Fuzzball Proposal Talk: My Advisor at CERN

[Ben Niehoff]

This is ths stuff I do. My advisor recently gave a talk at CERN:

http://cds.cern.ch/record/1537034?ln=en

I don't usually post in this forum, but someone else expressed interest in firewalls, and this is somewhat connected. I thought maybe some people might be interested.

 

[atyy]

Are any of your papers on the arxiv about fuzzballs?

 

[Ben Niehoff]

All of them are related to fuzzballs in some way, yes. A few of them are examples of fuzzballs.

 

[atyy]

It's an interesting talk - mainly I didn't know who else worked on fuzzballs apart from Mathur, and Warner says at the start there's not a monolithic "fuzzball people" group. It was a bit hard to read the blackboard on my screen, so I tried looking for a review by Warner. http://arxiv.org/abs/0810.2596 seems similar in spirit.

"In particular, a Microstate Geometry is defined to be any completely smooth, horizonless solution that matches the boundary conditions of a given black hole. One of the surprises of the last three years has been that there are a vast number of such geometries and a very rich underlying structure that matches very nicely with the dual holographic field theory description. It remains to be seen if these can provide a semi-classical accounting of the entropy but, as I will discuss, there is a reasonable chance that they might."

 

[Ben Niehoff]

I'd say the canonical review is this one: http://arxiv.org/abs/hep-th/0701216

Although, things have progressed a bit since then. As he mentions in the talk, what we're especially interested in now are smooth, horizonless solutions in 6 dimensions that depend on arbitrary functions of 2 variables. We've actually got solutions that depend on arbitrary functions of 2 variables (http://arxiv.org/abs/1203.1348), but these ones are singular. The "smooth" requirement results in a very tricky nonlinear equation that has thus far defied solution.

 

[Physics Monkey]

Ben, I would actually like to ask some questions about this research direction if you have the time.

Is it correct that the basic idea is to look for geometries which, when counted appropriately, give the entropy of a black hole? If so, how do we know that the microstates have a geometric interpretation? Also, presumably such geometric microstates would be somehow related to the notion of eigenstate thermalization; can one, in a holographic context for example, compute the entanglement entropy of the microstate using something like the Ryu-Takayanagi formula and see that one recovers thermal scaling for small subsystems?

 

[Ben Niehoff]

Is it correct that the basic idea is to look for geometries which, when counted appropriately, give the entropy of a black hole? If so, how do we know that the microstates have a geometric interpretation?

One can show, actually, that in the phase space of black hole microstates, the ones with a geometric interpretation are a set of measure zero. The rest are complicated string theory states. However, the hope is that the geometric ones are still a dense set, and thus are an appropriate sample of the phase space. This would lead at least to the correct scaling behavior for the entropy in terms of black hole charges.

In fact, we have yet to produce the correct scaling behavior. The next hope is that the "superstrata" microstates (that depend on arbitrary functions of 2 variables) will have enough entropy to give the correct scaling.

Furthermore, all of this so far is done only for extremal black holes (and usually supersymmetric also). Getting a non-extremal microstate geometry is very hard (and may be impossible).

Also, presumably such geometric microstates would be somehow related to the notion of eigenstate thermalization; can one, in a holographic context for example, compute the entanglement entropy of the microstate using something like the Ryu-Takayanagi formula and see that one recovers thermal scaling for small subsystems?

These are things I don't know about. I can say that no has yet found any microstate geometries that are easy to study holographically. No one has been able to find a microstate geometry asymptotic to AdS_5, for example (because the equations are horribly nonlinear).

 

[Physics Monkey]

Oh I see, how interesting. It seems like it would be really fantastic to have a microstate geometry with the right asymptotics and then to see that the holographic EE gave thermal entropy. Can the nonlinear equations be solved numerically?

 

[Ben Niehoff]

Oh I see, how interesting. It seems like it would be really fantastic to have a microstate geometry with the right asymptotics and then to see that the holographic EE gave thermal entropy. Can the nonlinear equations be solved numerically?

I've actually done a bit of work to try to get microstates in AdS_5. The equations of motion can be reduced to a coupled system of 6th-order nonlinear PDEs in 3 independent variables. So it is not amenable to numerical solution. :p

 

[atyy]

Ben, are your answers for Physics Monkey's questions only for the three-charge system, or also for the two-charge system?

