We explore a new class of supersymmetric models for lepton masses and mixing angles
where the role of flavour symmetry is played by modular invariance. The building blocks are …

On the space of three-dimensional conformal field theories with U (1) symmetry and a
chosen coupling to a background gauge field, there is a natural action of the group SL (2, Z) …

We show how particle-vortex duality implies the existence of a large non-Abelian discrete
symmetry group that relates the electromagnetic response for dual two-dimensional systems …

Transitions among quantum Hall plateaux share a suite of remarkable experimental
features, such as semicircle laws and duality relations, whose accuracy and robustness are …

A bstract We study the response of a conserved current to external electromagnetic fields in
a holographic system with boundaries using the recently proposed AdS/BCFT (boundary …

An analytic form for the conductivity tensor in crossover between two quantum Hall plateaux
is derived, which appears to be in good agreement with existing experimental data. The …

A bstract Experimental data for fractional quantum Hall systems can to a large extent be
explained by assuming the existence of a Γ 0 (2) modular symmetry group commuting with …

We show that, for the transition between any two quantum Hall states, the semicircle law and
the existence of a duality symmetry follow solely from the consistency of the law of …

In this Letter, we elaborate on the SL (2, Z) action on three-dimensional conformal field
theories with U (1) symmetry introduced by Witten, by trying to give an explicit verification of …

Low-energy transport measurements in quantum Hall systems have been argued to be
governed by emergent modular symmetries whose predictions are robust against many of …