Generalized Gradient Flow Equation and Its Application to Super Yang-Mills Theory

We generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of the gradient flow equation. It can be shown that the super gauge symmetry is preserved in the gradient flow. Furthermore, choosing an appropriate modification term to damp the gauge degrees of freedom, we obtain a gradient flow equation which is closed within the Wess-Zumino gauge.Comment: 35 pages, v2: typos corrected and references added, v3: published versio

Bosonization approach for "atomic collapse" in graphene

We study quantum electrodynamics with 2+1 dimensional massless Dirac fermion around a Coulomb impurity. Around a large charge with atomic number Z > 137, the QED vacuum is expected to collapse due to the strong Coulombic force. While the relativistic quantum mechanics fails to make reliable predictions for the fate of the vacuum, the heavy ion collision experiment also does not give clear understanding of this system. Recently, the "atomic collapse" resonances were observed on graphene where an artificial nuclei can be made. In this paper, we present our nonperturbative study of the vacuum structure of the quasiparticles in graphene with a charge impurity which contains multi-body effect using bosonization method.Comment: 18 pages, 7 figure

Intra-cone transition effect to magnetoconductivity in Dirac semimetal

We study the transport of the fermions with a small mass in the presence of Coulomb impurities, which could be realized in slightly distorted Dirac semimetals. Using the semiclassical Boltzmann equation, we derive the relaxation times for two kinds of intra-cone transition process. One is due to the effect of mass, and the other is due to the excited states in Landau levels under the weaker magnetic field. Hence we derive the mass dependence and the magnetic field dependence of the longitudinal magnetoconductivity in the presence of parallel electric and magnetic fields.Comment: 20 pages, 5 figure

Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.Comment: 8 pages, Proceedings of the 35th annual International Symposium on Lattice Field Theor