Related papers: A Duality Web in 2+1 Dimensions and Condensed Matt…
We consider 2D fermions on a plane with a perpendicular magnetic field, described by Landau levels. It is wellknown that, semiclassically, restriction to the lowest Landau levels (LLL) implies two constraints on a 4D phase space, that…
This thesis discusses various aspects of duality in quantum field theory and string theory. In the first part we consider duality in topological quantum field theories, concentrating on the Donaldson and Seiberg-Witten theories as (dual)…
We consider minimally supersymmetric QCD in 2+1 dimensions, with Chern-Simons and superpotential interactions. We propose an infrared $SU(N) \leftrightarrow U(k)$ duality involving gauge-singlet fields on one of the two sides. It shares…
Quenched studies of a global U(1) symmetric Wilson-Yukawa model in two dimensions show no evidence of a charged fermion in the vortex phase at strong Wilson-Yukawa coupling while there is strong indication of a massive neutral fermion.…
We consider 1+1 dimensional SU(N) gauge theory coupled to a multiplet of massive Dirac fermions transforming in the adjoint representation of the gauge group. The only global symmetry of this theory is a U(1) associated with the conserved…
In this paper, two things are done. First, we analyze the compatibility of Dirac fermions with the hidden duality symmetries which appear in the toroidal compactification of gravitational theories down to three spacetime dimensions. We show…
We study a formal extension of the Dirac equation in the framework of a non-commutative two-sheeted space-time. It is shown that this approach naturally extends the classical Dirac theory by doubling the number of fermionic states, which…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…
Using the duality between seemingly different (2+1)d conformal field theories (CFT) proposed recently, we study a series of (2+1)d stable self-dual interacting CFTs. These CFTs can be realized (for instance) on the boundary of the (3+1)d…
It is well-known that the tight-binding Hamiltonian of graphene describes the low-energy excitations that appear to be massless chiral Dirac fermions. Thus, in the continuum limit one can analyze the crystal properties using the formalism…
The conductivity of a finite temperature 1+1 dimensional fermion gas described by the massive Thirring model is shown to be related to the retarded propagator of the dual boson sine-Gordon model. Duality provides a natural resummation which…
We propose new infinite families of non-supersymmetric IR dualities in three space-time dimensions, between Chern-Simons gauge theories (with classical gauge groups) with both scalars and fermions in the fundamental representation. In all…
We give evidence for 3d bosonization in Conformal Field Theories (CFTs) by computing monopole operator scaling dimensions in 2+1 dimensional quantum electrodynamics (QED3) with Chern-Simons level $k$ and $N$ complex bosons in a large $N,k$…
We review the parity anomaly of the massless Dirac fermion in $2+1$ dimensions from the Hamiltonian, as opposed to the path integral, point of view. We have two main goals for this note. First, we hope to make the parity anomaly more…
In this paper we study particle-vortex duality and the effect of theta terms from the point of view of AdS/CMT constructions. We can construct the duality in 2+1 dimensional field theories with or without a Chern-Simons term, and derive an…
We study some consequences of dimensionally reducing systems with massless fermions and Abelian gauge fields from 3+1 to 2+1 dimensions. We first consider fermions in the presence of an external Abelian gauge field. In the reduced theory,…
We propose a framework for a new type of finite field theories based on a hidden duality between an ultra-violet and an infra-red region. Physical quantities do not receive radiative corrections at a fundamental scale or the fixed point of…
A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are…
Pointlike interactions between bosons in 1D are related to pointlike interactions between fermions through the Girardeau mapping. This mapping is a strong-weak duality since the coupling constants in the bosonic and fermionic cases are…
Bosonization in curved spacetime maps massive Thirring model (self-interacting Dirac fermions) to a generalized sine-Gordon model, both living in $1+1$-dimensional curved spacetime. Applying this duality we have shown that the Thirring…