Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeneralised Kahler Structure on $mathbb{C}P^2$ and Elliptic Functions
138
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We construct a toric generalised Kahler structure on $mathbb{C}P^2$ and show that the various structures such as the complex structure, metric etc are expressed in terms of certain elliptic functions. We also compute the generalised Kahler potential in terms of integrals of elliptic functions.
rate research
Read More
The scalar curvature equation for rotation invariant Kahler metrics on $mathbb{C}^n backslash {0}$ is reduced to a system of ODEs of order 2. By solving the ODEs, we obtain complete lists of rotation invariant zero or positive csck on $mathbb{C}^n backslash {0}$ in lower dimensions. We also prove that there does not exist negative csck on $mathbb{C}^n backslash {0}$ for $n=2,3$.
In this short note we show that the existence of bilaterally symmetric extremal Kahler metrics on $mathbb{CP}^2sharp 2bar{mathbb{CP}^2}$.
In this semi-expository paper we study two examples of coherent states based on the Weyl- Heisenberg group and the group of $2 times 2$ upper triangular matrices. It is known that sometimes the coherent states provide us with a Kahler embedding of a coadjoint orbit into the projective Hilbert space ${mathbb C}P^n$ or ${mathbb C}P^{infty}$. We show an explicit computation of this in the above two examples. We also note the presence of other coadjoint orbits which only embed symplectically into the projective Hilbert space. These correspond to squeezed states, which have several applications in physics. Our exposition includes a detailed study of the geometric quantisation of the coadjoint orbits of the Lie Algebra of upper triangular matrices. This reveals the presence of distinguished orbits which correspond to coherent states, as well as others corresponding to squeezed states. The coadjoint orbit of $SUT^{+}$ we consider is intimately connected to the $2$-dimensional Toda system.
Each hypersurface of a nearly Kahler manifold is naturally equipped with two tensor fields of $(1,1)$-type, namely the shape operator $A$ and the induced almost contact structure $phi$. In this paper, we show that, in the homogeneous NK $mathbb{S}^6$ a hypersurface satisfies the condition $Aphi+phi A=0$ if and only if it is totally geodesic; moreover, similar as for the non-flat complex space forms, the homogeneous nearly Kahler manifold $mathbb{S}^3timesmathbb{S}^3$ does not admit a hypersurface that satisfies the condition $Aphi+phi A=0$.
We report the results of the lattice simulation of the ${mathbb C} P^{N-1}$ sigma model on $S_{s}^{1}$(large) $times$ $S_{tau}^{1}$(small). We take a sufficiently large ratio of the circumferences to approximate the model on ${mathbb R} times S^1$. For periodic boundary condition imposed in the $S_{tau}^{1}$ direction, we show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as the compactified circumference is decreased, where the peak of the associated susceptibility gets sharper for larger $N$. For ${mathbb Z}_{N}$ twisted boundary condition, we find that, even at relatively high $beta$ (small circumference), the regular $N$-sided polygon-shaped distributions of Polyakov loop leads to small expectation values of Polyakov loop, which implies unbroken ${mathbb Z}_{N}$ symmetry if sufficient statistics and large volumes are adopted. We also argue the existence of fractional instantons and bions by investigating the dependence of the Polyakov loop on $S_{s}^{1}$ direction, which causes transition between ${mathbb Z}_{N}$ vacua.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
