Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTopological terms of (2+1)d flag-manifold sigma models
105
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We examine topological terms of $(2+1)$d sigma models and their consequences in the light of classifications of invertible quantum field theories utilizing bordism groups. In particular, we study the possible topological terms for the $U(N)/U(1)^N$ flag-manifold sigma model in detail. We argue that the Hopf-like term is absent, contrary to the expectation from a nontrivial homotopy group $pi_3(U(N)/U(1)^N)=mathbb{Z}$, and thus skyrmions cannot become anyons with arbitrary statistics. Instead, we find that there exist ${N(N-1)over 2}-1$ types of Chern-Simons terms, some of which can turn skyrmions into fermions, and we write down explicit forms of effective Lagrangians.
rate research
Read More
This review is dedicated to two-dimensional sigma models with flag manifold target spaces, which are generalizations of the familiar $CP^{n-1}$ and Grassmannian models. They naturally arise in the description of continuum limits of spin chains, and their phase structure is sensitive to the values of the topological angles, which are determined by the representations of spins in the chain. Gapless phases can in certain cases be explained by the presence of discrete t Hooft anomalies in the continuum theory. We also discuss integrable flag manifold sigma models, which provide a generalization of the theory of integrable models with symmetric target spaces. These models, as well as their deformations, have an alternative equivalent formulation as bosonic Gross-Neveu models, which proves useful for demonstrating that the deformed geometries are solutions of the renormalization group (Ricci flow) equations, as well as for the analysis of anomalies and for describing potential couplings to fermions.
We study the promising idea of using dipolar molecular systems as analog quantum simulators for quantum link models, which are discre
One dimensional SU($n$) chains with the same irreducible representation $mathcal{R}$ at each site are considered. We determine which $mathcal{R}$ admit low-energy mappings to a $text{SU}(n)/[text{U}(1)]^{n-1}$ flag manifold sigma model, and calculate the topological angles for such theories. Generically, these models will have fields with both linear and quadratic dispersion relations; for each $mathcal{R}$, we determine how many fields of each dispersion type there are. Finally, for purely linearly-dispersing theories, we list the irreducible representations that also possess a $mathbb{Z}_n$ symmetry that acts transitively on the $text{SU}(n)/[text{U}(1)]^{n-1}$ fields. Such SU($n$) chains have an t Hooft anomaly in certain cases, allowing for a generalization of Haldanes conjecture to these novel representations. In particular, for even $n$ and for representations whose Young tableaux have two rows, of lengths $p_1$ and $p_2$ satisfying $p_1 ot=p_2$, we predict a gapless ground state when $p_1+p_2$ is coprime with $n$. Otherwise, we predict a gapped ground state that necessarily has spontaneously broken symmetry if $p_1+p_2$ is not a multiple of $n$.
QCD lattice simulations determine hadron masses as functions of the quark masses. From the gradients of these masses and using the Feynman-Hellmann theorem the hadron sigma terms can then be determined. We use here a novel approach of keeping the singlet quark mass constant in our simulations which upon using an SU(3) flavour symmetry breaking expansion gives highly constrained (i.e. few parameter) fits for hadron masses in a multiplet. This is a highly advantageous procedure for determining the hadron mass gradient as it avoids the use of delicate chiral perturbation theory. We illustrate the procedure here by estimating the light and strange sigma terms for the baryon octet.
QCD lattice simulations yield hadron masses as functions of the quark masses. From the gradients of the hadron masses the sigma terms can then be determined. We consider here dynamical 2+1 flavour simulations, in which we start from a point of the flavour symmetric line and then keep the singlet or average quark mass fixed as we approach the physical point. This leads to highly constrained fits for hadron masses in a multiplet. The gradient of this path for a hadron mass then gives a relation between the light and strange sigma terms. A further relation can be found from the change in the singlet quark mass along the flavour symmetric line. This enables light and strange sigma terms to be estimated for the baryon octet.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