 

[Ben Niehoff]

All my work has been in 3-charge systems. I don't know much about 2-charge systems, but I think the correct entropy scaling has been obtained in that case, using supertubes (which allow arbitrary functions of 1 variable).

 

[Physics Monkey]

Maybe you've already answered this, but I wasn't clear if your comments covered the two charge case as well. Is there an asymptotic AdS solution in the 2 charge case? If so, has anything about the entanglement entropy been considered?

 

[Ben Niehoff]

There are no asymptotically-AdS_5 solutions at all.

However, in both the 2-charge and 3-charge case, you can get asymptotically AdS_3 x S^2. I'm not sure what holographic studies have been done on such systems, but I assume it's been done.

You can also get other near-horizon metrics with less symmetry; for example, in one of my papers we have asymptotically-near-horizon-BPMV, with rotation parameters strictly bounded above zero.

 

[Physics Monkey]

AdS_3 solutions would, I think, also be fine for my interests. Is there a good reference for this?

 

[Ben Niehoff]

It looks like the AdS_3 case has been pretty extensively studied by Skenderis and Taylor. They have a number of papers on fuzzballs from a holographic perspective.

 

[Physics Monkey]

I found several papers by Skenderis and Taylor, but they seem to make no mention of entanglement. I found checks of one point functions, for example, but given that one seems to have explicit solutions it might be very interesting to look at the entanglement. I guess unfortunately I don't have too much sense for what these solutions "look like".

 

[atyy]

These papers by Bena and colleagues also have comments on the 3-charge case and AdS/CFT.
http://arxiv.org/abs/hep-th/0408186
http://arxiv.org/abs/hep-th/0608217

Footnote 5 of the latter: "We originally considered calling these microstates “deep-throat microstates” but decided against it to avoid the obvious tasteless jokes."

These guys also wrote One Ring to Rule Them All ... and in the Darkness Bind Them?.

Who's the joker, Bena or Warner?

 

[Ben Niehoff]

I'm not sure who's the joker. I have also met Bena, they both have a sense of humor. They both have plenty of papers with serious titles. But Warner is responsible for "Hair in the back of the throat" in my first paper.

I've noticed actually most people are jokers, occasionally, especially if a topic has just caught on. Look at Joe Polchinski and Clifford Johnson, for example. Joe has some old TASI lectures that mention in the introduction "There will be no puns".

 

[atyy]

I found several papers by Skenderis and Taylor, but they seem to make no mention of entanglement. I found checks of one point functions, for example, but given that one seems to have explicit solutions it might be very interesting to look at the entanglement. I guess unfortunately I don't have too much sense for what these solutions "look like".

Maybe http://arxiv.org/abs/1108.2510 ? They mention the eigenstate thermalization hypothesis, and try to follow up Takayanagi and Ugajin's speculative paper, but with the D1-D5 system instead. (They are mentioned in Hartman & Maldacena's tensor network paper.)

But Warner is responsible for "Hair in the back of the throat" in my first paper.

 

[atyy]

Also, presumably such geometric microstates would be somehow related to the notion of eigenstate thermalization; can one, in a holographic context for example, compute the entanglement entropy of the microstate using something like the Ryu-Takayanagi formula and see that one recovers thermal scaling for small subsystems?

Ben mentioned that all the solutions so far are for extremal black holes. Would "thermalization" work with extremal black holes, which are at T=0? In their paper on thermalization in the D1-D5 system, Asplund and Avery presume that the process is dual to forming a non-extremal black hole. I suppose that for extremal black holes one would do something more like your http://arxiv.org/abs/0908.1737, with the Ryu-Takayanagi formula still expected to hold?

BTW, hope you aren't affected by the terrible events in Boston.

 

[Physics Monkey]

Ben mentioned that all the solutions so far are for extremal black holes. Would "thermalization" work with extremal black holes, which are at T=0? In their paper on thermalization in the D1-D5 system, Asplund and Avery presume that the process is dual to forming a non-extremal black hole. I suppose that for extremal black holes one would do something more like your http://arxiv.org/abs/0908.1737, with the Ryu-Takayanagi formula still expected to hold?

BTW, hope you aren't affected by the terrible events in Boston.

This is a good point. Perhaps my hope is somewhat misguided, although I do still wonder what the entanglement looks like.

Fortunately, despite many friends running in the marathon, no one I knew was hurt. The explosions were just steps from the church where my wife often sings, so we got very lucky. All the crimes in cambridge last night took place very near where we live, so it's all rather disturbing and crazy.