Related papers: Complexity for Conformal Field Theories in General…
Following on from a general observation in an earlier paper, we consider the continuous symmetries of a certain class of conformal field theories constructed from lattices and their reflection-twisted orbifolds. It is shown that the naive…
Nielsen's geometric approach offers a powerful framework for quantifying the complexity of unitary transformations. In this formulation, complexity is defined as the length of the minimal geodesic in a suitably constructed geometric space…
A method for consistent quantization of conformal gravity treating conformal symmetry in a very controllable way is presented. First, we discuss local conformal symmetry in the framework of gravitational interactions, where we view it as an…
We construct logarithmic conformal field theories starting from an ordinary conformal field theory -- with a chiral algebra C and the corresponding space of states V -- via a two-step construction: i) deforming the chiral algebra…
Conformal field theory finds applications across diverse fields, from statistical systems at criticality to quantum gravity through the AdS/CFT correspondence. These theories are subject to strong constraints, enabling a systematic…
We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one…
We present a systematic method to expand the quantum complexity of interacting theory in series of coupling constant. The complexity is evaluated by the operator approach in which the transformation matrix between the second quantization…
The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are…
The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…
We use the separate universe framework to study cosmological perturbations within the group field theory formalism for quantum gravity, based on multi-condensate quantum states. Working with a group field theory action for gravity minimally…
The emergence of Lorentzian geometries in spin-foams and group field theories is investigated. The spectral dimension of periodic Euclidean spin-foam frusta is studied. At large scales, the spectral dimension is generically four. At lower…
Motivated by the recent interest in the criticality of open quantum many-body systems, we study nonlinear sigma models with complexified couplings as a general framework for nonunitary field theory. Applying the perturbative…
We reexamine two-dimensional Lorentzian conformal field theory using the formalism previously developed in a study of sine-square deformation of Euclidean conformal field theory. We construct three types of Virasoro algebra. One of them…
Two different systems of the generalized coherent states for the de Sitter group are constructed. These systems have the physical sense of particles and antiparticles over de Sitter space and obeys the Klein-Gordon equation. Using these…
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…
A conformal field theory (CFT) is a quantum field theory which is invariant under conformal transformations; a group action that preserve angles but not necessarily lengths. There are two traditional approaches to the construction of CFTs:…
We study conformal field theories (CFTs) and their classifications from a modern perspective based on the abstract algebraic formalism of symmetries or conserved charges, known as symmetry topological field theories (SymTFTs). By studying…
We revise the use of 8-dimensional conformal, complex (Cartan) domains as a base for the construction of conformally invariant quantum (field) theory, either as phase or configuration spaces. We follow a gauge-invariant Lagrangian approach…
We study non-relativistic conformal field theory on a flat space in the presence of a planar boundary. We compute correlation functions of primary operators and obtain the expression for the boundary conformal block. We also discuss the…
By interpreting the fusion matrix as an adjacency matrix we associate a loop model to every primary operator of a generic conformal field theory. The weight of these loop models is given by the quantum dimension of the corresponding primary…