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What's the difference between open string field theory and closed string field theory?
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Originally posted by meteor
What's the difference between open string field theory and closed string field theory?
Originally posted by selfAdjoint
Absolutely none. Open strings can become closd by joining their ends. Closed strings can become open by breaking at some point. Strings can join to make things like figure eights and more, and they can part just as easily. The constant mutation of the strings in all kinds of topologies is the string theory equivalent of the interaction of particles.
Originally posted by sol
U(1)=photon
If photon starts out as a one dimensional string(?) can we consider this longitudal, and be used as a determination of the nergy contained in the photons length?
Originally posted by sol
I apologize if this seems like a stupid question.
Originally posted by selfAdjoint
Well that's a bit harsh
Originally posted by selfAdjoint
I define as a single theory that produces the real predictions of GR
Originally posted by selfAdjoint
It's not enough to generate some U(1) x SU(2) x SU(3) generic theory.
Originally posted by selfAdjoint
do you know of an online tutorial for string field theory?
Originally posted by selfAdjoint
Trying to understand it from research papers is a bummer.
Originally posted by selfAdjoint
I want to say this gently..
Originally posted by selfAdjoint
You say they haven't got GR, but they do have approximations
Originally posted by selfAdjoint
Strings contain the graviton which is a spin 2 boson and by prior theory a spin 2 boson will couple to matter like the einstein tensor.
Originally posted by selfAdjoint
GR is a generally covariant, background independent theory, and string theory is not. The point of background independence isn't just a barb, it's the nub of the whole contention. and you say strings contain GR which is false.
Originally posted by selfAdjoint
People say string field theory, in at least some of its forms, is background free, but I haven't come upon a real refer3nce to this.
Originally posted by sol
You would be scare of my mystical approach then
Originally posted by sol
Just know, that I endeavor to understand and do not want to be criticized for my thinking outside of this issue:0)
Originally posted by sol
Leading from the length( amplitude?) the transverse understanding of information is understood in the brane? Does this contradict what you have said
Originally posted by sol
could you explain SU(2)
Originally posted by sol
In the undertanding I am developing...
Originally posted by selfAdjoint
Jeff, can you expand some detail on how this:
Consider the following equation which appears in the bosonic theory as a consistency requirement on the world-sheet theory, namely that it be weyl-invariant
ƒ¿?ŒRƒÊƒË + 2ƒ¿?Œ?ÞƒÊ?ރ˃³ - (ƒ¿?Œ/4)HƒÊƒÉƒÖHƒËƒÉƒÖ = 0.
This is einstein's equation with sources the antisymmetric tensor field and dilaton that arise in string theory. This is a good example of what string theorists mean when they say that strings contain GR. What it means is that strings can propagate consistently only in a background that satisfies appropriate field equations (this bothers me more than anything else in ST).
constrains the background? (Sorry about what copy did to the notation). In general I have problems understanding how definitions on the worldsheet work out in terms of background propagation.
Originally posted by jeff
Finally, to move beyond U(1) to non-abelian U(n) gauge symmetry, we need to introduce Chan-Paton factors.
Originally posted by jeff
There's no need to be gentle as long as you're talking about physics. I'm not gentle with anyone when it comes to physics, unless they turn out to be psychotic or something.
Originally posted by selfAdjoint
(but see Lubos Motl's takedown of LQG on yesterday's s.p.r)
Originally posted by selfAdjoint
Lethe - Motl made the comments in a discussion of John Baez's latest "This Week's Finds" which was posted at sci.physics.reaearch the day my post appeared. Do an in-site search on Motl and you should be able to find it.
Originally posted by selfAdjoint
...I'm going to print it and study it some more because it makes some of the things (operator-product correspondence for one) a lot clearer.
Originally posted by lethe
...quick and dirty explanation of what a Chan-Paton factor is?
Originally posted by sol
Is it possible to have a generalization put in front of this equative formulation on a simpler level.
Originally posted by jeff
selfAdjoint,
This is the most direct approach I could come up with:
Transition amplitudes in ST are defined in a 1st quantized formalism based on the world-sheet action
SG = - (1/4πα′) ∫ dμγγabGμν(X)∂aXμ∂bXν
in which the basic fields Xμ of the theory embed the world-sheet with metric γab and measure dμγ in a background spacetime with metric Gμν. Recall that in QFT the tree level feynman diagram for an interaction consists of a vertex where legs representing incoming and outgoing particles meet. Analogously, for closed strings we have a sphere with punctures to which are glued the ends of "world-tubes" representing incoming or outgoing strings. The invariance, known as weyl-invariance, of SG under rescalings γab → eφγab of the world-sheet metric allows the projection (continuous deformation) of world-tubes onto the punctures, effectively sealing each one by insertion of a point sitting at which is a vertex operator defined in terms of Xμ and it's world-sheet derivatives and carrying the quantum numbers of the original incoming/outgoing string state vector: This is known as the state-operator correspondence, an example of which is given at the end of this post. Higher order interactions are obtained as compact oriented boundaryless surfaces of genus g with a vertex operator insertion Vi(ki) for each incoming/outgoing closed string of momentum ki. Hence, amplitudes for n external string states have the form of a sum of path-integrals with insertions
<V1(k1)⋅⋅⋅Vn(kn)> ~ ∑g=0,1,2,... ∫g DγabDXμ V1(k1)⋅⋅⋅Vn(kn)e-SG.
