Journal
PHYSICAL REVIEW D
Volume 89, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.89.026005
Keywords
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Funding
- Pappalardo Fellowship in Physics at MIT
- Purcell Fellowship at Harvard University
- U.S. National Science Foundation [DMR-1103860]
- John Templeton Foundation
- Perimeter Institute for Theoretical Physics
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research and Innovation
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1103860] Funding Source: National Science Foundation
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We study (2 + 1)-dimensional conformal field theories (CFTs) with a globally conserved U(1) charge, placed in a chemical potential which is periodically modulated along the spatial direction x with zero average: mu(x) = V cos(kx). The dynamics of such theories depends only on the dimensionless ratio V/k, and we expect that they flow in the infrared to new CFTs whose universality class changes as a function of V/k. We compute the frequency-dependent conductivity of strongly coupled CFTs using holography of the Einstein-Maxwell theory in four-dimensional anti-de Sitter space. We compare the results with the corresponding computation of weakly coupled CFTs, perturbed away from the CFT of free, massless Dirac fermions (which describes graphene at low energies). We find that the results of the two computations have significant qualitative similarities. However, differences do appear in the vicinities of an infinite discrete set of values of V/k: the universality class of the infrared CFT changes at these values in the weakly coupled theory, by the emergence of new zero modes of Dirac fermions which are remnants of local Fermi surfaces. The infrared theory changes continuously in holography, and the classical gravitational theory does not capture the physics of the discrete transition points between the infrared CFTs. We briefly note implications for a nonzero average chemical potential.
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