How Does Ed Witten's Latest Paper Advance Superstring Perturbation Theory?

[QGravity]

Superstring Perturbation Theory Revisited
Abstract:
Perturbative superstring theory is revisited, with the goal of giving a simpler
and more direct demonstration that multi-loop amplitudes are gauge-invariant (apart from
known anomalies), satisfy space-time supersymmetry when expected, and have the ex-
pected infrared behavior. The main technical tool is to make the whole analysis, including
especially those arguments that involve integration by parts, on supermoduli space, rather
than after descending to ordinary moduli space.

Supplements of this paper are:

Notes On Super Riemann Surfaces And Their Moduli
Abstract:
These are notes on the theory of super Riemann surfaces and their moduli
spaces, aiming to collect results that are useful for a better understanding of superstring
perturbation theory in the RNS formalism.

Notes On Supermanifolds and Integration
Abstract:
These are notes on the theory of supermanifolds and integration on them, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.

 

[atyy]

Ref 14: "Super Gaga Principle" ! What is that?

 

[bcrowell]

Ref 14: "Super Gaga Principle" ! What is that?

Some people have an easier time than others comprehending the Super Gaga Principle. It's intuitively obvious to those of us who were born this way.

 

[MathematicalPhysicist]

Ref 14: "Super Gaga Principle" ! What is that?

Like we have Saiyan and then we have Super Saiyan.

Then we have Lady Gaga so we must have Super Gaga.



;-)

 

[marcus]

For the benefit of those not fortunate enough to be born with an understanding of these matters,
GAGA is French for Algebraic Geometry⇔Analytic Geometry
Serre, Jean-Pierre (1956), "Géométrie algébrique et géométrie analytique", Université de Grenoble. Annales de l'Institut Fourier 6: 1–42.

the first deals with algebraic varieties, the second with analytic manifolds, and gaga principles carry results on the first over to apply to the second.
"Super" is a functor defined on certain categories and making them super, as in
strings → superstrings
Riemann surface → Super Riemann surface
man ifold → superman ifold

 

[MathematicalPhysicist]

I remember reading GAFA, but that's for functional analysis.

http://www.tau.ac.il/~gafa/

 

[MathematicalPhysicist]

For the benefit of those not fortunate enough to be born with an understanding of these matters,
GAGA is French for Algebraic Geometry⇔Analytic Geometry
Serre, Jean-Pierre (1956), "Géométrie algébrique et géométrie analytique", Université de Grenoble. Annales de l'Institut Fourier 6: 1–42.

the first deals with algebraic varieties, the second with analytic manifolds, and gaga principles carry results on the first over to apply to the second.
"Super" is a functor defined on certain categories and making them super, as in
strings → superstrings
Riemann surface → Super Riemann surface
man ifold → superman ifold

Which categories are we talking about? What's the domain and codomain?

 

[marcus]

Which categories are we talking about? What's the domain and codomain?

Tongue in cheek categories, of course.

 

[MathematicalPhysicist]

 

[atyy]

No wonder marcus considers string theory reductive!

 

[MathematicalPhysicist]

No wonder marcus considers string theory reductive!

They talk too much...

 

[Nano-Passion]

I wonder how long a paper like this took him.

 

[Devils]

I wonder how long a paper like this took him.

Especially with the supplements it is close to 400 pages.

 

[MathematicalPhysicist]

I wonder what he does besides math and physics...

 

[Nano-Passion]

I wonder what he does besides math and physics...

Probably physics and math.

I think someone should send him a sincere email asking him what he does with his free time.

Does he answer emails though?

 

[haushofer]

I think he has found a way to put his office in a Godel universe.

 

[Nano-Passion]

I think he has found a way to put his office in a Godel universe.

It can't be? So he can keep going into the past every time to make sure he finished 1 paper/week? Now it all makes sense.

 

[tom.stoer]

The papers are way beyond the level I am able to follow (as a non-expert in string theory).

Can anybody comment on the significance of his work?

As far as I can see it is about a more rigorous definition of perturbative string theory. But in which sense is this relevant to understand the main open problems which (as far as I can see) are related to a non-perturbative treatment of strings.

 

[MathematicalPhysicist]

It's a pitty that only one person can understand his work, and it's him. :-D

 

[PAllen]

Even Lubos Motl described these papers as mathematics rather than physics (i.e. no new physical insights; extra rigor not of much interest to string theorists as physicists). Motl is generally a huge fan of Witten.

 

[marcus]

Even Lubos Motl described these papers as mathematics rather than physics (i.e. no new physical insights; extra rigor not of much interest to string theorists as physicists). Motl is generally a huge fan of Witten.

Yes, though his doubts about the relevance of the recent work are sweetened and softened by the tactful way he expresses them:
==quote Wednesday 26 September blog==
Witten's work is impressive but just like with many things, I can't avoid thinking that it's right to classify it as maths. String theory's engine to calculate the amplitudes is in principle very simple and straightforward and you may efficiently learn it. If one writes 400 pages about some technicalities, it just doesn't match my idea about the underlying simplicity and naturalness of the rules. Of course, I may only say such a thing because I adopt certain semi-heuristic arguments that are OK for physicists. Mathematicians may expand these arguments to hundreds of pages of rigorous maths. In most cases, they confirm what the physicists have known all the time. In exceptional cases, they find out that the answer is different.

Witten's new papers seem to follow the first scenario.

However, the reasons why I am sometimes dissatisfied by the length of Witten's papers goes beyond the rigor. They seem to contain pretty much all the intermediate steps etc. so the "concentration of action" (in the Hollywood sense) is reduced and not much is left for the reader's own re-discovery. So while I think that Witten's papers are excellent, they don't quite match my preferred genre which is dominated by excitement and the opportunity for the reader to rediscover things and find his or her own proofs (or disproofs) of the assertions.
==endquote==

 

[Nano-Passion]

However, the reasons why I am sometimes dissatisfied by the length of Witten's papers goes beyond the rigor. They seem to contain pretty much all the intermediate steps etc. so the "concentration of action" (in the Hollywood sense) is reduced and not much is left for the reader's own re-discovery. So while I think that Witten's papers are excellent, they don't quite match my preferred genre which is dominated by excitement and the opportunity for the reader to rediscover things and find his or her own proofs (or disproofs) of the assertions.
==endquote==

It seemed to me as a pedagogical paper the way it is written. If so then what is the big deal, it looks almost as it was written to be a book for non-experts in string theory or those who want to learn a bit more about string theory.

 

[tom.stoer]

The paper is closely related to his talk at "Strings 2012"; so perhaps somebody who participated can give us a hint regarding his intention

 

[mitchell porter]

Tom, I don't think it's different to the situation in QFT where there are so many assumptions and constructions which aren't absolutely validated mathematically, but which still serve as the starting point for calculations that work. Witten isn't providing ultimate foundations for the subject (i.e. answering that question, "what is string theory"), but he is introducing extra rigor and order to perturbative string theory, including, as I understand it, some technical innovations about how the integrals are performed.

 

[tom.stoer]

OK, thanks, that was my impression as well, but it's good to hear this from you (instead of relying on my own guesswork)