scholarly journals AdS bulk locality from sharp CFT bounds

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Simon Caron-Huot ◽  
Dalimil Mazáč ◽  
Leonardo Rastelli ◽  
David Simmons-Duffin
Keyword(s):  
Central Charge ◽  
Flat Space ◽  
Effective Field ◽  
Dispersion Relations ◽  
Sharp Form ◽  
Conformal Bootstrap ◽  
S Matrix ◽  
Higher Spin ◽  
Single Trace ◽  
Infrared Divergences

Abstract It is a long-standing conjecture that any CFT with a large central charge and a large gap ∆gap in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS. We prove a sharp form of this conjecture by deriving numerical bounds on bulk Wilson coefficients in terms of ∆gap using the conformal bootstrap. Our bounds exhibit the scaling in ∆gap expected from dimensional analysis in the bulk. Our main tools are dispersive sum rules that provide a dictionary between CFT dispersion relations and S-matrix dispersion relations in appropriate limits. This dictionary allows us to apply recently-developed flat-space methods to construct positive CFT functionals. We show how AdS4 naturally resolves the infrared divergences present in 4D flat-space bounds. Our results imply the validity of twice-subtracted dispersion relations for any S-matrix arising from the flat-space limit of AdS/CFT.

scholarly journals Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
A. Liam Fitzpatrick ◽  
Kuo-Wei Huang ◽  
David Meltzer ◽  
Eric Perlmutter ◽  
David Simmons-Duffin
Keyword(s):  
Stress Tensor ◽  
Central Charge ◽  
Effective Field ◽  
Tree Level ◽  
Probe Field ◽  
Conformal Field ◽  
Primary Operator ◽  
Higher Dimensional ◽  
Higher Spin ◽  
Light Probe

Abstract Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge CT, we clarify the properties of stress tensor composite primary operators of minimal twist, [Tm], using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling $$ \left\langle {\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^m\right]\right\rangle $$ O L O L T m , where $$ {\mathcal{O}}_L $$ O L is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling $$ \left\langle TT{\mathcal{O}}_L\right\rangle $$ TT O L , the three-point coupling $$ \left\langle {\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^2\right]\right\rangle $$ O L O L T 2 is modified at large CT if $$ \left\langle TT{\mathcal{O}}_L\right\rangle \sim \sqrt{C_T} $$ TT O L ∼ C T . This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to $$ {\mathcal{O}}_L $$ O L can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin-ℓ ≥ 2 bulk field at tree level, or any spin ℓ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.

scholarly journals A GENERALIZED MODEL FOR TWO-DIMENSIONAL QUANTUM GRAVITY AND DYNAMICS OF RANDOM SURFACES FOR d>1

1994 ◽  
Vol 09 (22) ◽  
pp. 2009-2018 ◽  
Author(s):  
M. MARTELLINI ◽  
M. SPREAFICO ◽  
K. YOSHIDA
Keyword(s):  
Quantum Gravity ◽  
Effective Field Theory ◽  
Continuum Model ◽  
Central Charge ◽  
Flat Space ◽  
Effective Field ◽  
Two Dimensional ◽  
Large Area ◽  
Random Surfaces ◽  
Area Expansion

The possible interpretations of a new continuum model for the two-dimensional quantum gravity for d>1 (d=matter central charge), obtained by carefully treating both diffeomorphism and Weyl symmetries, are discussed. In particular we note that an effective field theory is achieved in low energy (large area) expansion, that may represent smooth self-avoiding random surfaces embedded in a d-dimensional flat space-time for arbitrary d. Moreover the values of some critical exponents are computed, that are in agreement with some recent numerical results.

scholarly journals Towards bootstrapping RG flows: sine-Gordon in AdS

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
António Antunes ◽  
Miguel S. Costa ◽  
João Penedones ◽  
Aaditya Salgarkar ◽  
Balt C. van Rees
Keyword(s):  
Perturbation Theory ◽  
Correlation Functions ◽  
Detailed Comparison ◽  
Flat Space ◽  
Quantum Field ◽  
De Sitter ◽  
Conformal Bootstrap ◽  
S Matrix ◽  
Space Limit ◽  
Entire Flow

