# Tag Info

3

While keeping the array page $9$ in ref1, already given, in mind, we add a new ref2, especially fig $1$ page $7$, paragraph $2.2.3$. $D = 6$, page $11$, table $5$ page $13$, and discussion page $12$ From fig $1$, page $7$, we see, that in $D=6$, the $N=2$ supersymmetry corresponds to a $(N_+, N_-) = (1,0)$ supersymmetry Looking at the discussion page $12$, ...

2

The value $R=\alpha^{\prime 1/2}$ is the self-dual radius under T-duality. One may indeed extract the massless spectrum – the spectrum of all fields much lighter than $\alpha^{\prime -1/2}$. Because the CFT has an $SU(2)\times SU(2)$ symmetry, as can be seen from the OPEs of the currents, the spacetime physics has this symmetry, too. Because one finds ...

2

Again, thanks to the $SU(2)$ PSG proposed by prof.Wen, I can answer my question now, $THT^{-1}$ is in fact $SU(2)$ gauge equivalent to $H$, and the statement "$H$ is also not SU(2) gauge equivalent to the time-reversal transformed Hamiltonian $THT^{-1}$" in my question is wrong. Let's rewrite the Hamiltonian as ...

2

I don't know the article you refer to, but I believe the Hamiltonian you discuss should get a $\pi$-phase shift after one turn around a (2D) lattice cell. So I guess it should read $H=F^{\dagger}\cdot H_{\pi}\cdot F$ with H_{\pi}=t\left(\begin{array}{cccc} 0 & e^{\mathbf{i}\pi/4} & 0 & e^{-\mathbf{i}\pi/4}\\ e^{-\mathbf{i}\pi/4} & 0 & ...

2

You can derive the desired expression in the following way: \begin{align}\delta(R_{ab}R^{ab}) &=\delta R_{ab} R^{ab}+R_{ab}\delta R^{ab}\\ &=\delta R_{ab}R^{ab}+R_{ab}\delta R_{cd}g^{ca}g^{db}\\ &=\delta R_{ab}R^{ab}+R^{cd}\delta R_{cd}\\ &=2R^{ab}\delta R_{ab}\\ &=2R^{ab}\delta(R_{cadb}g^{cd})\\ ...

1

For static polarizability calculations it seems that both B3LYP and PBE functionals do a pretty good job; for benzene and napthalene I am getting numbers within a few percent of experimental values. What is much more important is the basis set. In particular, it's absolutely necessary to include diffuse functions. For benzene it's so extreme that ...

1

I would recommend to use a different functional, preferentially one having dispersion corrections and range separation. An experimentalist once asked me for polarizability data for organic molecular chains; I used $\omega$B97XD and got results with an errors of 1% or less with respect to experiment. I didn't bothered to do B3LYP and PBE but I doubt they can ...

1

Can we simply comment that the $\text{Tr}[T^a_rT^b_r]\equiv C(r) \delta^{ab}$ depends on the representation. For the case of SU(2) and SO(3), we can relate this to the spin-S representation. By the manner that for SU(2) group is in a spin 1/2 representation and SO(3) group is in a spin 1 representation. One can write down the relation of spin operators as: ...

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