Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

  What progress needs to be made in string theory for computational science/physics to be of use?

+ 3 like - 0 dislike
2945 views

I'm thinking about going into computational physics and was wondering if the fields would ever intersect.

asked Apr 28, 2015 in Computational Physics by coarsegrained (60 points) [ no revision ]
retagged Apr 28, 2015 by dimension10

I cannot comment on the details but a friend of mine has been studying boundary states in open string field theory numerically: http://arxiv.org/pdf/1401.7980v1.pdf I think that due to the status of string theory most numerics in string theory will not try to compute outcomes of very specific situations and will try to stick to as scalable results as possible. Personally, I would rather enter field+computer+physics for such exciting things as neutron star dynamics from lattice QCD...

1 Answer

+ 6 like - 0 dislike

This is for me an extremely pressing question, as the limits of analytic techniques often have little to do with the limits of nature. There are several ways in which computers have contributed to string theory already, but they are not the type of things I care about. For instance, computer algebra was used (in the 1970s!) to derive the precise form of the 11d SUGRA action, but this is just a computer working like a human physicist, working algebraically, it isn't really using the power of the machine to simulate analytically intractable situations.

The main obstacle to simulations in systems which represent string theory as it is understood today is that there is no universal good method to put arbitrary supersymmetric theories on a lattice for simulation. You can do it in artificial ways, by putting the theories on a lattice without any supersymmetry, and fine tuning parameters, but this is in practice hopeless, as the supersymmetric points are very finely tuned in this point of view, and you will never extract anything from the simulation. There exceptions are the cases where you know the Nicolai map in an explicit local way. Simon Catterall has been working very diligently to expand the domain of this limited set of examples as far as possible, and perhaps there has been some breakthrough from Syracuse recently, I haven't checked in a while. This group is simulating supersymmetric theories, and there are other groups in Japan.

The Nicolai map is a stochastic system whose Parisi-Sourlas Supersymmetry implies a normal relativistic supersymmetry of the solutions of the stochastic equation. There are really only two meaty examples, unfortunately. Fortunately, one of them includes all of flat-space M-theory!

The two examples are 1-d SUSY-QM, which is in reality the stochastic equation:

$$ \dot{x} - V' = \eta $$

Which, when you formulate as a path integral, produces a determinant which reproduces the SUSY-QM Fermionic content. This gives the small research fields of shape-invariance (or Schrodinger generalized raising and lowering operators). You can generalize this to arbitrary 1-d systems with enough supersymmetry, and the BFSS model has a ton of supersymmetry, so you're in luck. This means we can right now simulate M-theory efficiently on a computer, using stochastic equations for BFSS matrices.

This is not solving all the world's problems, because BFSS is the most notoriously hard to understand version of AdS/CFT, since the entire space is reconstructed from the dynamics of the branes in large N limit, and the limits are hard, and the physics is opaque. Still, people have made simulations of this in recent years, although what results they got, I don't know. Even the classical solutions to BFSS are not understood in any way, nor is it even obvious what the classical solutions even mean physically (at least not to me).

The other case where the stochastic formulation is know is 2-d N=2,2 Wess-Zumino model, which is defined by the stochastic equations:

$$\partial_x \phi_1  + \partial_y \phi_2 + V_r  = \eta_1$$

$$\partial_y\phi_1 - \partial_x\phi_2 + V_i = \eta_2 $$

Where (V_r + iV_i) together are the real and imaginary components of a holomorphic function of $\phi_1 + i \phi_2$.

These two examples have been the only real examples for going on 30 years now. It is clear simply from the form of supersymmetric Lagrangians that it should be possible to this trick in general somehow, for every single supersymmetric field theory. Once you do it, the supersymmetric theory is actually easier to simulate than the non-supersymmetric one. As a warning, I should tell you that banging my head on this (self-imposed) problem probably cost me a PhD. But it only takes one idea for a breakthrough, and it is going to come eventually, although I hope not in 100 years.

Once we know how to do stochastic formulation of some kind for general SUSY theories, then one can simulate AdS/CFT cases which are higher dimensional, where the physical applications are more direct, like N=4 SUSY gauge theory. From this, it is easier to answer the questions one is interested in. The stochastic formulation is the sole obstacle.

There are potential applications of computers in the "mechanical physicist" sense, to compute properties of OPE's and such things, but I think you are interested in direct simulation, because that's what I was interested in.

answered Apr 29, 2015 by Ron Maimon (7,730 points) [ revision history ]
edited Apr 29, 2015 by Ron Maimon

Which of the two examples ''includes all of flat-space M-theory''?

@ArnoldNeumaier: The 1-d SUSY-QM includes the BFSS matrix model, and it is relatively easy to simulate on a computer. It is just difficult to know what the simulations mean exactly.

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysic$\varnothing$Overflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...