Abstract The boundary correlation functions for a Quantum Field Theory (QFT) in an Anti-de Sitter (AdS) background can stay conformally covariant even if the bulk theory undergoes a renormalization group (RG) flow. Studying such correlation functions with the numerical conformal bootstrap leads to non-perturbative constraints that must hold along the entire flow. In this paper we carry out this analysis for the sine-Gordon RG flows in AdS2, which start with a free (compact) scalar in the UV and end with well-known massive integrable theories that saturate many S-matrix bootstrap bounds. We numerically analyze the correlation functions of both breathers and kinks and provide a detailed comparison with perturbation theory near the UV fixed point. Our bounds are often saturated to one or two orders in perturbation theory, as well as in the flat-space limit, but not necessarily in between.

scholarly journals Towards the Virasoro-Shapiro amplitude in AdS5×S5

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Theresa Abl ◽  
Paul Heslop ◽  
Arthur E. Lipstein
Keyword(s):  
Effective Field Theory ◽  
Flat Space ◽  
Effective Field ◽  
Tree Level ◽  
Yang Mills ◽  
Additional Information ◽  
Tree Level Amplitude ◽  
Covariant Derivatives ◽  
Type Iib String Theory ◽  
Single Trace

Abstract We propose a systematic procedure for obtaining all single trace 1/2-BPS correlators in $$ \mathcal{N} $$ N = 4 super Yang-Mills corresponding to the four-point tree-level amplitude for type IIB string theory in AdS5 × S5. The underlying idea is to compute generalised contact Witten diagrams coming from a 10d effective field theory on AdS5 × S5 whose coefficients are fixed by the flat space Virasoro-Shapiro amplitude up to ambiguities related to commutators of the 10d covariant derivatives which require additional information such as localisation. We illustrate this procedure by computing stringy corrections to the supergravity prediction for all single trace 1/2-BPS correlators up to $$ \mathcal{O} $$ O (α′7), and spell out a general algorithm for extending this to any order in α′.

scholarly journals All-order quartic couplings in highly symmetric D-brane-anti-D-brane systems

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ehsan Hatefi ◽  
Per Sundell
Keyword(s):  
Closed String ◽  
Effective Field ◽  
Gauge Fields ◽  
S Matrix ◽  
Holographic Duals ◽  
Higher Spin ◽  
Dual Channels ◽  
Infinite Collection ◽  
Superstring Theories ◽  
String Amplitudes

Abstract We compute six-point string amplitudes for the scattering of one closed string Ramond-Ramond state, two tachyons and two gauge fields in the worldvolume of D-brane-anti-D-brane systems in the Type II superstring theories. From the resulting S-matrix elements, we read off the precise form of the couplings, including their exact numerical coefficients, of two tachyons and two gauge fields in the corresponding highly symmetric effective field eheory (EFT) Lagrangian in the worldvolume of D-brane-Anti-D-brane to all orders in α′, which modify and complete previous proposals. We verify that the EFT reproduces the infinite collection of stringy gauge field singularities in dual channels. Inspired by interesting similarities between the all-order highly symmetric EFTs and holographic duals of Vasiliev’s higher spin gravities à là Nilsson and Vasiliev, we make a proposal for tensionless limits of D-brane-anti-D-brane systems.

scholarly journals 6d (2, 0) and M-theory at 1-loop

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Luis F. Alday ◽  
Shai M. Chester ◽  
Himanshu Raj
Keyword(s):  
Flat Space ◽  
Lagrangian Description ◽  
Loop Correction ◽  
Higher Derivative ◽  
Weakly Coupled ◽  
S Matrix ◽  
Space Limit ◽  
Tensor Multiplet ◽  
First Time ◽  
M Theory

