Hidden global conformal symmetry without Virasoro extension in theory of elasticity

TL;DR

This paper reveals that the 2D theory of elasticity exhibits a hidden global conformal symmetry of SL(2,R) x SL(2,R) without extending to the Virasoro algebra, challenging previous assumptions about its conformal properties.

Contribution

The work demonstrates the presence of hidden global conformal symmetry in the 2D elasticity theory without Virasoro extension, using a four-derivative scalar potential formulation.

Findings

Correlation functions embed into a global conformal field theory.

The energy-momentum tensor cannot be improved to traceless, lacking Virasoro symmetry.

The theory violates reflection positivity due to the scalar potential formulation.

Abstract

The theory of elasticity (a.k.a. Riva-Cardy model) has been regarded as an example of scale invariant but not conformal field theories. We argue that in $d=2$ dimensions, the theory has hidden global conformal symmetry of $SL(2,\mathbb{R}) \times SL(2,\mathbb{R})$ without its Virasoro extension. More precisely, we can embed all the correlation functions of the displacement vector into a global conformal field theory with four-derivative action in terms of two scalar potential variables, which necessarily violates the reflection positivity. The energy-momentum tensor for the potential variables cannot be improved to become traceless so that it does not show the Virasoro symmetry even with the existence of global special conformal current.