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 Causality, unitarity and symmetry in effective field theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Timothy Trott
Keyword(s):  
Effective Field ◽  
Tree Level ◽  
Global Symmetry ◽  
Fundamental Limits ◽  
Effective Interactions ◽  
Effective Contact ◽  
Higher Dimensional ◽  
Forward Limit ◽  
Mass Dimension ◽  
Flavour Violation

Abstract Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the S-matrix, these imply that the size of higher dimensional corrections to transition amplitudes between different states is bounded by the strength of their contributions to elastic forward scattering processes. This places fundamental limits on the extent to which hypothetical symmetries can be broken by effective interactions. All analysis is for dimension 8 operators in the forward limit. Included is a thorough derivation of all positivity bounds for a chiral fermion in SU(2) and SU(3) global symmetry representations resembling those of the Standard Model, general bounds on flavour violation, new bounds for interactions between particles of different spin, inclusion of loops of dimension 6 operators and illustration of the resulting strengthening of positivity bounds over tree-level expectations, a catalogue of supersymmetric effective interactions up to mass dimension 8 and 4 legs and the demonstration that supersymmetry unifies the positivity theorems as well as the new bounds.

scholarly journals Quantum null energy condition and its (non)saturation in 2d CFTs

2019 ◽  
Vol 6 (3) ◽  
Author(s):  
Christian Ecker ◽  
Daniel Grumiller ◽  
Wilke van der Schee ◽  
Shahin Sheikh-Jabbari ◽  
Philipp Stanzer
Keyword(s):  
Central Charge ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Einstein Gravity ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Leading Order ◽  
Conformal Field ◽  
Primary Operator ◽  
Vacuum Solutions

We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions (CFT_22). We show that QNEC saturates for all states dual to vacuum solutions of AdS_33 Einstein gravity, including systems that are far from thermal equilibrium. If the Ryu-Takayanagi surface encounters bulk matter QNEC does not need to be saturated, whereby we give both analytical and numerical examples. In particular, for CFT_22 with a global quench dual to AdS_33-Vaidya geometries we find a curious half-saturation of QNEC for large entangling regions. We also address order one corrections from quantum backreactions of a scalar field in AdS_33 dual to a primary operator of dimension h in a large central charge expansion and explicitly compute both, the backreacted Ryu–Takayanagi surface part and the bulk entanglement contribution to EE and QNEC. At leading order for small entangling regions the contribution from bulk EE exactly cancels the contribution from the back-reacted Ryu-Takayanagi surface, but at higher orders in the size of the region the contributions are almost equal while QNEC is not saturated. For a half-space entangling region we find that QNEC is gapped by h/4h/4 in the large h expansion.

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 ABJ correlators with weakly broken higher spin symmetry

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Damon J. Binder ◽  
Shai M. Chester ◽  
Max Jerdee
Keyword(s):  
Stress Tensor ◽  
Higher Spin Symmetry ◽  
Spin Symmetry ◽  
Tree Level ◽  
Ward Identities ◽  
Free Theory ◽  
Higher Spin ◽  
Breaking Parameter ◽  
Tensor Multiplet ◽  
Good Agreement

Abstract We consider four-point functions of operators in the stress tensor multiplet of the 3d $$ \mathcal{N} $$ N = 6 U(N)k× U(N + M)−k or SO(2)2k× USp(2 + 2M)−k ABJ theories in the limit where M and k are taken to infinity while N and λ ∼ M/k are held fixed. In this limit, these theories have weakly broken higher spin symmetry and are holographically dual to $$ \mathcal{N} $$ N = 6 higher spin gravity on AdS4, where λ is dual to the bulk parity breaking parameter. We use the weakly broken higher spin Ward identities, superconformal Ward identities, and the Lorentzian inversion formula to fully determine the tree level stress tensor multiplet four-point function up to two free parameters. We then use supersymmetric localization to fix both parameters for the ABJ theories in terms of λ, so that our result for the tree level correlator interpolates between the free theory at λ = 0 and a parity invariant interacting theory at λ = 1/2. We compare the CFT data extracted from this correlator to a recent numerical bootstrap conjecture for the exact spectrum of U(1)2M× U(1 + M)−2M ABJ theory (i.e. λ = 1/2 and N = 1), and find good agreement in the higher spin regime.

