The h Bar

Ryder Rude

15:00

@glS but this says he got rude with a troll and didnt stop arguing

@glS oh this was just a 1 hour suspension

Slereah

Mr. Brian David Gilbert also did a bit that concern us all btw :

I read every Halo novel and became the Master Chief of loneliness | Unraveled

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Oops

Wrong link

ACuriousMind

lol

Slereah

Brian David Gilbert - Academic Papers

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glS

15:19

@RyderRude I mean, the post itself makes it pretty obvious to me why he ended up suspended. You keep being like and essentially being a form of conspiracy theorist, at some point people get fed up by you. Even without knowing the specific event that triggered the final suspension, it's obviously due to him complaining without end and making absurd claims about, I don't know, probably reptilians taking over SE or something.

I'm sure he insulted plenty of people in the process, hence the inevitable conclusion

Slereah

It was me

I banned Ron Maimon

To suppress the truth

glS

makes sense. These truthists cannot be allowed to expose the shadow SE government

Ryder Rude

@glS yes. i'm just saying that that post was not about his permanent suspension. he latter protested against some mod election which led to the permanent suspension

he has good physics answers but he also seems very rigid/conspiracy-ish in his views, like u say

user 726941

sometimes unhealthy people need to be removed

glS

ehi now, it's not a permanent suspension. I'm sure he'll be waiting eagerly to be back on SE in 269 years

Ryder Rude

15:29

he could've made an alt i guess but he doesnt want to participate anymore

ACuriousMind

@RyderRude circumventing account suspensions by making new accounts is also against the rules and we regularly suspend and/or delete accounts doing this

Ryder Rude

yes, but, in principle, it can be done and no one would be able to track you

unless u reveal it in ur writing style

Sanjana

Why does string theory constrain the number of spacetime dimensions?
I mean I understand the math part, where it follows from Lorentz invariance/Weyl anomaly and other stuff? But what is the fundamental reason as in why do other theories like QFTs don't offer such restrictions?

ACuriousMind

What about the constraint of not having anomalies is not a "fundamental reason"?

QFT is just less restrictive than string theory: Every string theory has a QFT as its low-energy limit, but not every QFT is the low-energy limit of a string theory

Sanjana

Why don't QFTs get constrained then?
What's so special about strings?

user 726941

15:33

@RyderRude good point

Slereah

0-branes don't have conformal symmetry

user 726941

@RyderRude I'm sure you could find him if you searched long enough

Slereah

No symmetry to worry about there

ACuriousMind

@Sanjana plenty of QFTs with similar restrictions once you narrow down "QFT" a bit

Slereah

Well they do have it I guess, but only trivially since there's only one metric on a line

Ryder Rude

15:35

lubos motl is not suspended but he barely answers now

ACuriousMind

e.g. if you say you want to have a SUGRA QFT, then you get 11 dimensions as the maximum and exactly 5 distinct theories in 10d

Ryder Rude

his account doesnt say anything

ACuriousMind

(those 5 correspond exactly to the low-energy limits of the 5 string theories, meaning strings essentially force SUGRA)

Slereah

You can find all the restrictions for various dimensions of branes

There's a big diagram of it somewhere

ACuriousMind

it's just that "QFT" is a much more general framework than "string theory" so you get less restrictions, I don't find this particularly mysterious.

Ryder Rude

15:37

knzhou is also very knowledgeable

oh knzhou has answered in may

Sanjana

@ACuriousMind Yeah basically I should have asked why are QFTs less restrictive than string theories---is it by construction or what? I see I got an extra Weyl symmetry on the WS which is missing from the case of point particle...so can this the reason?

ACuriousMind

@Sanjana It's much more than that

QFT just says "pick a spacetime of any dimension and give me any number of fields and let's see what happens"

there isn't really anything that can go wrong there, the "worst" that happens is that your theory is non-renormalizable, really

Sanjana

@Slereah But are 0-branes the only p-branes which don't have conformal symmetry?