Now, take
Gμν(X) = ημν + εμν(X)
with
εμν(X) = ∫ d26k εμν(k)eik⋅X
everywhere small compared to ημν. Then
e-SG = e-(Sη + Sε) = e-Sη ∑n=0,1,...(- 4πα′)-n(1/n!) ∫ d26k1⋅⋅⋅d26kn V(k1)⋅⋅⋅V(kn)
in which
V(k) ≡ εμν(k)Vμν(k) ≡ εμν(k) ∫ dμγ γab∂aXμ∂bXνeik⋅X
is a vertex operator coupling strings to fluctuations in the background metric Gμν. Note that like all vertex operators, V is an integral over the world-sheet since it can be inserted at any point. Next, observe that εμν picks out the symmetric part of Vμν, so V is the vertex operator of a spin-2 state. Also, since the state-operator correspondence (see the example at the end of this post) requires that vertex operators transform like the string state vectors they represent, they must include the factor eik⋅X to transform properly under spacetime translations Xμ → Xμ + aμ. Now, any insertion must respect the local weyl symmetry of the theory. In particular, demanding that V be weyl-invariant requires (see polchinski I Chap 3.6)
k2 = k2εμν(k) = 0 ↔ ⇑εμν(X) = ⇑Gμν(X) = 0
kμεμν(k) = 0 ↔ ∂μεμν(X) = ∂μGμν(X) = 0,
εμμ(k) = 0 ↔ εμμ(X) = 0.
In addition to showing that the spin-2 excitations are massless, because the ricci tensor Rμν satisfies
Rμν ∝ ∂μ∂νελλ - 2∂λ∂(μεμ)λ + ⇑εμν + O(ε2),
this also shows that to leading order in metric fluctuations, weyl-invariance in the pure helicity-2 theory requires that the background Gμν satisfy the vacuum einstein equations Rμν = 0.
Because massless states are transversally polarized, V must be invariant under the shift
εμν(k) → εμν(k) + kμξν + kνξμ
by longitudinal polarizations. In terms of the metric, this gauge-invariance
εμν(X) → εμν(X) + kμξν(X) + kνξμ(X)
is an infinitesimal diffeomorphism generated by the vector field ξμ(X) in the approximation where O(ε2) terms are neglected and under which Rμν = 0 is invariant. In fact Rμν = 0 is the only spacetime diffeo-invariant equation that reduces to ⇑Gμν(X) = 0 in the linearized limit.
In sum, weyl-invariance requires spin-2 excitations be massless and couple in a gauge-invariant way, that is, it requires the general covariance of GR, justifying the interpretation of helicity-2 excitations as gravitons.
State-operator correspondence for the graviton vertex operator:
Define world-sheet coordinates
z = e-iσ + τ , z* = eiσ + τ
with σ = σ + 2π the periodic coordinate along the string and τ the time coordinate on the world-sheet. We then have
V ∝ εμν∫d2z ∂zXμ(z)∂z*Xν(z*)eik⋅X(z,z*)
in which we've taken the world-sheet metric in "conformal gauge" so that it effectively drops out. Then (up to proportionality) the state-operator correspondence is
∂zXμ(0) ↔ α-1μ , ∂z*Xμ(0) ↔ (α-1μ)* , eik⋅X(0,0) ↔ |0;0;k>
where α-1μ and (α-1μ)* excite left- and right-moving n = 1 modes.
Putting these together gives
V ↔ εμνα-1μ(α-1ν)*|0;0;k>.
Originally posted by ranyart
Jeff, I detect as much panic in your posts as your peers, you are not alone!
Here is a link to a paper that has PANIC written (not witten!)all through it:http://uk.arxiv.org/abs/hep-th/0308055
As Aristotle said..urhmm I am off!
Originally posted by lethe
ouch, that was tough. i can t wait to see Baez' reply.
Originally posted by Tom
PANIC is an international conference on particles and nuclei.
Originally posted by ranyart
I see that the reply to my post from jeff dissapeared? unless he re-routed it into a different 'sum-over-history'!
Anyway, I do not think Jeff got the hidden variable contained in the post? It actually relates to the 'Stanford crew', and I must say I agreed totally with his acclamation of the said Theorists, I for one have examined a vast number of their pre-print papers for some while, and I am in awae at their persistence in the devolpment of Inflaton field Evolution theory, if that's a correct term?
Question, what causes Strings? Nature or Theorists?
