Conformal field theory in momentum space and anomaly actions in gravity: The analysis of three- and four-point function

2022 ◽  
Vol 952 ◽  
pp. 1-95
Author(s):  
Claudio Corianò ◽  
Matteo Maria Maglio
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Momentum Space ◽  
Point Function ◽  
Conformal Field

scholarly journals Celestial superamplitude in $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hongliang Jiang
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Momentum Space ◽  
Ward Identity ◽  
Yang Mills ◽  
Conformal Field ◽  
New Perspective ◽  
Celestial Sphere

Abstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $$ \mathcal{N} $$ N = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $$ \mathcal{N} $$ N = 4 SYM amplitudes via 2D celestial conformal field theory.

scholarly journals Anomalies from correlation functions in defect conformal field theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Christopher P. Herzog ◽  
Itamar Shamir
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Effective Action ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Point Function ◽  
Perfect Agreement ◽  
Conformal Field ◽  
Density Anomaly ◽  
The One

Abstract In previous work, we showed that an anomaly in the one point function of marginal operators is related by the Wess-Zumino condition to the Euler density anomaly on a two dimensional defect or boundary. Here we analyze in detail the two point functions of marginal operators with the stress tensor and with the displacement operator in three dimensions. We show how to get the boundary anomaly from these bulk two point functions and find perfect agreement with our anomaly effective action. For a higher dimensional conformal field theory with a four dimensional defect, we describe for the first time the anomaly effective action that relates the Euler density term to the one point function anomaly, generalizing our result for two dimensional defects.

scholarly journals The cosmological bootstrap: weight-shifting operators and scalar seeds

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Daniel Baumann ◽  
Carlos Duaso Pueyo ◽  
Austin Joyce ◽  
Hayden Lee ◽  
Guilherme L. Pimentel
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Massive Scalar ◽  
Point Function ◽  
Conformal Field ◽  
Slow Roll ◽  
Bootstrap Approach ◽  
Raising Operator ◽  
Theoretical Foundations ◽  
Weight Shifting

Abstract A key insight of the bootstrap approach to cosmological correlations is the fact that all correlators of slow-roll inflation can be reduced to a unique building block — the four-point function of conformally coupled scalars, arising from the exchange of a massive scalar. Correlators corresponding to the exchange of particles with spin are then obtained by applying a spin-raising operator to the scalar-exchange solution. Similarly, the correlators of massless external fields can be derived by acting with a suitable weight-raising operator. In this paper, we present a systematic and highly streamlined derivation of these operators (and their generalizations) using tools of conformal field theory. Our results greatly simplify the theoretical foundations of the cosmological bootstrap program.

scholarly journals 4-point function from conformally coupled scalar in AdS6

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Jae-Hyuk Oh
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Ward Identity ◽  
Conformal Symmetry ◽  
Classical Solutions ◽  
Point Function ◽  
Conformal Theory ◽  
Conformal Field ◽  
Linear Limit

Abstract We explore conformally coupled scalar theory in AdS6 extensively and their classical solutions by employing power expansion order by order in its self-interaction coupling λ. We describe how we get the classical solutions by diagrammatic ways which show general rules constructing the classical solutions. We study holographic correlation functions of scalar operator deformations to a certain 5-dimensional conformal field theory where the operators share the same scaling dimension ∆ = 3, from the classical solutions. We do not assume any specific form of the micro Lagrangian density of the 5-dimensional conformal field theory. For our solutions, we choose a scheme where we remove co-linear divergences of momenta along the AdS boundary directions which frequently appear in the classical solutions. This shows clearly that the holographic correlation functions are free from the co-linear divergences. It turns out that this theory provides correct conformal 2- and 3- point functions of the ∆ = 3 scalar operators as expected in previous literature. It makes sense since 2- and 3- point functions are determined by global conformal symmetry not being dependent on the details of the conformal theory. We also get 4-point function from this holographic model. In fact, it turns out that the 4-point correlation function is not conformal because it does not satisfy the special conformal Ward identity although it does dilation Ward identity and respect SO(5) rotation symmetry. However, in the co-linear limit that all the external momenta are in a same direction, the 4-point function is conformal which means that it satisfy the special conformal Ward identity. We inspect holographic n-point functions of this theory which can be obtained by employing a certain Feynman-like rule. This rule is a construction of n-point function by connecting l-point functions each other where l < n. In the co-linear limit, these n-point functions reproduce the conformal n-point functions of ∆ = 3 scalar operators in d = 5 Euclidean space addressed in arXiv:2001.05379.

