Related papers: Complexity for Conformal Field Theories in General…
We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR's of the conformal groups with Lie algebras $so(2,d)$. We classify gauge theories invariant under $so(2,d)$, both integral and half-integral spins. A…
Conformal primary fields are of central importance in a conformal field theory with d > 2 spacetime dimensions. They can be defined in two ways. A first definition involves commutators between the field and the generators of the conformal…
We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory…
Conformal field theories based on $g/u(1)^d$ coset constructions where $g$ is a reductive algebra are studied.It is shown that the theories are equivalent to constrained WZNW models for $g.$ Generators of extended symmetry algebras and…
Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in…
The periods of arbitrary abelian forms on hyperelliptic Riemann surfaces, in particular the periods of the meromorphic Seiberg-Witten differential, are shown to be in one-to-one correspondence with the conformal blocks of correlation…
This is a review of two-dimensional conformal field theory including some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is as elementary and flexible as possible at the same time.…
We answer to the question whether a system of the 3rd order ODEs describes geodesics of a conformal structure. We construct a functor from a category of conformal geometries to a category of Cartan geometries associated to the 3rd order…
In this paper, we will make an attempt to clarify the relation between three-dimensional euclidean loop quantum gravity with vanishing cosmological constant and quantum field theory in the continuum. We will argue, in particular, that in…
We study relevant deformations of conformal field theory on a cylinder using conformal perturbation theory, and in particular the one point function of the deformation operator and the energy in a system after a quench. We do the one point…
An important conjecture within the AdS/CFT correspondence relates holographic spacetime to the quantum computational complexity of the dual quantum field theory. However, the quantitative understanding of this relation is still an open…
Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
The idea of "summing over all intermediate states" that is central for implementing locality in quantum systems can be realized by coend constructions. In the concrete case of systems of conformal blocks for a certain class of conformal…
The aim of this paper is to describe the geometry of conformal structures in Lorentzian signature, which admit a lightlike conformal Killing vector field whose corresponding adjoint tractor acts as complex structure on the standard tractor…
The role of the conformal group in electrodynamics in four space-time dimensions is re-examined. As a pedagogic example we use the application of conformal transformations to find the electromagnetic field for a charged particle moving with…
We construct field theories in $2+1$ dimensions with multiple conformal symmetries acting on only one of the spatial directions. These can be considered a conformal extension to "subsystem scale invariances", borrowing the language often…
The loss of criticality in the form of weak first-order transitions or the end of the conformal window in gauge theories can be described as the merging of two fixed points that move to complex values of the couplings. When the complex…
The aim of this paper is to study three dimensional Lorentzian conformal field theories in twistor space. We formulate the conformal Ward identities and solve for two and three point Lorentzian Wightman functions. We found that the Helicity…
We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two dimensional magnetohydrodynamics is…