### Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

_{T}(ω) and $$\bar{p}$$

_{T}(ω), which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S, the q

^{4}coefficient of the static structure factor S

_{4}, and the high-frequency shear modulus of the ground state μ

_{∞}, which is precisely defined. We confirm an inequality, first suggested by Haldane, that S

_{4}is bounded from below by |S–1|/8. The Laughlin wavefunction saturates this bound, which we argue to imply that systems with ground state wavefunctions close to Laughlin’s absorb gravitons of predominantly one circular polarization. We consider a nonlinear model where the sum rules are saturated by a single magneto-roton mode. In this model, the magneto-roton arises from the mixing between oscillations of an internal metric and the hydrodynamic motion. Implications for experiments are briefly discussed.

- Publication Date:

- OSTI Identifier:
- 1327326

- Grant/Contract Number:
- FG02-90ER40560

- Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Research Org:
- Univ. of Chicago, Chicago, IL (United States)

- Sponsoring Org:
- USDOE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS field theories in lower dimensions; sum rules; effective field theories