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Algebraic Conditions for Conformal Superintegrability in Arbitrary Dimension
We consider second order (maximally) conformally superintegrable systems and explain how the definition of such a system on a (pseudo-)Riemannian...
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On the vector conformal models in an arbitrary dimension
The conventional model of the gauge vector field is invariant under the local conformal symmetry only in the four-dimensional space (4 d ). Conformal...
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Conformal Symmetry
The trace or conformal anomalies are the second important family of anomalies. They affect the trace of the energy-momentum tensor of a theory and...
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Carrollian conformal correlators and massless scattering amplitudes
The theory of particle scattering is concerned with transition amplitudes between states that belong to unitary representations of the Poincaré...
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Classical Conformal Transformations
This chapter introduces conformal transformations of the coordinates in their infinitesimal form, from which finite conformal transformations and the...
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The Conformal Bootstrap
In this chapter, the elements of the previous chapters are put together and used to present the modern conformal bootstrap approach to conformal...
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Conformal Correlation Functions
This chapter discusses the central object in conformal field theory: correlation functions. It is shown how Wightman functions can be analytically...
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Geometry of conformal manifolds and the inversion formula
Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly...
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Forbidden conformal dark matter at a GeV
We introduce a model of dark matter (DM) where the DM is a composite of a spontaneously broken conformal field theory. The DM is a thermal relic with...
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On higher-spin points and infinite distances in conformal manifolds
Distances in the conformal manifold, the space of CFTs related by marginal deformations, can be measured in terms of the Zamolodchikov metric. Part...
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Conformal symmetry and effective potential: II. Evolution
We present the second part of the paper series devoted to the study of the multi-loop effective potential evolution (or anomalous dimension) in
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Holographic light dilaton at the conformal edge
We study a simple holographic model for gauge theories near the conformal edge to show that the dilaton can be parametrically lighter than any other...
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Boundaries in free higher derivative conformal field theories
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method...
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Dark matter from a conformal Dark Sector
We consider theories in which a dark sector is described by a Conformal Field Theory (CFT) over a broad range of energy scales. A coupling of the...
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Holographic Carrollian conformal scalars
We provide holographic realisations in Minkowski spacetime of a free conformal Carrollian scalar field living at null infinity. To this end, we first...
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Bootstrap** smooth conformal defects in Chern-Simons-matter theories
The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large N ...
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Anomalous Ward identities for on-shell amplitudes at the conformal fixed point
Conformal symmetry underlies many massless quantum field theories, but little is known about the consequences of this powerful symmetry for on-shell...
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Conformal Quantum Field Theory
In this chapter, a non-perturbative definition of quantum field theory in Minkowski space-time is given starting from the Wightman axioms. The...
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Global conformal blocks via shadow formalism
We study 𝔰𝔩 2 and 𝔰𝔩 3 global conformal blocks on a sphere and a torus, using the shadow formalism. These blocks arise in the context of Virasoro...
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Conformal multi-Regge theory
We propose and explore the Regge limit for correlation functions of five local primary operators in conformal field theories. After reviewing some...