Fractional Electromagnetism in Quantum Matter and High-Energy Physics

Abstract

We present here a theory of fractional electro-magnetism which is capable of describing phenomenon as disparate as the non-locality of the Pippard kernel in superconductivity and anomalous dimensions for conserved currents in holographic dilatonic models. The starting point for our analysis is the observation that the standard current conservation equations remain unchanged if any differential operator that commutes with the total exterior derivative multiplies the current. Such an operator, effectively changing the dimension of the current, increases the allowable gauge transformations in electromagnetism and is at the heart of Nöther's second theorem. Here we develop a consistent theory of electromagnetism that exploits this hidden redundancy in which the standard gauge symmetry in electromagnetism is modified by the rotationally invariant operator, the fractional Laplacian. We show that the resultant theories all allow for anomalous (non-traditional) scaling dimensions of the gauge field and the associated current. Using well known extension theorems and the membrane paradigm, we show that either the boundary (UV) or horizon (IR) theory of holographic dilatonic models are both described by such fractional electromagnetism. We also show that the non-local Pippard kernel introduced to solve the problem of the Meissner effect in elemental superconductors can also be formulated as a special case of fractional electromagnetism. We show that the standard charge quantization rules fail when the gauge field acquires an anomalous dimension. The breakdown of charge quantization is discussed extensively in terms of the experimentally measurable modified Aharonov-Bohm effect in the strange metal phase of the cuprate superconductors.

arXiv comment16 pages, 4 figures. Published version

References in corpus (25)

• Gauge Theory Correlators from Non-Critical String Theory
• An extension problem related to the fractional Laplacian
• Invariant Variation Problems
• Electrodynamics of Correlated Electron Materials
• Lévy walks
• Unparticle Physics
• Powerlaw optical conductivity with a constant phase angle in high Tc superconductors
• Doping dependent optical properties of Bi2Sr2CaCu2O8+d
• What angle-resolved photemission experiments tell about the microscopic theory for high-temperature superconductors
• Optimum inhomogeneity of local lattice distortions in La2CuO4+y
• Determining the Wiedemann-Franz ratio from the thermal Hall conductivity: Application to Cu and YBa_2Cu_3O_6.95
• Quantum critical lines in holographic phases with (un)broken symmetry
• Scaling theory of the cuprate strange metals
• Noether's Second Theorem and Ward Identities for Gauge Symmetries
• Universal scaling properties of extremal cohesive holographic phases
• Gauge invariance in fractional field theories
• Breakdown of One-Paramater Scaling in Quantum Critical Scenarios for the High-Temperature Copper-oxide Superconductors
• Conductivities for Hyperscaling Violating Geometries
• Unparticle as a field with continuously distributed mass
• Quantum Phase Transitions in a Cuprate Superconductor Bi_{2}Sr_{2-x}La_{x}CuO_{6+δ}
• Un-Fermi Liquids: Unparticles in Strongly Correlated Electron Matter
• Renormalization of the Vector Current in QED
• Gauge Invariant Fractional Electromagnetic Fields
• Unparticles and Anomalous Dimensions in the Cuprates
• Geodesically Complete Metrics Induce Boundary Non-locality in Holography: Consequences for the Entanglement Entropy

Cited by in corpus (14)

• Reconciling scaling of the optical conductivity of cuprate superconductors with Planckian resistivity and specific heat
• Colloquium: Hydrodynamics and holography of charge density wave phases
• Renormalization and conformal invariance of non-local quantum electrodynamics
• Synthetic gauge field and chiral physics on two-leg superconducting circuits
• Finite electrodynamics from T-duality
• Quantization of nonlocal fractional field theories via the extension problem
• Classification of Non-local Actions: Area versus Volume Entanglement Entropy
• Zero sound and higher-form symmetries in compressible holographic phases
• Polyakov's confinement mechanism for generalized Maxwell theory
• Anomalous diffusion and Noether's second theorem
• Defect QED: Dielectric without a Dielectric, Monopole without a Monopole
• Fractional Particle and Sigma Model
• Landau Quasiparticles in Weak Power-Law Liquids
• Stranger than Metals