Superconducting and Antiferromagnetic Phases of Space-Time

Deepak Vaid

doi:10.1155/2017/7935185

Abstract

A correspondence between the SO5 theory of high-TC superconductivity and antiferromagnetism, put forward by Zhang and collaborators, and a theory of gravity arising from symmetry breaking of a SO5 gauge field is presented. A physical correspondence between the order parameters of the unified SC/AF theory and the generators of the gravitational gauge connection is conjectured. A preliminary identification of regions of geometry, in solutions of Einstein’s equations describing charged-rotating black holes embedded in de Sitter space-time, with SC and AF phases is carried out.

Highlights

Two of the outstanding problems in theoretical physics today are those of high-T퐶 superconductivity (HTSC) on the one hand and quantum gravity (QG) on the other
(3) Both d-wave SC and AF can be described in terms of the behavior of singlet pairs in the Hubbard model at half-filling. These singlet pairs can describe either an AF phase, a SC phase, or a so-called “spin-bag” phase where both the phases coexist. If both AF and SC arise in different regimes of a system with the same underlying physics, the Hubbard model at half-filling, and can coexist under certain conditions, it follows that one would be well-advised to seek out a lowtemperature, long-wavelength effective field theory which can describe both phases
On the condensed matter side, it is understood that the SO(5) formalism for high-T퐶 superconductivity and antiferromagnetism is only an approximation [29, 30] that arises in the long-wavelength low-energy limit of the physics of some underlying fundamental dynamics

Summary

Introduction

Two of the outstanding problems in theoretical physics today are those of high-T퐶 superconductivity (HTSC) on the one hand and quantum gravity (QG) on the other. If both AF and SC arise in different regimes of a system with the same underlying physics, the Hubbard model at half-filling, and can coexist under certain conditions, it follows that one would be well-advised to seek out a lowtemperature, long-wavelength effective field theory which can describe both phases Such a theory should contain a SO(3) × U(1) symmetry, which should arise after some symmetry breaking transition. In order to able to write down the generators of the SO(5) Lie algebra, with respect to which n푎 transforms as an SO(5) vector, we need to define the operators which generate the symmetries of the system These are S푖, Q, and π푖 which correspond, respectively, to the total spin, total charge, and AF-to-SC transformation operators, respectively.

Cartan Decomposition

BF Theory

Physical Interpretation

Discussion

Notational Conventions