Gil Young Cho

Framing anomaly in the effective theory of the fractional quantum hall effect

We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.

Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions

Quantum anomalies, breakdown of classical symmetries by quantum effects, provide a sharp definition of symmetry protected topological phases. In particular, they can diagnose interaction effects on the non-interacting classification of fermionic symmetry protected topological phases. In this paper, we identify quantum anomalies in two kinds of (3+1)-dimensional fermionic symmetry protected topological phases: (i) topological insulators protected by CP (charge conjugation

Geometry of Fractional Quantum Hall Fluids

times

Conflicting symmetries in topologically ordered surface states of three-dimensional bosonic symmetry protected topological phases

reflection) and electromagnetic

Theory of nematic fractional quantum hall states

mathrm{U}(1)

Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds

symmetries, and (ii) topological superconductors protected by reflection symmetry. For the first example, which is related to, by CPT-theorem, time-reversal symmetric topological insulators, we show that the CP-projected partition function of the surface theory is not invariant under large

Surface Collective Modes in the Topological Insulators Bi2Se3 and Bi0.5Sb1.5Te3-xSex

mathrm{U}(1)

Topological phases protected by reflection symmetry and cross-cap states

gauge transformations, but picks up an anomalous sign, signaling a

Topological superconducting phases from inversion symmetry breaking order in spin-orbit-coupled systems

mathbb{Z}_2

Universal Entanglement Spectra of Gapped One-dimensional Field Theories

topological classification. Similarly, for the second example, which is related to, by CPT-theorem, time-reversal symmetric topological superconductors, we discuss the invariance/non-invariance of the partition function of the surface theory, defined on the three-torus and its descendants generated by the orientifold projection, under large diffeomorphisms (3d modular transformations). The connection to the collapse of the non-interacting classification by an integer (