An interesting paper which I have been fascinated by recently is the paper by Holger Nielsen and Masao Ninomiya, which shows that there exists a no-go theorem concerning fermion doubling with chiral fermions on a lattice. Naively, the idea is that the Hamiltonian for fermion field has fermion doubling if the following conditions are satisfied: (1) translational invariance is satisfied, (2) the charges are conserved and quantized, and (3) the interaction Hamiltonian is Hermitian and local. In this sense, there is a no-go theorem, the original arguments of which concern homotopy theory. There is also a very good paper by Friedan on a proof of this theorem. There were some arguments concerning if one could be a little more lenient with the hermiticity condition, and impose something like the PT symmetry, see for instance The Nielsen-Ninomiya theorem, PT-invariant non-Hermiticity and single 8-shaped Dirac cone. There is also a very good paper on the approach from loop quantum gravity by Jake Barnett and Lee Smolin, which seems to have some interesting features. Seemingly, there seems to be emphasis on circumventing the Nielsen-Ninomiya theorem in LQG, which seems to be an interesting remark. A part of the theorem's popularity also lies with the motivation it provides to other things with fermions, most famously massive fermions, which is something that David Tong has worked on.
Holography and Theory Journal Club
We're launching a journal club, for which I am the organizer, called Holography and Theory Journal Club, where we will have weekly or bi-weekly (i.e. every other week) discussion meetings or invited talks on recent works in hep-th. We accept the submission of meeting abstracts, for which a forms link is provided in the website, https://sites.google.com/view/htjc. Kindly note that all talks will be by invitation only, whereas paper discussion meeting abstracts are welcome unsolicited. Preferably, the papers are from the hep-th arXiv in the week of submission itself, so that there are no misses of important papers. We will also have a mailing list ready this by Monday, so just drop in an email for participating in the journal club till then!
P.S. Working on a set of notes on Ricci flows in Kahler manifolds.
Black Hole Information Paradox Notes
Notes on the black hole information problem, which I wrote in a very elementary fashion have been complete. I must say that a part of my inspiration to write this was from Aayush's notes, and I wanted to add on to the discussion in a slightly more elaborate way. Keep in mind that this is not a very AdS/CFT oriented thing, so it may seem to be off-topic for the title. However, in the next set of notes, I talk about the Almheiri, Engelhardt, Marolf and Maxfield + Pennington works exclusively. This series of notes, Bulk Physics, Algebras and All That was originally a three-part series. Now, it is an $N$-part series in the large $N$ limit.
Bulk Physics, Algebras and All That -- Part Two: Black Hole Information Problem
Black Hole Interior in AdS/CFT
Black holes in AdS/CFT are interesting things. One could ask if, following along with the usual bulk-boundary description, there is a way to find CFT operators dual to bulk fields in the exterior and interior of a large AdS-Schwarzschild black hole. The exterior is simple enough; it is our usual HKLL scheme that has to be used. This is following the extrapolate dictionary,
\[\mathcal{O}(t, \Omega )=\lim _{r\to \infty }r^{\Delta }\phi (r, t, \Omega )\;,\]
where $\Delta $ is the usual conformal weight. One could also sit in the Poincare setting for working with the expansion of these operators and modes. The primary idea here is that dual to a bulk field, one can either take a set of local operators that are ``smeared", or a family of nonlocal operators instead. For instance, solving $(\Box -m^{2})\phi =0$, and compressing each set of Bessel functions and denoting the normalizable mode by $\xi _{\omega , k}(t, x, z)$ as in 1211.6767, a nonlocal CFT operator in the Poincare patch looks like
\[\Phi _{\text{CFT}}(t, x, z)=\int \frac{d\omega d^{D-1}k}{(2\pi )^{D}}\;\mathcal{O}_{\omega , k}\xi _{\omega , k}(t, x, z)+\mathcal{O}^{\dagger }\xi ^{*}_{\omega , k}(t, x, z)\;.\]
Then, operators in region II of the Penrose diagram can be written as
\[\phi ^{\text{II}}_{\text{CFT}}(t, x, z)=\int _{\omega >0}\frac{d\omega d^{D-1}k}{(2\pi )^{D}}\; \mathcal{O}_{\omega , k}g^{(1)}_{\omega , k}(t, x, z)+\tilde{\mathcal{O}}_{\omega , k}g^{(2)}_{\omega , k}(t, x, z)+\dots \;.\]
This is obtained from interpolation between operators in the regions I and III. Read more on this in 1211.6767 and 1310.6334. More on this will be detailed in Part Two of my Bulk Physics, Algebras and All That notes, which will come out by tomorrow.