ACuriousMind

string theory doesn't start with that kind of choice - in one viewpoint, it's about choosing a 2d SCFT (a very special kind of QFT!) living on the worldsheets as a $\sigma$-model

so right from the start there isn't quite as much freedom there

Ryder Rude

and you need to have unitarity too. it's not guaranteed like in Qft becuz u dont have a hamiltonian formulation

ACuriousMind

15:41

and then when you compute the anomaly coming from those $\sigma$-models you find out the target space has to be 10 dimensional for this idea to even be consistent

Slereah

2 dimensions is kind of an odd duck as far as conformal symmetries go

Ryder Rude

so unitarity is a constraint

Slereah

It's not true for higher dimensions either, but then there are other reasons for them not working

That I'm sure @ACuriousMind will tell you all about

Sanjana

@ACuriousMind Okay...I am not sure but doesn't there exist a non-traditional QFT formalism which is similar in spirit to string theory...starting with a worldline of a point particle?

Slereah

Like thr conformal group is fucking huge in 2D and it's the only dimension where that is true

Ryder Rude

15:42

the unitarity of the worldsheet formulation can be proven. but not ever worldsheet path integral is unitary, I think

ACuriousMind

@Sanjana the worldline formalism is pretty much fiction, no one thinks about QFT in that way

Slereah

What about me

ACuriousMind

it just exists to make explicit the analogy between the perturbation series for the string scattering amplitude as a sum over worldsheets as the "one dimension higher" version of the QFT scattering amplitude as a sum over Feynman diagrams

Slereah

I believe

Ryder Rude

@Sanjana there are differences like the worldline feynman diagrams do not form a manifold becuz of the intersections

Sanjana

15:45

Oh?? So the restriction of dimensions goes over to the quantum case too!
I knew that classically SUGRA has a maximum of 11 dimensions...

Ryder Rude

but the string theory worldsheet is a manifold

Slereah

But really there's plenty of quantization obstructions, it's not a particularly weird thing

ACuriousMind

but really, the similarity is deceptive: Think about how in string theory we just have a worldsheet and some vertices where the particle states are inserted, while Feynman diagrams consist of different kinds of lines and it matters whether the loop you drew inside is a fermion loop or a boson loop, etc.

Slereah

We just notice it more for string theory because dimension is a weird constraint

Ryder Rude

remember that this restriction on dimensions is actually a restriction on SUGRA QFTs @Sanjana

ACuriousMind

15:47

@Sanjana all that changes in the quantum case is that the theory won't really be renormalizable, which is why people didn't like SUGRA before the string theorists hyped it up (since the UV limit there is string theory and not just SUGRA field theory the effective theories of string theories are allowed to be non-renormalizable)

Loong

Slereah

You can just work out the cases of 1D v. 2D for quantization

geocalc33

I mean quantum computing is just a derivative of interactions on the worldsheet

Slereah

They will have a different BRST algebra due to their different symmetries

Ryder Rude

Véronique Sanson - Chanson sur ma drôle de vie (Audio officiel)

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This song is very good too @PM2Ring

ACuriousMind

15:54

@geocalc33 nice buzzword salad

Slereah

I'm not sure if anything cool happens in 3D and up

It is not much discussed

ACuriousMind

@Slereah you don't get anything

there's no "brane theory"

Slereah

I mean there is, obviously, the question is what's wrong with it

ACuriousMind

anomalies, I think

Ryder Rude

@geocalc33 how

ACuriousMind

15:55

I'm certain I've seen papers showing what goes wrong there

but I'm lazy

Ryder Rude

quantum computing is just 2 dimensional Hilbert space QM, I think

worldsheet stuff shouldnt be related

geocalc33

At first sight quantum information and string theory seem unrelated fields, but they are deeply connected

Ryder Rude

how

what is a brane in simple terms

im seeing this term a lot in string theory

user 726941

@ACuriousMind what kind of dressing would you like with it :P

Slereah

A brane is what string theorists call a submanifold

Ryder Rude

16:00

oh

i think it has to do with the compactified dimensions

Slereah

A $p$-brane is a $p+1$-dimensional submanifold

ACuriousMind

@RyderRude no it doesn't

Ryder Rude

oh

ACuriousMind

you really need to stop guessing and just actually learn stuff when you're interested in it

any intro to string theory (as in, a book, or a script, not something shorter) should explain in detail what the notion of brane is

Ryder Rude

string theory has very cool math

ACuriousMind

16:01

like, this isn't a hard thing to figure out

you just need to put in a bit of effort

Ryder Rude

but im conflicted becuz it has no evidence

im both interested and uninterested in string theory. i dont know what to do

it is most likely just a math theory because any QG theory is more likely to be wrong than right

