# Notes

### Joe Polchinski

Different notions of state dependence:
1. $a = \sum_i a_i P_i$ where the $P_i$ are projection operators. This is consistent with linear quantum mechanics. The kind of state dependence described for example in HMPS, 1201.3664, at the beginning of section 3, is linear in this way, although it did not use projection operators explicitly.
2. "You give me any state and I will construct an operator" S. Raju
This is not linear quantum mechanics. In linear quantum mechanics, you give me the operator (which might contain projections) before you know the state, I give you the state at the same time, and we act on the state with the operator in a linear way. The PR construction depends on the state in a way that cannot be written in terms of projection operators or otherwise as a linear operator.
• Here's an example of linear state dependence that does not work: if we consider two qubits $b$ and $\tilde b$, there are the usual 4 ways to entangle them, and so four different operators $a_i$ that annihilate these respectively. So we divide our Hilbert space into 4 subspaces according to the $b\tilde b$ entanglement, and define $a = \sum_i P_i a_i$. But then $a$ annihilates every state. This is Bousso's frozen vacuum: ordinary QFT operations near the horizon which would excite $a^\dagger$ do not work.

### Eva Silverstein :

Consider naturally formed states far from the infalling vacuum, let's call these |FW>_i. These states are in the CFT. Therefore so is the operator |FW>_i <FW|_i. This is a linear operator which distinguishes naturally formed firewall states from naturally formed non firewall states. These naturally formed firewall states contain the b tilde dagger gravitational waves, but not independently of other excitations which makes them natural. So there is no contradiction with the nonexistence of b tilde dagger by itself as an operator. I don't see why we need the latter.

Some people have asked about the string-theory generalization of particle production and Bogoliubov coefficients that I mentioned briefly. Our current notes are
, it's a fun calculation (the BH version is in there, still in progress). I had also intended to mention a precedent for UV complete physics revealing an instability that low energy EFT is blind to: this is fermi seasickness" in AdS/CMT (
Regarding the dynamics of the D3-brane model, some fairly extensive unpublished notes are which include basic relations such as the location of the horizon in terms of the probe SU(n) collective coordinate as well as the scales involved in winding condensation and the analogue of confinement that I brought up as a candidate for horizon dynamics. The talk notes from CERN say a little more (with refs) on the Wilson line dynamics as described using classic methods on the gauge theory side, another set of questions that came up in the talk.
Finally, I didn't intend to engage in an argument about the dictionary, in fact the point was to take some time to explain the issues, arguments (both sides) and what facts are really known currently. From the laughter this morning I see that this failed...the one thing I feel I should re-emphasize is that however it is described in the CFT, the probe is an independent degree of freedom from the (su-)gravity waves. It obeys a speed limit which is enforced by its DBI action, something not respected by other tracers of the moduli space geometry such as the boundary chiral fields. ( This action takes the form of a series of higher dimension terms suppressed by the W mass, with a simple understanding of why this dominates over W production at large lambda, with the opposite being true at small lambda.) This zeroeth order" behavior (i.e. before folding in couplings to gravity waves) is in itself a beautiful aspect of AdS/CFT which encodes bulk causality in a different way from e.g. commutators of bulk sugra fields, so it gives another angle on some of these questions, at the very least. Naturally formed gravity waves such as those outside the BH and also those created inside by known processes such as brane scattering can also be included. Non-naturally formed gravity waves which one might like to use to describe the infaller's QM don't exist as CFT operators, as proved and emphasized by A(MP)S(S) in various ways, so they cannot be folded in (at least not in the same way). As I keep saying, it is not clear to me (yet) that those are needed in order to determine whether firewall dynamics occurs. For example, if the inside were excised then the D-brane collective coordinate's moduli space would be reduced from $\approx R^6$ (times Wilson lines) to something else with a large region around the origin removed.

### Steve Avery

(A comment on the literature):
I would like to use this space to point out a result that appeared in v2 of my paper 1109.2911, which may have been missed in the flurry of papers. Mathur's argument against small corrections is logically incomplete, although qualitatively correct. If one wants to rigorously argue that unitarity requires large corrections to Hawking evaporation, then one needs to use the whole space of corrections. This is especially important in light of results in Giddings-Shi 1205.4732, which shows the particular correction considered in Mathur 0909.1038 never restores unitarity no matter how large it is. My paper fills this gap. My sincere apologies for the spam.

### Samir Mathur:

We (David Turton and I) have had several discussions with Don Marolf about "Fuzzball Complementarity", and we have come to the following common understanding with Don:

(a) The notion of fuzzball complementarity detailed in Mathur and Turton arxiv:1306.5488 (MT) provides a scenario where the following situation holds. We fix our theory of the standard model, and also fix the infalling observer. If we now take the black hole mass to be sufficiently large, we will have both of the following
• (i) The evaporation is unitary
• (ii) The infalling observer will feel no drama in the sense that the number of particles they intercept goes to zero, as does the energy of each particle intercepted (as measured in the infalling frame). Nevertheless, the density of energy quanta remains much larger than that predicted by the Hawking state.

(b) For generic compactifications of string theory, the term 'sufficiently large' would mean M>>m_p. Marolf has pointed out, however, that our Universe has standard model parameters that have a large hierarchy, in both particle masses and coupoling. Let us characterize this hierarchy a number L>>1. Then it may be that the term 'sufficiently large' in would mean M>> L^\alpha m_p, for some \alpha>0. Since L~10^{40} for the standard model, it is possible that even the largest astrophysical holes end up being too small to satisfy the condition of being 'sufficiently large'.

### Steve Giddings:

In my talk I attempted to paraphrase some comments Lenny and Joe had made; there were some questions about these. In the interest of improving my accuracy regarding what they had said, here are the quotes from the relevant talks:

Lenny's blackboard lunch talk (starting around 47:50):

"I myself … and others, think there's something correct about the idea that the distant Hawking radiation is information-theoretically holographically a description of the interior of the black hole, but there are other paradoxes…" (This appeared to match his earlier description of how A=R_B works, see around 44:00.)

Joe's comment on Eva's talk (around 1:04:30):

"It respects the broader message I was trying to make, which is the CFT really doesn't give you a good description of the bulk for many reasons, and you need an independent theory of the bulk."

(For some of my own concerns about how and whether through AdS/CFT the boundary theory accurately describes the bulk, see http://arxiv.org/abs/arXiv:1105.6359 . This question has provoked controversy. Some of my thoughts regarding the need to find such an independent theory, and regarding possible approaches and guideposts, are mentioned there, and are reflected in my talk, and in ongoing work of recent years.)

### Marty Einhorn

I'd like to remind people of a JHEP paper (arXiv:hep-th/0508217) written by Brustein, Yarom, and me in 2005 concerning entanglement entropy. It is somewhat stronger or at least different from the discussions I've heard last week and this. It does not assume perturbation theory but depends on duality to argue that the thermofield double is real. Secondly, by using a Euclidean path integral formalism, it establishes the area law and Hawking temperature for an interacting scalar field. So, without assuming free field theory or the existence of a Bogliubov transformation to an Unruh vacuum, the black hole entropy can be derived, up to a constant, which was fixed by other work. We also introduce a nonsingular coordinate transformation that covers both the inside and outside of the Euclidean black hole. It doesn't completely resolve the firewall issue, but certainly suggests that the horizon is nonsingular.

### John Preskill:

http://quantumfrontiers.com/2013/08/29/whats-inside-a-black-hole/

### Scott Aaronson:

http://www.scottaaronson.com/blog/?p=1508