanifolds”) have been considered in the context of multi-trace deformations [28, 29]. We have also observed that when a non-trivial potential is considered, the asymptotic form”
• Holographic and Wilsonian renormalization groups (2010, background): “ace couplings, and because of the apparently misplaced prejudice that single-trace actions are the norm in taking large-N limits, with multi-trace actions arising in exotic applications such as Refs. [12, 13, 14]. The total amplitude is independent of the radius at which the division is made, 0 = d ”
• Semi-holographic Fermi liquids (2010, background): “(10)These perturbations are nonlocal in the compact directions of the bulk dual [24], but this does not lead to any pathologies.”