scholarly journals Double copy structure of parity-violating CFT correlators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Flat Space ◽  
Field Theories ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Spin ◽  
Space Limit ◽  
Double Copy ◽  
Conserved Currents ◽  
Massless Fields

Abstract We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators. Splitting up the CFT correlator into two parts — called homogeneous and non-homogeneous — we show that double copy relations exist for each part separately. We arrive at similar conclusions regarding double copy structures using tree-level correlators of massless fields in dS4. We also discuss the flat space limit of these correlators. We further extend the double copy analysis to correlators involving higher-spin conserved currents, which suggests that the spin-s current correlator can be thought of as s copies of the spin one current correlator.

scholarly journals Towards Feynman rules for conformal blocks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Hoback ◽  
Sarthak Parikh
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Hypergeometric Functions ◽  
Power Series Expansion ◽  
Effective Field ◽  
Conformal Block ◽  
Tree Level ◽  
Conformal Blocks ◽  
Simple Set ◽  
Feynman Rules

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

scholarly journals Interplay of New Physics effects in (g − 2)ℓ and h → ℓ+ℓ− — lessons from SMEFT

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Svjetlana Fajfer ◽  
Jernej F. Kamenik ◽  
M. Tammaro
Keyword(s):  
Closed Operator ◽  
Higgs Doublet ◽  
New Physics ◽  
Effective Field ◽  
Tree Level ◽  
Electroweak Symmetry ◽  
Scalar Leptoquark ◽  
Doublet Model ◽  
The One ◽  
Two Higgs Doublet Model

Abstract We explore the interplay of New Physics (NP) effects in (g− 2)ℓ and h→ℓ+ℓ− within the Standard Model Effective Field Theory (SMEFT) framework, including one-loop Renormalization Group (RG) evolution of the Wilson coefficients as well as matching to the observables below the electroweak symmetry breaking scale. We include both the leading dimension six chirality flipping operators including a Higgs and SU(2)L gauge bosons as well as four-fermion scalar and tensor operators, forming a closed operator set under the SMEFT RG equations. We compare present and future experimental sensitivity to different representative benchmark scenarios. We also consider two simple UV completions, a Two Higgs Doublet Model and a single scalar LeptoQuark extension of the SM, and show how tree level matching to SMEFT followed by the one-loop RG evolution down to the electroweak scale can reproduce with high accuracy the (g−2)ℓ and h→ℓ+ℓ− contributions obtained by the complete one- and even two-loop calculations in the full models.

scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

scholarly journals Bootstrap bounds on closed Einstein manifolds

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
James Bonifacio ◽  
Kurt Hinterbichler
Keyword(s):  
Compact Riemannian Manifold ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Einstein Manifolds ◽  
Consistency Conditions ◽  
Conformal Field ◽  
Geometric Data ◽  
Conformal Bootstrap ◽  
Laplacian Operators ◽  
Kaluza Klein

Abstract A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

scholarly journals Searching for elusive dark sectors with terrestrial and celestial observations

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Roberto Contino ◽  
Kevin Max ◽  
Rashmish K. Mishra
Keyword(s):  
Field Theory ◽  
Broad Class ◽  
High Energy ◽  
Effective Field ◽  
Dark Sector ◽  
Minimum Requirement ◽  
Conformal Field ◽  
Starting Point ◽  
The Standard Model ◽  
Visible Sector

Abstract We consider the possible existence of a SM-neutral and light dark sector coupled to the visible sector through irrelevant portal interactions. Scenarios of this kind are motivated by dark matter and arise in various extensions of the Standard Model. We characterize the dark dynamics in terms of one ultraviolet scale Λuv, at which the exchange of heavy mediator fields generates the portal operators, and by one infrared scale ΛIR, setting the mass gap. At energies ΛIR « E « Λuv the dark sector behaves like a conformal field theory and its phenomenology can be studied model independently. We derive the constraints set on this scenario by high- and low-energy laboratory experiments and by astrophysical observations. Our results are conservative and serve as a minimum requirement that must be fulfilled by the broad class of models satisfying our assumptions, of which we give several examples. The experimental constraints are derived in a manner consistent with the validity of the effective field theory used to define the portal interactions. We find that high-energy colliders give the strongest bounds and exclude UV scales up to a few TeV, but only in specific ranges of the IR scale. The picture emerging from current searches can be taken as a starting point to design a future experimental strategy with broader sensitivity.

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