scholarly journals On Galilean conformal bootstrap

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Bin Chen ◽  
Peng-xiang Hao ◽  
Reiko Liu ◽  
Zhe-fei Yu
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Inversion Formula ◽  
Conformal Symmetry ◽  
Taylor Series Expansion ◽  
Point Function ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
Free Theory ◽  
Exact Agreement

Abstract In this work, we develop conformal bootstrap for Galilean conformal field theory (GCFT). In a GCFT, the Hilbert space could be decomposed into quasiprimary states and its global descendants. Different from the usual conformal field theory, the quasiprimary states in a GCFT constitute multiplets, which are block-diagonized under the Galilean boost operator. More importantly the multiplets include the states of negative norms, indicating the theory is not unitary. We compute global blocks of the multiplets, and discuss the expansion of four-point functions in terms of the global blocks of the multiplets. Furthermore we do the harmonic analysis for the Galilean conformal symmetry and obtain an inversion formula. As the first step to apply the Galilean conformal bootstrap, we construct generalized Galilean free theory (GGFT) explicitly. We read the data of GGFT by using Taylor series expansion of four-point function and the inversion formula independently, and find exact agreement. We discuss some novel features in the Galilean conformal bootstrap, due to the non-semisimpleness of the Galilean conformal algebra and the non-unitarity of the GCFTs.

scholarly journals PCT theorem, Wightman axioms and conformal bootstrap

2021 ◽  
Vol 36 (11) ◽  
pp. 2150072
Author(s):  
Jnanadeva Maharana
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Analytic Continuation ◽  
Crucial Role ◽  
Point Function ◽  
Bootstrap Equation ◽  
Conformal Field ◽  
Local Commutativity ◽  
Conformal Bootstrap ◽  
Wightman Axioms

The axiomatic Wightman formulation for nonderivative conformal field theory is adopted to derive conformal bootstrap equation for the four-point function. The equivalence between PCT theorem and weak local commutativity, due to Jost plays a very crucial role in axiomatic field theory. The theorem is suitably adopted for conformal field theory to derive the desired equations in CFT. We demonstrate that the two Wightman functions are analytic continuation of each other.

scholarly journals Four-point correlation modular bootstrap for OPE densities

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Carlos Cardona ◽  
Cynthia Keeler ◽  
William Munizzi
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Spectral Decomposition ◽  
Large Dimension ◽  
Two Dimensional ◽  
Point Function ◽  
Conformal Field ◽  
Virasoro Symmetry ◽  
Point Correlation ◽  
Conserved Currents

Abstract In this work we apply the lightcone bootstrap to a four-point function of scalars in two-dimensional conformal field theory. We include the entire Virasoro symmetry and consider non-rational theories with a gap in the spectrum from the vacuum and no conserved currents. For those theories, we compute the large dimension limit (h/c ≫ 1) of the OPE spectral decomposition of the Virasoro vacuum. We then propose a kernel ansatz that generalizes the spectral decomposition beyond h/c ≫ 1. Finally, we estimate the corrections to the OPE spectral densities from the inclusion of the lightest operator in the spectrum.

scholarly journals A scattering amplitude in Conformal Field Theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Marc Gillioz ◽  
Marco Meineri ◽  
João Penedones
Keyword(s):  
Field Theory ◽  
Fourier Transform ◽  
Form Factor ◽  
Conformal Field Theory ◽  
Scattering Amplitude ◽  
Form Factors ◽  
Point Function ◽  
Partial Wave Expansion ◽  
Conformal Field ◽  
The Fourier Transform

Abstract We define form factors and scattering amplitudes in Conformal Field Theory as the coefficient of the singularity of the Fourier transform of time-ordered correlation functions, as p2 → 0. In particular, we study a form factor F(s, t, u) obtained from a four-point function of identical scalar primary operators. We show that F is crossing symmetric, analytic and it has a partial wave expansion. We illustrate our findings in the 3d Ising model, perturbative fixed points and holographic CFTs.

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