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 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 𝜖-expansion in critical ϕ3-theory on real projective space from conformal field theory

2017 ◽  
Vol 32 (07) ◽  
pp. 1750045 ◽  
Author(s):  
Chika Hasegawa ◽  
Yu Nakayama
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Projective Space ◽  
Equations Of Motion ◽  
Conformal Symmetry ◽  
Real Projective Space ◽  
Point Function ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
The One

We use a compatibility between the conformal symmetry and the equations of motion to solve the one-point function in the critical [Formula: see text]-theory (a.k.a. the critical Lee–Yang model) on the [Formula: see text] dimensional real projective space to the first nontrivial order in the [Formula: see text]-expansion. It reproduces the conventional perturbation theory and agrees with the numerical conformal bootstrap result.

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 NONCOMMUTATIVE CONFORMAL FIELD THEORY IN THE TWIST-DEFORMED CONTEXT

2008 ◽  
Vol 23 (39) ◽  
pp. 3307-3315 ◽  
Author(s):  
FEDELE LIZZI ◽  
PATRIZIA VITALE
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Noncommutative Geometry ◽  
Conformal Symmetry ◽  
Two Dimensional ◽  
Moyal Product ◽  
Conformal Field ◽  
Noncommutative Plane

We discuss conformal symmetry on the two-dimensional noncommutative plane equipped with Moyal product in the twist deformed context. We show that the consistent use of the twist procedure leads to results which are free from ambiguities. This lends support to the importance of the use of twist symmetries in noncommutative geometry.

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.

Perturbative pomeron vertices and the conformal bootstrap

2016 ◽  
Vol 31 (28n29) ◽  
pp. 1645012
Author(s):  
Carlo Ewerz
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Perturbative Qcd ◽  
High Energy ◽  
Conformal Field ◽  
Energy Scattering ◽  
Conformal Bootstrap ◽  
High Energy Scattering

High energy scattering processes in QCD can be described in terms of interacting pomerons. Vertices for the interaction of pomerons have been derived in perturbative QCD. Their properties hint at the existence of a 2+1-dimensional conformal field theory of interacting pomerons. Here we study in particular the 1-to-2 and the 1-to-3 pomeron vertex and find them to be related to each other by a conformal bootstrap relation.

scholarly journals Effects of non-conformal boundary on entanglement entropy

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Andrew Loveridge
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Conformal Field Theory ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Conformal Symmetry ◽  
Entanglement Entropy ◽  
Mixed Boundary Conditions ◽  
De Sitter ◽  
Conformal Field

Abstract Spacetime boundaries with canonical Neuman or Dirichlet conditions preserve conformal invarience, but “mixed” boundary conditions which interpolate linearly between them can break conformal symmetry and generate interesting Renormalization Group flows even when a theory is free, providing soluble models with nontrivial scale dependence. We compute the (Rindler) entanglement entropy for a free scalar field with mixed boundary conditions in half Minkowski space and in Anti-de Sitter space. In the latter case we also compute an additional geometric contribution, which according to a recent proposal then collectively give the 1/N corrections to the entanglement entropy of the conformal field theory dual. We obtain some perturbatively exact results in both cases which illustrate monotonic interpolation between ultraviolet and infrared fixed points. This is consistent with recent work on the irreversibility of renormalization group, allowing some assessment of the aforementioned proposal for holographic entanglement entropy and illustrating the generalization of the g-theorem for boundary conformal field theory.

scholarly journals Integrability and conformal bootstrap: One dimensional defect conformal field theory

2022 ◽  
Vol 105 (2) ◽  
Author(s):  
Andrea Cavaglià ◽  
Nikolay Gromov ◽  
Julius Julius ◽  
Michelangelo Preti
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
One Dimensional ◽  
Conformal Field ◽  
Conformal Bootstrap

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.

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