Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantisation of the SU(N) WZW Model at Level $k$
155
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The quantisation of the Wess-Zumino-Witten model on a circle is discussed in the case of $SU(N)$ at level $k$. The quantum commutation of the chiral vertex operators is described by an exchange relation with a braiding matrix, $Q$. Using quantum consistency conditions, the braiding matrix is found explicitly in the fundamental representation. This matrix is shown to be related to the Racah matrix for $U_t(SL(N))$. From calculating the four-point functions with the Knizhnik-Zamolodchikov equations, the deformation parameter $t$ is shown to be $t=exp({ipi /(k+N)})$ when the level $kge 2$. For $k=1$, there are two possible types of braiding, $t=exp({ipi /(1+N)})$ or $t=exp(ipi)$. In the latter case, the chiral vertex operators are constructed explicitly by extending the free field realisation a la Frenkel-Kac and Segal. This construction gives an explicit description of how to chirally factorise the $SU(N)_{k=1}$ WZW model.
rate research
Read More
The classic argument by Polyakov showing that monopoles produce confinement in the Higgs phase of the Georgi-Glashow model is generalized to study the spectrum of k-strings. We find that the leading-order low-density approximation yields Casimir scaling in the weakly-coupled 3-d SU(N) Georgi-Glashow model. Corrections to the Casimir formula are considered. When k is of the order of N, the non-diluteness effect is of the same order as the leading term, indicating that non-diluteness can significantly change the Casimir-scaling behavior. The correction produced by the propagating Higgs field is also studied and found to increase, together with the non-diluteness effect, the Casimir-scaling ratio. Furthermore, a correction due to closed k-strings is also computed and is shown to yield the same k-dependence as the one due to non-diluteness, but with the opposite sign and a nontrivial N-dependence. Finally, we consider the possible implications of our analysis for the SU(N) analogue of compact QED in four dimensions.
82 -
Wilson Oliveira
, Jorge Ananias Neto (Physics Department
, n Universidade Federal de Juiz de Fora
1995
We apply The Batalin-Tyutin constraint formalism of converting a second class system into a first class system for the rotational quantisation of the SU(2) Skyrme model. We obtain the first class constraint and the Hamiltonian in the extended phase space. The vacuum functional is constructed and evaluated in the unitary gauge and a multiplier dependent gauge. Finally, we discuss the spectrum of the extended theory. The use of the BT formalism on the collective coordinates quantisation of the SU(2) Skyrme model leads an additional term in the usual quantum Hamiltonian that can improve the phenomenology predicted by the Skyrme model.
Generalizations of the AGT correspondence between 4D $mathcal{N}=2$ $SU(2)$ supersymmetric gauge theory on ${mathbb {C}}^2$ with $Omega$-deformation and 2D Liouville conformal field theory include a correspondence between 4D $mathcal{N}=2$ $SU(N)$ supersymmetric gauge theories, $N = 2, 3, ldots$, on ${mathbb {C}}^2/{mathbb {Z}}_n$, $n = 2, 3, ldots$, with $Omega$-deformation and 2D conformal field theories with $mathcal{W}^{, para}_{N, n}$ ($n$-th parafermion $mathcal{W}_N$) symmetry and $widehat{mathfrak{sl}}(n)_N$ symmetry. In this work, we trivialize the factor with $mathcal{W}^{, para}_{N, n}$ symmetry in the 4D $SU(N)$ instanton partition functions on ${mathbb {C}}^2/{mathbb {Z}}_n$ (by using specific choices of parameters and imposing specific conditions on the $N$-tuples of Young diagrams that label the states), and extract the 2D $widehat{mathfrak{sl}}(n)_N$ WZW conformal blocks, $n = 2, 3, ldots$, $N = 1, 2, ldots, .$
We investigate some properties of the standard rotator approximation of the SU$(N)times,$SU$(N)$ sigma-model in the delta-regime. In particular we show that the isospin susceptibility calculated in this framework agrees with that computed by chiral perturbation theory up to next-to-next to leading order in the limit $ell=L_t/Ltoinfty,.$ The difference between the results involves terms vanishing like $1/ell,,$ plus terms vanishing exponentially with $ell,$. As we have previously shown for the O($n$) model, this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant. Here we confront this expectation with analytic nonperturbative results on the spectrum in 2 dimensions for $N=3,.$
We analyze unoriented Wess-Zumino-Witten models from a geometrical point of view. We show that the geometric interpretation of simple current crosscap states is as centre orientifold planes localized on conjugacy classes of the group manifold. We determine the locations and dimensions of these planes for arbitrary simply-connected groups and orbifolds thereof. The dimensions of the O-planes turn out to be given by the dimensions of symmetric coset manifolds based on regular embeddings. Furthermore, we give a geometrical interpretation of boundary conjugation in open unoriented WZW models; it yields D-branes together with their images under the orientifold projection. To find the agreement between O-planes and crosscap states, we find explicit answers for lattice extensions of Gaussian sums. These results allow us to express the modular P-matrix, which is directly related to the crosscap coefficient, in terms of characters of the horizontal subgroup of the affine Lie algebra. A corollary of this relation is that there exists a formal linear relation between the modular P- and the modular S-matrix.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
