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Emergence and Effective Field Theories in Gravitational Physics

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This talks will focus on a particular example of emergent phenomenon in a particular system. By adding to our repertoire of emergent phenomena, it may help deepen our discussions of the topic in the abstract. The system belongs to the new family that has swept condensed matter physics and goes by the name of topological insulators, which paradoxically also includes super°uids and superconductors for these too have no low energy excitations in the bulk. While no one cared much about insulators (except while standing on one of them to change a light bulb or fuse) things changed when it was realized that insulators come in two kinds. The topological ones have gapless excitations at the edge while the others do not. The bulk topological quantum number implies a gapless edge and prevents any smooth or continuous perturbation like disorder from producing a gap. Consider the d dimensional bulk superconductor with its N-particle wavefunction ©(r1; ; ; rN). The gapless edge has d¡1 spatial dimensions and a d dimensional Euclidean spacetime. Let G(r1; ; ; rN) denote its N-point correlation functions of Heisenberg ¯eld operators. It had been noticed that quite remarkably ©(r1; ; ; rN) = G(r1; ; ; rN) for a family of superconductors and super°uids. How can a nonrelativistic thing like a wave function in the bulk equal relativistic correlation function at the edge? Ashvin Vishwanath (Berkeley) and I showed that this follows from the approximate Lorentz invariance of the Euclidean action. Our explanation along with necessary background will be furnished.