We present a top-down string theory holographic model of strongly interacting relativistic 2 + 1-dimensional fermions, paying careful attention to the discrete symmetries of parity and time reversal invariance. Our construction is based on probe D7-branes in AdS 5 × S 5 , stabilized by internal fluxes. We find three solutions, a parity and time reversal invariant conformal field theory which can be viewed as a particular deformation of Coulomb interacting graphene, a parity and time reversal violating but gapless field theory and a system with a parity and time reversal violating charge gap. We show that the Chern-Simons-like electric response function, which is generated perturbatively at oneloop order by parity violating fermions and which is protected by a no-renormalization theorem at orders beyond one loop, indeed appears with the correctly quantized coefficient in the charge gapped theory. In the gapless parity violating solution, the Chern-Simons response function obtains quantum corrections which we compute in the holographic theory.
An appropriately oriented D3-D7-brane system is the holographic dual of relativistic Fermions occupying a 2+1-dimensional defect embedded in 3+1-dimensional spacetime. The Fermions interact via fields of N = 4 Yang-Mills theory in the 3+1-dimensional bulk. Recently, using internal flux to stabilize the system in the probe N 7 << N 3 limit, a number of solutions which are dual to conformal field theories with Fermion content have been found. We use holographic techniques to study perturbations of a particular one of the conformal field theories by relevant operators. Generally, the response of a conformal field theory to such a perturbation grows and becomes nonperturbative at low energy scales. We shall find that a perturbation which switches on a background magnetic field B and Fermion mass m induces a renormalization group flow that can be studied perturbatively in the limit of small m 2 /B. We solve the leading order explicitly. We find that, for one particular value of internal flux, the system exhibits magnetic catalysis, the spontaneous breaking of chiral symmetry enhanced by the presence of the magnetic field. In the process, we derive formulae predicting the Debye screening length of the Fermion-antiFermion plasma at finite density and the diamagnetic moment of the ground state of the Fermion system in the presence of a magnetic field.
The leading order of the large N limit of the O(N) symmetric phi-six theory in three dimensions has a phase which exhibits spontaneous breaking of scale symmetry accompanied by a massless dilaton which is a Goldstone boson. At the next-to-leading order in large N, the phi-six coupling has a beta function of order 1/N and it is expected that the dilaton acquires a small mass, proportional to the beta function and the condensate. In this note, we show that this "light dilaton" is actually a tachyon. This indicates an instability of the phase of the theory with spontaneously broken approximate scale invariance.The scenario where a quantum field theory can have a parametrically small beta function resulting in approximate scale invariance has attracted attention, particularly when the approximate scale symmetry can be spontaneously broken, generating a pseudo-Goldstone boson in the form of a light dilaton. For example, the notion that the tree level scale invariance of the SU (2) × U (1) electroweak theory is softly broken by the Higgs potential or dynamically broken by some physical mechanism beyond the standard model leaves the Higgs boson itself as the dilaton, with some testable physical consequences One of the prototypical examples of spontaneously broken scale symmetry occurs in the large N limit of the tricritical O(N) symmetric g 2 ( φ 2 ) 3 -theory in three spacetime dimensions which is an interesting quantum field theory in its own right. The g 2 ( φ 2 ) 3 interaction is scale invariant at the classical level. Its beta-function is of order 1/N and it is therefore suppressed at large N. As a result, g 2 ( φ 2 ) 3 remains exactly marginal at the leading order in the large N expansion and, at the next-to-leading order g 2 , it becomes a slowly running coupling and the theory is approximately scale invariant. The beta function, depicted in FIG.
Based on some theoretical arguments, it has been suggested that electromagnetic response of 3D Weyl semimetals with non-zero chiral-chemical potential may have a Chern-Simons term, 1 2 k µ µνρσ F νρ A σ , in their effective action for the gauge field. An independent numerical study has shown that such a term is absent in a similar system. In this paper, we investigate the non-equilibrium and equilibrium response of 3D Weyl semi-metals. We argue that the controversy in literature stems from the difference in response of these two distinct states. We then develop a method to deal with well-known ambiguities in quantum electrodynamics in 3D (QED 3+1 ) with non-zero chiral-chemical potential and calculate the Chern-Simons term unambiguously. We find that timelike Chern-Simons term can exist in non-equilibrium conditions. We observe that there does not exist any chiralmagnetic effect in equilibrium and anomalous Hall effect replaces it.
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