Multipoint correlators of conformal field theories: Implications for quantum critical transport

Abstract

Abstract:We compute three-point correlators between the stress-energy tensor and conserved currents of conformal field theories (CFTs) in 2+1 dimensions. We first compute the correlators in the large-flavor-number expansion of conformal gauge theories and then do the computation using holography. In the holographic approach, the correlators are computed from an e↵ective action on 3+1 dimensional anti-de Sitter space (AdS 4 ), and depend upon the co-e cient, , of a four-derivative term in the action. We find a precise match between the CFT and the holographic results, thus fixing the values of . The CFTs of free fermions and bosons take the values = 1/12, 1/12 respectively, and so saturate the bound | |  1/12 obtained earlier from the holographic theory; the correlator of the conserved gauge flux of U(1) gauge theories takes intermediate values of . The value of also controls the frequency dependence of the conductivity, and other properties of quantum-critical transport at non-zero temperatures. Our results for the values of lead to an appealing physical interpretation of particle-like or vortex-like transport near quantum phase transitions of interest in condensed matter physics. This paper includes appendices reviewing key features of the AdS/CFT correspondence for condensed matter physicists.

Conserved current correlators of conformal field theories in 2+1 dimensions

“…(17) using Tensoria and subsequently decompose them into transversal and longitudinal components as shown in Table I. As we explain in more depth in Appendix A, Tensoria is built around recursion relations of Davydychev [24,38,41,42] that transform tensor-valued momentum integrals into a permuted series of scalar integrals. Adding the values in Table I, we obtain (19) in agreement with Cha et al [8].…”

“…These methods should also be applicable to other conserved current correlators of CFTs, including those of the stress-energy tensor [23], and multi-point correlators [24].…”

Study of the indirect interaction in a non-Fermi liquid within the AdS/CFT correspondence framework

“…More specifically, the relevance of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence formalism for this family of phenomena has been underscored. 1,2 In particular, the AdS/CFT correspondence between the theory of superstrings and the CFT provides a significant progress as it allows to gain access to the analytical expressions of the Green's functions for various systems. [7][8][9] In turn, accounting for the fact that solid state physics provides numerous experimental methods and tools, some of the essential general consequences associated with the AdS/CFT A. V. Zhukov et al theory can thereby be indirectly tested and verified.…”

Dynamics of few cycle optical pulses in a non-Fermi liquid and AdS/CFT correspondence

“…[1][2][3] As it is well known, the idea of the AdS/CFT correspondence between conformal field theory and superstring theory in spacetime with dimension greater by one unit lies in the fact that some effective conformal field theory on a "surface" which is a border of a "space" is associated with superstring theory in this "space". Note that this correspondence is namely that constructing the effective theory, which is equivalent to original one in sense of average computation, but gives the possibility to detect several characteristics of conformal theory, for example, such as Green's functions.…”