Related papers: Geometry of Complexity in Conformal Field Theory
Defining complexity in quantum field theory is a difficult task, and the main challenge concerns going beyond free models and associated Gaussian states and operations. One take on this issue is to consider conformal field theories in 1+1…
We study circuit complexity for conformal field theory states in arbitrary dimensions. Our circuits start from a primary state and move along a unitary representation of the Lorentzian conformal group. Different choices of distance…
We define circuits given by unitary representations of Lorentzian conformal field theory in 3 and 4 dimensions. Our circuits start from a spinning primary state, allowing us to generalize formulas for the circuit complexity obtained from…
We examine the circuit complexity of coherent states in a free scalar field theory, applying Nielsen's geometric approach as in [1]. The complexity of the coherent states have the same UV divergences as the vacuum state complexity and so we…
We investigate notions of complexity of states in continuous quantum-many body systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the…
We formulate Nielsen's geometric approach to complexity in the context of two dimensional conformal field theories, where series of conformal transformations are interpreted as unitary circuits. We show that the complexity functional can be…
Holographic complexity proposals have sparked interest in quantifying the cost of state preparation in quantum field theories and its possible dual gravitational manifestations. The most basic ingredient in defining complexity is the notion…
We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d+2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d=(1,3)…
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…
We define and calculate versions of complexity for free fermionic quantum field theories in 1+1 and 3+1 dimensions, adopting Nielsen's geodesic perspective in the space of circuits. We do this both by discretizing and identifying…
We present a general construction of a geometric notion of circuit complexity for Gaussian states (both bosonic and fermionic) in terms of Riemannian geometry. We lay out general conditions that a Riemannian metric function on the space of…
Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such…
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…
The theory described by the sum of the Einstein-Hilbert action and the action of conformal scalar field possesses the duality symmetry which includes some special conformal transformation of the metric, and also inversion of scalar field…
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…
In the context of the AdS/CFT correspondence, an explicit relation between the physical degrees of freedom of 2+1d gravity and the stress tensor of 1+1d conformal field theory is exhibited. Gravity encodes thermodynamic state variables of…
Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…
To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a…
Early efforts to understand complexity in field theory have primarily employed a geometric approach based on the concept of circuit complexity in quantum information theory. In a parallel vein, it has been proposed that certain deformations…
We study circuit complexity for free fermionic field theories and Gaussian states. Our definition of circuit complexity is based on the notion of geodesic distance on the Lie group of special orthogonal transformations equipped with a…