Charge Of Conformal Field Theories Research Articles

Bound on the central charge of CFTs in large dimension

In this paper, we use crossing symmetry and unitarity constraints to put a lower bound on the central charge of conformal field theories in large space-time dimensions D. Specifically, we work with the four-point function of identical scalars ϕ with scaling dimension ∆ϕ, and use a certain class of analytic functionals to show that the OPE coefficient squared {c}_{phi phi {T}^{mu nu}}^2 must be exponentially small in D. For this to hold, we need to make a certain assumption about the nature of the spectrum below 2∆ϕ. Our argument is robust and can be applied to any OPE coefficient squared {c}_{phi phi O}^2 with ∆O< 2∆ϕ. This suggests that conformal field theories in large dimensions (if they exist) must be exponentially close to generalized free field theories.

Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis

We calculate various quantities that characterize the dissimilarity of reduced density matrices for a short interval of length ℓ in a two-dimensional (2D) large central charge conformal field theory (CFT). These quantities include the Rényi entropy, entanglement entropy, relative entropy, Jensen-Shannon divergence, as well as the Schatten 2-norm and 4-norm. We adopt the method of operator product expansion of twist operators, and calculate the short interval expansion of these quantities up to order of ℓ9 for the contributions from the vacuum conformal family. The formal forms of these dissimilarity measures and the derived Fisher information metric from contributions of general operators are also given. As an application of the results, we use these dissimilarity measures to compare the excited and thermal states, and examine the eigenstate thermalization hypothesis (ETH) by showing how they behave in high temperature limit. This would help to understand how ETH in 2D CFT can be defined more precisely. We discuss the possibility that all the dissimilarity measures considered here vanish when comparing the reduced density matrices of an excited state and a generalized Gibbs ensemble thermal state. We also discuss ETH for a microcanonical ensemble thermal state in a 2D large central charge CFT, and find that it is approximately satisfied for a small subsystem and violated for a large subsystem.

Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT

We investigate a weak version of subsystem eigenstate thermalization hypothesis (ETH) for a two-dimensional large central charge conformal field theory by comparing the local equivalence of high energy state and thermal state of canonical ensemble. We evaluate the single-interval Rényi entropy and entanglement entropy for a heavy primary state in short interval expansion. We verify the results of Rényi entropy by two different replica methods. We find nontrivial results at the eighth order of short interval expansion, which include an infinite number of higher order terms in the large central charge expansion. We then evaluate the relative entropy of the reduced density matrices to measure the difference between the heavy primary state and thermal state of canonical ensemble, and find that the aforementioned nontrivial eighth order results make the relative entropy unsuppressed in the large central charge limit. By using Pinsker’s and Fannes-Audenaert inequalities, we can exploit the results of relative entropy to yield the lower and upper bounds on trace distance of the excited-state and thermal-state reduced density matrices. Our results are consistent with subsystem weak ETH, which requires the above trace distance is of power-law suppression by the large central charge. However, we are unable to pin down the exponent of power-law suppression. As a byproduct we also calculate the relative entropy to measure the difference between the reduced density matrices of two different heavy primary states.

Supergravity dual ofc-extremization

Recently, a general principle, called $c$-extremization, which determines the exact $R$ symmetry of two-dimensional conformal field theories with $\mathcal{N}=(0,2)$ supersymmetry, was identified. In this work we show that the supergravity dual corresponds to the extremization of the $T$ tensor of $\mathcal{N}=2$ gauged supergravity in three dimensions. To support this claim, we demonstrate that the expected central charge of conformal field theories arising from twisted compactifications of four-dimensional $\mathcal{N}=4$ Super-Yang-Mills on Riemann surfaces, whose gravity dual is a reduction of five-dimensional $U(1{)}^{3}$ gauged supergravity, is recovered in the three-dimensional framework.

Dilogarithm identities for conformal field theories and cluster algebras: Simply laced case

AbstractThe dilogarithm identities for the central charges of conformal field theories of simply laced type were conjectured by Bazhanov, Kirillov, and Reshetikhin. Their functional generalizations were conjectured by Gliozzi and Tateo. They have been partly proved by various authors. We prove these identities in full generality for any pair of Dynkin diagrams of simply laced type based on the cluster algebra formulation of the Y-systems.

Dilogarithm identities for conformal field theories and cluster algebras: Simply laced case

AbstractThe dilogarithm identities for the central charges of conformal field theories of simply laced type were conjectured by Bazhanov, Kirillov, and Reshetikhin. Their functional generalizations were conjectured by Gliozzi and Tateo. They have been partly proved by various authors. We prove these identities in full generality for any pair of Dynkin diagrams of simply laced type based on the cluster algebra formulation of the Y-systems.

Gauge symmetry in background charge conformal field theory

We present a mechanism to construct four-dimensional charged massless Ramond states using the discrete states of a fivebrane Liouville internal conformal field theory. This conformal field theory has background charge, and admits an inner product which allows positive norm states. A connection among supergravity soliton solutions, Liouville conformal field theory, non-critical string theory and their gauge symmetry properties is given. A generalized construction of the SU(2) super Kac-Moody algebra mixing with the N = 1 super Virasoro algebra is analyzed. How these Ramond states evade the DKV no-go theorem is explained.

Gauge symmetry in background charge conformal field theory

Gauge symmetry in background charge conformal field theory

Renormalization group flows in generalized Toda field theories

We study the scaling properties and renormalization-group flows of models that describe SU( N) Toda field theories in the presence of a background charge. In the Kosterlitz-Thouless region the N > 2 affine Toda theory is not renormalizable and additional couplings must be included. We consider the SU(3) case in detail and compute in perturbation theory the renormalization group beta-functions. We exhibit RG trajectories connecting UV and IR fixed points where the central charge matches the values of the central charge of conformal field theories with a W 3 algebra. Finally, we generalized out results to arbitrary N.