The h Bar

@ACuriousMind working on an answer and don't wan to to be an idiot, so I am making some general statements. please tell me if i am heading into a ditch. I was going to just post this first since I promised to post something Hi @cows

I am looking at [this][1] and [this][2]. Generally, for some solutions , for a given k. It seems one might need to read up on collective coordinates. We are thinking about the global gauge transformations g $\in$ G .

[1]: https://arxiv.org/pdf/hep-th/0509216.pdf

ACuriousMind

@GeroldBroser intermittently

@0celouvsky Yay?

Cows

@ACuriousMind so can i post that to start?

ACuriousMind

Post that where?

I can't even tell what you're trying to say

Cows

for the question i asked

ACuriousMind

What is k, what is G, why is "I might need to read up on collective coordinates" information anyone but yourself needs to know?

Cows

10:32 PM

SU(2)

ACuriousMind

Currently, I'd delete that as a link-only answer because all the information is in the links, not what you've written

Cows

well I just wanted to know if i am on the right track before I write anything

ACuriousMind

You need to try to get away from throwing around buzzwords and instead present a coherent argument: Define all your terms and variables, explain how they are related and what you are thinking about.

Cows

I want to do that, but I just wanted some reassurance that I am going in the right direction.

ACuriousMind

@Cows Since I still don't really know what you are asking about - you didn't answer any of my clarifying questions in the comment I left - I could not possibly tell whether you are on the right track or not.

Cows

10:34 PM

so ok

let me try

0celouvsky

@ACuriousMind yay indeed

everything seems to work just fine!

all the armor and weapons mods are activated correctly

the UI works fine

the map is updated

i don't know about the DLCs

Cows

screw it i will just talk and recieve humiliation

we get instantons solutions, and look at k =1

then the g is the gauge orientation stuff.

ACuriousMind

Instanton solutions of what theory? What is k, what is "gauge orientation stuff"?

0celouvsky

lol

Cows

how many times you go around

S 3 ≈ SU(2) ⊂ SU(N)

like the paper says

ACuriousMind

10:41 PM

@0celouvsky You should be able to tell that rather soon, right? Whether you get the quests that start their quest lines or not

0celouvsky

@ACuriousMind I have two modded DLCs, which are a big reason why I stopped playing

the modded DLC + textures + meshes + SkyRe made for an extremely buggy and difficult game

I don't actually know how to start those DLCs

there might be a level

@ACuriousMind e.g. Dawnguard requires level 15, I am level 5 right now

or is it 10?

ACuriousMind

@Cows What paper? Why can you not just tell me what theory you're talking about?

0celouvsky

but the fact that I can startthe game without it freezing is a big improvement, as I'm sure you remember :)

ACuriousMind

@0celouvsky Oh, that might be

@Cows I know enough about instantons and string theory that you should be able to communicate to me what exactly you're looking at without having me read a paper.

That's a spacetime, not a theory.

Cows

6d 2,0

ACuriousMind

10:48 PM

C'mon, complete sentences, please. Do you mean a 6d $\mathcal{N}=(2,0)$ super Yang-Mills theory?

Cows

yes

Yes. I am talking about that theory.

ACuriousMind

Okay, carry on then, what do you want to know/say about that theory?

By the way, since your question is about something related to M5-branes, I think that you actually want to talk about the superconformal theory that contains a higher gauge field that is the worldvolume theory of the M5, not a SYM theory.

Cows

I am just reading this, and am learning the vocabulary. I am wondering what gauge orientation zero modes means. Is this just something to do with g and collective coordinates?

higher gauge fields so extensions of su(n)

?

g $\in$ G(extensions of su(n)

?

ACuriousMind

@Cows No

A higher gauge field is one that is not a 1-form, but a p-form for p > 1.

The (2,0) worldvolume theory has a 2-form

Cows

i meant what g becomes

ACuriousMind

11:01 PM

I still have no idea what your g even is.

Cows

ok, so far so good p>1,

now

what does "gauge orientation zero modes" mean?

I am still trying to learn some vocabulary

ok let me make contact with a paper I am looking at

@ACuriousMind https://arxiv.org/abs/hep-th/0004186v2 (2.16) The gauge orientation zero modes can be obtained from (2.16). By expanding 5 U(θ) =
exp(−2θ a T a ) infinitesimally in (2.16) we get

.....

@ACuriousMind I am using the language in this paper arxiv.org/abs/hep-th/0004186v2

eq 2.16,

page 8

the g i refered to is in their notation

I swear I am not trying to waste your time, nor am I trolling you

gauge orientation zero modes. sorry said oriented instead of orientation

honest mistake

@ACuriousMind I realize this must be frustrating. I am using this paper to learn vocabulary and concepts first before, I learn the good stuff.

ACuriousMind

11:16 PM

@Cows The "zero mode" simply refers to it being a zero mode (i.e. eigenvector with zero eigenvalue) of that operator $M$ acting on the gauge field. The "gauge orientation zero modes" are those zero modes that lie in the subspace that corresponds to the "orientation" of the instanton.

Cows

@ACuriousMind aha, thank you

ACuriousMind

That's more or less explicitly said on page 16/17 of the paper you linked, btw :P

I have a feeling you either didn't actually read that paper very thoroughly, or that you lack much of the prerequisites to actually understand it.

Cows

I did not read the paper thoroughly yet. I found it last night, and glanced through. I am reading from page one now. The math is ok, although I am learning some new vocabulary as I go. It is mostly new words to fairly tractable ideas.