Slereah

you should also probably learn math, too

Ryder Rude

omg a brane is just the space-like hypersurface of a worldsheet

it shows in google images

Slereah

it's not spacelike or a hypersurface

ACuriousMind

no it isn't

Ryder Rude

16:08

i mean that a worldsheet is a propagating brane

ACuriousMind

no it isn't

or, well, you can call strings 1-branes if you really want to but that's not enlightening as to the nature of "branes" (which really are usually D-branes) at all

Ryder Rude

im seeing this image : images.app.goo.gl/f81pMMLLZJdkTPst5

ACuriousMind

so when I said "any intro to string theory (as in, a book, or a script, not something shorter) should explain in detail what the notion of brane is" what you got is "I'll look at a random picture with the word 'brane' in it and continue guessing"

Ryder Rude

sorry i shouldnt hav said worldsheet

it is a worldvolume

i had never heard of worldvolumes

@ACuriousMind i got it. i will pick up a book on it and stop guessing

but this is the first time im seeing a worldvolume

even tho string theory never allows 2D strings. it only allows 1D strings

perhaps the worldvolume represents smthing else

Sanjana

So umm...why dimensions of the target space out of other stuff?

Tracing back for SUGRAs I can see dimensions are constrained because the number of components is dimension-dependent which is pretty obvious.

ACuriousMind

16:16

@Sanjana I mean it just turns out that that dimension is what determines the anomaly?

Slereah

In Poincaré's second book he devotes a chapter to time, probably pushed by recent events

ACuriousMind

not really sure what kind of reason you're looking for here

Slereah

sometimes you have peculiar cases of things that happen only in a specific number of dimensions

It happens a lot for a variety of things

Unfortunately for us there's a lot of cases in 2 and 4 dimensions [or perhaps we know a lot of those since we study those manifolds a lot]

Sanjana

@ACuriousMind Hehe...nice. I guess I exhausted the full depth of recursion tree of "why"s :p

Slereah

32

Q: Accidents of small $n$

In studying mathematics, I sometimes come across examples of general facts that hold for all $n$ greater than some small number. One that comes to mind is the Abel–Ruffini theorem, which states that there is no general algebraic solution for polynomials of degree $n$ except when $n \leq 4$. It s...

Many such cases

Sanjana

16:20

Thank you everyone...Whenever I ask for something, I get to know more than what I asked for...It's so good to be here.

Slereah

I mean there's plenty of ways to express why strings only work in n dimensions

But I don't think any of them will be satisfying

I recently saw that there's some definition of quantum anomalies in derived geometry

But I doubt it will be extremely useful a definition

Sanjana

@Slereah Interesting...I have sometimes seen people arguing that these accidents are artificial because we defined some mathematical structure and found out a special thing...These people don't seem to be excited about finiteness of the number of sporadic groups and say "they exist because we wanted them to exist"

What are your views on this?

Slereah

I guess just that for most mathematical structures, the differences between two numbers will not generally make much difference unless the numbers are small?

ACuriousMind

I think facts are cool

I don't obsess over why the facts are the facts :P

Slereah

plus there are only so many small numbers

a small amount

and it is typically the most studied cases

Like a lot of geometry is done only in the 2D and 3D case

It's pretty rare for a manifold to even crack 2 digits as far as dimensions go

Sanjana

16:32

Hmmm

Slereah

Very annoying to me because a lot of interesting math is primarily done on the plane which I would like to apply to spacetime

Sanjana

Do you know of any really "cool facts" website? I mean I know the term is relative...but whenever I search for them I get some site with "Did you know? Black holes are not black" kind of thing :(

Slereah

Your local library?

Ryder Rude

the answer by Alon Amit is a great explanation of finite simple groups : quora.com/Intuitively-what-is-a-finite-simple-group

what are the advantages of doing a phd?

Alon says classification of finite simple groups is the deepest discovery humanity has made

there is some kind of universality to problems like this

geocalc33

17:01

dam I just got 2 quick downvotes on my riemann hypothesis question

riemann hypothesis is not physics by the way

I guess RH is taboo or something

Ryder Rude

83

A: Was mathematics invented or discovered?

There are things that are discovered, and things that are invented. The boundary is put at different places by different people. I put myself on the list and I believe that my position is objectively justifiable, and others are not. Definitely discovered: finite stuff By probabilistic considerati...

this is a very good insight about the levels of infinities and if infinites really exist

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