Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Duality Web in 2+1 Dimensions and Condensed Matter Physics
103
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Building on earlier work in the high energy and condensed matter communities, we present a web of dualities in $2+1$ dimensions that generalize the known particle/vortex duality. Some of the dualities relate theories of fermions to theories of bosons. Others relate different theories of fermions. For example, the long distance behavior of the $2+1$-dimensional analog of QED with a single Dirac fermion (a theory known as $U(1)_{1/2}$) is identified with the $O(2)$ Wilson-Fisher fixed point. The gauged version of that fixed point with a Chern-Simons coupling at level one is identified as a free Dirac fermion. The latter theory also has a dual version as a fermion interacting with some gauge fields. Assuming some of these dualities, other dualities can be derived. Our analysis resolves a number of confusing issues in the literature including how time reversal is realized in these theories. It also has many applications in condensed matter physics like the theory of topological insulators (and their gapped boundary states) and the problem of electrons in the lowest Landau level at half filling. (Our techniques also clarify some points in the fractional Hall effect and its description using flux attachment.) In addition to presenting several consistency checks, we also present plausible (but not rigorous) derivations of the dualities and relate them to $3+1$-dimensional $S$-duality.
rate research
Read More
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 qualitative features both with 3d bosonization and with 4d Seiberg duality. We provide a few consistency checks of the proposal, mapping the structure of vacua and performing perturbative computations in the $varepsilon$-expansion.
We consider Quantum Electrodynamics with an even number $N_f$ of bosonic or fermionic flavors, allowing for interactions respecting at least $U(N_f/2)^2$ global symmetry. Both in the bosonic and in the fermionic case, we find four interacting fixed points: two with $U(N_f/2)^2$ symmetry, two with $U(N_f)$ symmetry. Large $N_f$ arguments suggest that, lowering $N_f$, all these fixed points merge pairwise and become complex CFTs. In the bosonic QEDs the merging happens around $N_fsim 9{-}11$ and does not break the global symmetry. In the fermionic QEDs the merging happens around $N_fsim3{-}7$ and breaks $U(N_f)$ to $U(N_f/2)^2$. When $N_f=2$, we show that all four bosonic fixed points are one-to-one dual to the fermionic fixed points. The merging pattern suggested at large $N_f$ is consistent with the four $N_f=2$ boson $lra$ fermion dualities, providing support to the validity of the scenario.
In the last few years it was realized that every fermionic theory in 1+1 dimensions is a generalized Jordan-Wigner transform of a bosonic theory with a non-anomalous $mathbb{Z}_2$ symmetry. In this note we determine how the boundary states are mapped under this correspondence. We also interpret this mapping as the fusion of the original boundary with the fermionization interface.
We discuss bosonic models with a moat spectrum, where in momentum space the minimum of the dispersion relation is on a sphere of nonzero radius. For spinless bosons with $O(N)$ symmetry, we emphasize the essential difference between $N=2$ and $N > 2$. When $N=2$, there are two phase transitions: at zero temperature, a transition to a state with Bose condensation, and at nonzero temperature, a transition to a spatially inhomogeneous state. When $N > 2$, previous analysis suggests that a mass gap is generated dynamically at any temperature. In condensed matter, a moat spectrum is important for spin-orbit-coupled bosons. For cold nuclear or quarkyonic matter, we suggest that the transport properties, such as neutrino emission, are dominated by the phonons related to a moat spectrum; also, that at least in the quarkyonic phase the nucleons may be a non-Fermi liquid.
A famous example of gauge/gravity duality is the result that the entropy density of strongly coupled ${cal N}=4$ SYM in four dimensions for large N is exactly 3/4 of the Stefan-Boltzmann limit. In this work, I revisit the massless O(N) model in 2+1 dimensions, which is analytically solvable at finite temperature $T$ for all couplings $lambda$ in the large N limit. I find that the entropy density monotonically decreases from the Stefan-Boltzmann limit at $lambda=0$ to exactly 4/5 of the Stefan-Boltzmann limit at $lambda=infty$. Calculating the retarded energy-momentum tensor correlator in the scalar channel at $lambda=infty$, I find that it has two logarithmic branch cuts originating at $omega=pm 4 T ln frac{1+sqrt{5}}{2}$, but no singularities in the whole complex frequency plane. I show that the ratio 4/5 and the location of the branch points both are universal within a large class of bosonic CFTs in 2+1 dimensions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