It is a 63 page paper. It would take me a while.

I had to look at tong's paper too, because he explains some stuff a bit more too. So I am looking at both papers.

I lack some vocabulary, but that's about it

I just wanted to be sure that I was looking for answers in the right set of notes before I devoted time to them

nbro

11:31 PM

Hi!

Cows

sup nbro

nbro I was just heading out, but @ACuriousMind is a great host :D

nbro

:D

G. Bergeron

@Slereah :D

@ACuriousMind Thanks anyway

nbro

I'm not studying physics, but I like physics, and whenever the occasion happens I read an article about a topic, like energy

most of the people have already seen the Einstein formula $E = mc^2$, which relates mass to energy in a linear way

well, c is actually a constant

so Energy would be just a scaling of mass

ACuriousMind

@G.Bergeron If you do find something out, let me know, the question sounded interesting ;)

nbro

11:39 PM

I know the solution to this question may be trivial, but since energy can be transferred (or acquired), we can actually increase and decrease the energy of everything that has mass and we can therefore also increase and decrease the mass of that same object, right?

G. Bergeron

@Slereah Wouldn't the tangent spaces of the two origins be canonically identified?

@nbro yes

@nbro a hot piece of metal is heavier than a cold piece of metal

ACuriousMind

@nbro Yes, although you have to be careful what you mean by "mass". In modern times, we often mean the invariant rest mass of an object which doesn't change when you "transfer energy" to the object e.g. by accelerating is.

It does change for certans "transfers" where you actually change the composition of the system, like charging a battery

G. Bergeron

@ACuriousMind Unless it forms a bound state :)

ACuriousMind

@G.Bergeron Right, and then we enter philosophical territory whether the new, heavier state consistutes "that same object" ;)

G. Bergeron

But yeah ''transfer'' by ideal elastic collisions will not change the mass

nbro

11:44 PM

mm.. ok

G. Bergeron

@ACuriousMind Ah come on, a warmed-up piece of metal can be seen as the same piece of metal. Anyway, in all practicality, we always work on equivalence classes of objects.

''What is a chair?'' :p

nbro

It seems to me, energy (and hence mass) is really an abstract concept

G. Bergeron

@nbro What concept isn't?

nbro

idk

G. Bergeron

@ACuriousMind I will. But I need to do read around more first.

ACuriousMind

11:47 PM

@G.Bergeron Oh, I just think the question of how we assign identity to objects (and persons) is one that's worth thinking about. I'm not saying you shouldn't claim the hot metal bar is the same as the cold one, but at what point during the transition to "molten pool of metal" does it stop being the same bar? Identity is odd.

G. Bergeron

@ACuriousMind Me too, but I think a satisfying answer is found in the concept of equivalence classes of ... qualia?

@ACuriousMind In the end, nothing intrinsic will tell you when to declare the switch, you decide and then work with the concepts. Agreed, by convention we try to synchronize as much as possible our definitions, but it's not really objective

nbro

What do you think when a person talks about a "source of energy"? What do you imagine?

G. Bergeron

@nbro Hence my question, what do you mean by saying ''is really an abstract concept''. Is it more or less abstract than the concept of ''tree''?

@nbro Somebody who is not rigorous

@nbro Or a big power plant, I guess. In movies: some scifi technology.

ACuriousMind

@G.Bergeron Ah, that works for the easy cases but I think you still have some issue with slow processes at whose beginning and end two clearly different objects are present, but where you can't pinpoint any instant where it changes from one object to the other - it's not an equivalence class if you can't clearly say which instants belong to the first and which to the second class, but declaring a new class for each instant seems...wasteful

nbro

There are different "trees", the idea of a natural tree, a tree of a family (or in computer science), but they are all ideas that describe or help to describe concrete objects, whatever concrete actually means

ACuriousMind

11:52 PM

@nbro I think of food.

I like thinking of food.

Cows

@ACuriousMind are you a grad student?

G. Bergeron

@ACuriousMind ''Everybody'' agrees at both end points, but they will assign the cut to different instant.

ACuriousMind

@Cows yes

Cows

USA?

or Europe

G. Bergeron

@nbro Ok, well energy and mass helps to describe concrete phenomenon/objects

nbro

11:55 PM

@G.Bergeron indeed

Cows

@ACuriousMind lol, just checked your profile. nice!

G. Bergeron

@ACuriousMind You're basically pinpointing the fuzzyness between those equivalence class for different observers. This is not a problem form the proposed framework, but a problem from langages: they are never exact in their description.

Have you ever seen people fight about wether that colour is blue or purple?

Cows

@ACuriousMind i thought it was heidelberg.edu in Ohio lol

ACuriousMind

@G.Bergeron Nah, I think your claim that all observers will make a cut is somewhat flawed. I mean, if you tell them "you must", then they will, but I don't think it is natural to expect that they will do so at all

G. Bergeron

@DanielSank Is that a valid expression in English?

ACuriousMind

11:58 PM

@Cows It says "Heidelberg, Germany" right on my profile :P

nbro

since energy can be transferred, every object that has mass is a source of energy, and when people say, e.g., the sun is a source of energy, I don't think they only mean that the energy associated with the sun is because of its mass

G. Bergeron

@ACuriousMind But don't you agree that this comes from langage? At what point does a tree becomes a wood table?

ACuriousMind

@nbro A "source of energy" is usually something from which energy can usefully or efficiently be transferred, in my impression

Cows

@ACuriousMind yeah I saw it :~)

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