Nic further reassures us that the talk will be mostly non-technical.

1. What is the philosophical interest of holographic duality?

2. What relevance does it have to the philosophy of quantum gravity?

Nic will connect (1) to other issues in philosophy of physics, and hope to illustrate (2).

Nic is about to kick off, with a reassuring 13 slides.

The title is: Philosophical Perspectives on Holographic Duality

Having to move much more quickly now, Huggett briefly goes over how ST implies General Relativity, first in empty space and then adding in some matter.  Question 6:  What is the significance of these results?

Huggett claims that one possible answer is: String theory is actually background independent.

Assume (i) that ST is an adequate TOE, in sense that the string spectrum includes quanta for all the background fields you like; and (ii) that the terms in the action accurately capture the effective behavior of those coherent states.  Then by (i) the G_mu_nu field is composed of stringy excitations, and by (ii) it satises the Einstein Field Equations (making it the gravitational field, and the excitations gravitons). In other words, in the most literal sense the general relativistic theory of spacetime is a low energy effective theory of strings.

Which ought to get philosophers excited!

No time for questions 😦

Huggett offers 2 alternative interpretations of T-duality, in connection with the 3rd question.   Two interpretive decisions need to be made:

•  First interpretive decision: either the T-duals agree on the physical world, or they do not. If they do . . .
• Second interpretive decision: do both say that strings literally live in a space of radius R (but represent that fact dierently); or do they represent facts the same way, and so say nothing beyond their shared consequences  (so that the radius is indeterminate between R and 1=R.)

Either way, both interpretations agree that the target space’s radius (i.e., the phenomenal space we live in) is very very big.  Whew!

On to part 2, Duality!

Strings can wrap around a compact dimension, which leads to a number w, the ‘winding number’ of the string.  Classically one would expect that to be fixed, but when we get interactions w will be able to change, i.e. be dynamic, and will have a corresponding quantum number.

Huggett goes on to explain T-duality.  Winding and momentum can change roles (n <–> w) in the Hamiltonian (and R <–> 1/R) .  The dynamics of the spatial wavefunction becomes the dynamics of the winding wavefunction in the dual, and vice-versa…  the pattern of observed quantities is preserved.  T-duality is like a translation manual between two theories.

This raises Huggett’s 3rd question: How should we understand T-duality?  Do duals describe physically distinct situations?

Huggett raises a new question: should the compact dimensions be considered “spatial” in the same sense of as the large dimensions?  Or are they better thought of as representing internal degrees of freedom?  Are there really 26 dimensions to spacetime in bosonic string theory?  

Somebody keeps editing my posts on Huggett.  The good news is that the edits are truth-preserving.

Huggett now is plowing through his simple classical example, the solutions for the string’s behaviour and stress-energy. One thing that pops out are the Virasoro constraints, which correspond to the conformal symmetry of the string on the worldsheet, which Huggett mentioned earlier.  Using these constraints one can show that the mass is a function of (or “comes from”) the vibration modes of the string.  

Huggett moves on to introducing the technical ideas and apparatus, beginning with a classical example.  Simple string in an n-dim relativistic spacetime.  Introduces the notion of a string worldsheet and its internal coordinates.  The action (Nambu-Goto action) giving the law for this string will be one that minimizes the relativistic area.  A special metric h is introduced on the 2-d worldsheet of the string, which is not connected to the full spacetime metric g, and should not have physical import in the end.

Huggett starts with some words on how to take his talk.  It started out as a talk for philosophers who have only been exposed to pop sci presentations of string theory, to get them to not be afraid of it.  It’s a bit like a travel log from an explorer to a strange country…

There will be 3 parts to the talk:

1. The formalism
2. Duality
3. General Relativity from String theory

For physicists, the hope is that this talk will help understand how philosophers are likely to think about ST (string theory, from here on), what they find interesting, etc.