Harvey: String Theory for Philosophers (of Physics)

Click here to download the slides.

2013-09-28 14:05:59: Title: Where is string theory today?

Hard to talk about where we are today without saying where we’ve been. Different eras of string theory: 

1968-74: Dual resonance era, ended with discovery of asymptotic freedom

1975-83: Quantum gravity Era, people pushing this idea were mostly ignored

1984-94: Unification Era, emphasis on CFT techniques

1995-1998: Duality Era, emphasis on spacetime point of view, and role of SUSY

Finally, we might be at the end of AdS/CFT era.

2013-09-28 14:09:39: Harvey will focus on later stages. 

Origins of string theory were to explain strong interactions, i.e. hadronic resonances and Regge behavior of scattering at high energies and fixed angles. This approach floundered because mathematical consistency required 26 or 10 dimensions, and because no mechanism was found to remove the massless spin 1 and spin2 states that didn’t match the hadronic resonances.

In 1974, Scherk, Schwarz and Yoneya proposed a reinterpretation. Massless spin 2 particles was graviton, massless spin one particles are gauge fields, and string theory was a method to unify gravity with gauge theory in a relativistic framework.

2013-09-28 14:14:26: Those people were mostly ignored.

In 1984, the discovery of anomaly cancellation, heterotic string, and Calabi-Yau compactification led to a cartoon version of the Standard Model. Initially very few Calabi-Yau manifolds were known, but mathematicians eventually found thousands…

Does this make string theory untestable? Harvey thinks this is too strong a statement, but that it does make test more difficult. It is also hard to know which gauge groups and representations to use for the gauge theories underlying the Standard Model. Harvey says that the fundamental problem with testing string theory is the energy scale we have access to.

Audience: are you thinking of string theory as a framework and not as a theory? E.g. like gauge field theory

Harvey: Yes, that’s a reasonable point of view. Yes that’s what I’m proposing.

2013-09-28 14:20:32: The duality era:

This started with an idea of Ashok Sen’s i.e. that N=4 Super-Yang-Mills has a weak-strong coupling, electric-magnetic duality. I.e., parameters have the symmetry SL(2,C).

Harvey shows picture of how values of parameters that label different theories lie in the fundamental region of SL(2,C). Can always map strong coupling to weak coupling.

This was quickly extended to SUSY string theories and led to results about Calabi-Yau spaces. Harvey thinks that the dualities should be understood as different descriptions of one underlying object.

Quotes Rickles as drawing an analogy between dualities and gauge symmetries. Harvey adds that there are examples where dualities really are the same as gauge symmetries (Duality=Gauge).

2013-09-28 14:24:45: First example of (Duality=Gauge) is the T-duality exhibited by string theory on a circle. R gets send to ~1/R.

At the fixed point of this transformation, the theory exhibits an SU(2) gauge symmetry and the T-duality transformation is a discrete transformation in SU(2). It is a redundancy at that point, hence at all points.

Second example: in N=4 SYM, the duality comes from large diffeomorphisms of a torus.

2013-09-28 14:33:32: Dualities led to the discovery of D-branes as solutions to string theory. 

At large N_c, one finds a decoupled set of states near coincident D-branes with two different descriptions. (i) as SU(N_c) SYM with N=4, and (ii) IIB string theory on AdS_5 \times S_5. Maldacena proposed that these are equivalent. 

Large N_c is a classical limit in the sense that the correlation functions factorize in a way similar to classical correlations (different from sending \hbar to zero).

This proposal was the start of the AdS/CFT era. One application is to analyze strongly coupled field theories. So some condensed matter theorists are learning GR!

This has a strange aspect to it — rather like Jeopardy. Example from Horowitz talk at String 2013.

Answer: A charged black hole in asymptotically AdS space has a frequency dependent optical conductivity that varies as X.

Question: What is the intermediate frequency dependence of the optical conductivity of the high T_c superconductor Y?

Harvey says that this matching is not well-justified. It may be correct if there are certain universal behaviors that can be captured by crude approximations.

Postmodern aspect: Here’s the calculation, let’s match it to the system…

2013-09-28 14:37:20: Where is string theory today?

Here’s the laundry list: 

– SUSY gauge theory and its application to the study of manifold invariants.

– Amplitudes i.e. reformulating the rules of perturbative calculations in SYM and SUGRA using twistor and other methods

– Higher spin gravity in AdS (Vasiliev) and its description in terms of CFTs

– application of AdS/CFT to condensed matter, hydrodynamics, quark-gluon plasma, study of entanglement entropy of quantum systems

– extended objects in M-theory

– Firewall debate (einstein-rosen = einstein-podolsky-rosen? see paper by Maldacena)

2013-09-28 14:46:16: Background independence:

In many cases, we write classical part of a field as background and consider small fluctuations around it. String theory as formulated in the mid 80s involves this sort of separation. But with no classical background, it’s hard to interpret what the theory means! What does GR describe when g_{\mu\nu} = 0?

AdS/CFT sheds light on this– in AdS space, we need boundary data in order to get a well-posed initial value problem (for massless particles). Harvey says that a formalism that is independent of boundary data may or may not exist, but it’s fine if we only have a formalism that depends on boundary data, because finite energy excitations will never affect the asymptotic boundary.

2013-09-28 14:56:48: Mathematical consistency:

It’s been claimed that superstring theory provides a UV finite theory. There have been some nagging wories about defining amplitudes on higher genus Riemann surfaces, but these have been laid to rest by Witten and collaborators.

Audience: does UV finite mean that there’s no need for renormalization?

Harvey: Yes.

As in any interesting theory, the perturbation theory is not convergent, and non-perturbative effects must be included. This is difficult, but there’s no reason to think that it can’t be done.

Finally, on philosophy:

Historically, people in GR have been more keen to engage with philosophy. String theorists believe that GR is just another non-renormalizable effective field theory. So they take this attitude to LQG. It doesn’t exist, in the same way that QED doesn’t exist (not well-defined to all energy scales).

Audience: Do you think string theory is well-defined at all scales?

Harvey: Yes, the strings get fuzzier below the Planck length, but they’re still well-defined.

Some particle theorists have been hostile towards philosophy. But that doesn’t reflect on the extent to which string theory could use philosophical work!

2013-09-28 15:07:13: Q&A:

Audience: There’s a part of the LQG community that doesn’t take the dynamics of GR as fundamental. Also the fundamental problems faced by researchers in LQG don’t have to do with the dynamics of GR.

Harvey: Point taken.

Harvey: In QFT the problem is connecting the UV to the IR. The real problem with a theory that doesn’t exist mathematically is whether you can start where you want in the UV and how to get to the IR. 

String theory doesn’t have a full description of what the fundamental degrees of freedom are. 

Audience: What about the other jeopardy game where you answer fundamental questions about the structure of the black hole by looking at the SYM theory. 

Harvey: In principle that can be done, but in practice it’s hard to have control over it. 

Audience: What role does SUSY play in the AdS/CFT correspondence?

Harvey: It’s not essential, but it’s a useful tool for checking it.

Audience: A worry about string theory: one uses concepts that don’t make sense without defining the metric. Doesn’t that make sense?

Harvey: That’s a valid critique; we don’t have the fundamental formulation. It only makes sense in certain limits

Audience: You said that you’re inclined to regard the two sides of a duality as surprisingly different descriptions of a single reality. Is that the most widespread view amongst practitioners? Also, if something is “gauge” at one point in the moduli space, does that really imply that it’s gauge in general?

Harvey: I think the majority do. 

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