Abstract We study the stress tensor multiplet four-point function in the 6d maximally supersymmetric (2, 0) AN−1 and DN theories, which have no Lagrangian description, but in the large N limit are holographically dual to weakly coupled M-theory on AdS7× S4 and AdS7× S4/ℤ2, respectively. We use the analytic bootstrap to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity R and the first higher derivative correction R4 vertices, which is the first 1-loop correction computed for a non-Lagrangian theory. We then take the flat space limit and find precise agreement with the corresponding terms in the 11d M-theory S-matrix, some of which we compute for the first time using two-particle unitarity cuts.

scholarly journals CFT unitarity and the AdS Cutkosky rules

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
David Meltzer ◽  
Allic Sivaramakrishnan
Keyword(s):  
Flat Space ◽  
Tree Level ◽  
Optical Theorem ◽  
Conformal Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Weakly Coupled ◽  
S Matrix ◽  
Space Limit ◽  
Diagrammatic Method

Abstract We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cutting rules. These rules are naturally formulated and derived in Lorentzian momentum space, where the double-commutator is manifestly related to the CFT optical theorem. Finally, we study the AdS cutting rules in explicit examples at tree level and one loop. In these examples, we confirm that the rules are consistent with the OPE limit and that we recover the S-matrix optical theorem in the flat space limit. The AdS cutting rules and the CFT dispersion formula together form a holographic unitarity method to reconstruct Witten diagrams from their cuts.

scholarly journals Light-front higher-spin theories in flat space

2017 ◽  
Vol 50 (9) ◽  
pp. 095401 ◽  
Author(s):  
Dmitry Ponomarev ◽  
Evgeny Skvortsov
Keyword(s):  
Flat Space ◽  
Light Front ◽  
Higher Spin

scholarly journals HIGHER SPIN REALIZATIONS OF THE BOSONIC STRING

1995 ◽  
Vol 10 (25) ◽  
pp. 1857-1864 ◽  
Author(s):  
H. LÜ ◽  
C.N. POPE ◽  
K.W. XU
Keyword(s):  
Central Charge ◽  
Bosonic String ◽  
Higher Spin

It has been shown that certain W algebras can be linearized by the inclusion of a spin-one current. This provides a way of obtaining new realizations of the W algebras. Recently such new realizations of W3 were used in order to embed the bosonic string in the critical and noncritical W3 strings. In this letter, we consider similar embeddings in W2,4 and W2,6 strings. The linearization of W2,4 is already known, and can be achieved for all values of central charge. We use this to embed the bosonic string in critical and noncritical W2,4 strings. We then derive the linearization of W2,6 using a spin-one current, which turns out to be possible only at central charge c=390. We use this to embed the bosonic string in a noncritical W2,6 string.

scholarly journals THERMAL FIELD THEORY IN A WIRE: APPLICATIONS OF THERMAL FIELD THEORY METHODS TO THE PROPAGATION OF PHOTONS IN A ONE-DIMENSIONAL PLASMA

2011 ◽  
Vol 26 (32) ◽  
pp. 5387-5402 ◽  
Author(s):  
JOSÉ F. NIEVES
Keyword(s):  
Field Theory ◽  
Thermal Field Theory ◽  
Thermal Field ◽  
Free Field ◽  
Dynamical Variable ◽  
Effective Field ◽  
Dispersion Relations ◽  
One Dimensional ◽  
Self Energy ◽  
The One

The Thermal Field Theory methods are applied to calculate the dispersion relation of the photon propagating modes in a strictly one-dimensional (1D) ideal plasma. The electrons are treated as a gas of particles that are confined to a 1D tube or wire, but are otherwise free to move, without reference to the electronic wave functions in the coordinates that are transverse to the idealized wire, or relying on any features of the electronic structure. The relevant photon dynamical variable is an effective field in which the two space coordinates that are transverse to the wire are collapsed. The appropriate expression for the photon free-field propagator in such a medium is obtained, the one-loop photon self-energy is calculated and the (longitudinal) dispersion relations are determined and studied in some detail. Analytic formulas for the dispersion relations are given for the case of a degenerate electron gas, and the results differ from the long-wavelength formula that is quoted in the literature for the strictly 1D plasma. The dispersion relations obtained resemble the linear form that is expected in realistic quasi-1D plasma systems for the entire range of the momentum, and which have been observed in this kind of system in recent experiments.

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