Originally posted by jeff
After Tom pointed out the panic thing I removed my moronic post. But thanks for the sentiments and sorry about that.
Originally posted by ranyart
No problem
Originally posted by jeff
I understood this part.
Originally posted by jeff
I understood this part.
Originally posted by jeff
This is going to take quite a bit of typing. I'll get to this sometime this week. Sorry for the delay.
In general I have problems understanding how definitions on the worldsheet work out in terms of background propagation.
Then usingV(k) ß ƒÃƒÊƒË(k)VƒÊƒË(k) ß ƒÃƒÊƒË(k) ç dƒÊƒÁ ƒÁabÝaXƒÊÝbXƒËeik⋅X
is a vertex operator coupling strings to fluctuations in the background metric GƒÊƒË. Note that like all vertex operators, V is an integral over the world-sheet since it can be inserted at any point.
Uhmm[?] care to insert this into Present Spacetime? what you mean(and if one goes back to the original paper of Jiangping Hu and Shou-Cheng Zhang) one cannot explicitly transform hydrodynamical modes from within a Boundery to the external boundery, it can only go one-way.
If one inserts a dynamical background that is part of a worldsheet that is not based in 3-dimensional PRESENT spacetime, then effectively you are folding/unfolding space/past/future inwardly, which is exactly what Hu and Zhang mentions in their Paper, I quote;Since the dimension of total configuration space is higher than the dimension of base space, this theory bares similarities to Kaluza-Klein Theory, but with two important differences. First the total confiruration space is topologically non-trivial fiber bundle. Second the iso-spin space does not have a small radius. This leads to the "embarrassment of riches" problem. In order to solve this problem we need to find a mechanism where higher iso-spin states obtain mass gaps dynamically, through interactions. This way the low energy degrees of freedom would scale correctly with the dimension of base space. end.
Then:The underlying mathematical structure of the current approach is the noncommutative
geometry [18] dened by Eq. (2). Unlike previous approaches [19], this relation
treats all four Euclidean dimensions on equal footing. If we interpret X4 as energy, which is
dual to time, this quantization rule seem to connect space, time, spin and the fundamental
length unit l0 in an unied fashion. In the lowest SO(5) level, there is no ordinary non-relativistic kinetic energy. All the single particle states are representations of this algebra.
The non-trivial features identied in this work all have their roots in this algebra.
Now why is it that all string theories have problems with background propergation?[?]
Originally posted by ranyart
Starting withIn general I have problems understanding how definitions on the worldsheet work out in terms of background propagation.
Then usingV(k) ?ß ƒÃƒÊƒË(k)VƒÊƒË(k) ?ß ƒÃƒÊƒË(k) ?ç dƒÊƒÁ ƒÁab?ÝaXƒÊ?ÝbXƒËeik⋅X
is a vertex operator coupling strings to fluctuations in the background metric GƒÊƒË. Note that like all vertex operators, V is an integral over the world-sheet since it can be inserted at any point.
Uhmm[?] care to insert this into Present Spacetime? what you mean(and if one goes back to the original paper of Jiangping Hu and Shou-Cheng Zhang) one cannot explicitly transform hydrodynamical modes from within a Boundery to the external boundery, it can only go one-way.
If one inserts a dynamical background that is part of a worldsheet that is not based in 3-dimensional PRESENT spacetime, then effectively you are folding/unfolding space/past/future inwardly, which is exactly what Hu and Zhang mentions in their Paper, I quote;Since the dimension of total configuration space is higher than the dimension of base space, this theory bares similarities to Kaluza-Klein Theory, but with two important differences. First the total confiruration space is topologically non-trivial fiber bundle. Second the iso-spin space does not have a small radius. This leads to the "embarrassment of riches" problem. In order to solve this problem we need to find a mechanism where higher iso-spin states obtain mass gaps dynamically, through interactions. This way the low energy degrees of freedom would scale correctly with the dimension of base space. end.
Then:The underlying mathematical structure of the current approach is the noncommutative
geometry [18] dened by Eq. (2). Unlike previous approaches [19], this relation
treats all four Euclidean dimensions on equal footing. If we interpret X4 as energy, which is
dual to time, this quantization rule seem to connect space, time, spin and the fundamental
length unit l0 in an unied fashion. In the lowest SO(5) level, there is no ordinary non-relativistic kinetic energy. All the single particle states are representations of this algebra.
The non-trivial features identied in this work all have their roots in this algebra.
Now why is it that all string theories have problems with background propergation?[?]
I don't doubt your sincerity, but help me out here. Could you begin again by raising just one very specific issue of concern to you in a brief - very very brief - clear and uncomplicated way?
Originally posted by jeff
I don't doubt your sincerity, but help me out here. Could you begin again by raising just one very specific issue of concern to you in a brief - very very brief - clear and uncomplicated way?
Originally posted by ranyart
A Note On The Chern-Simons
And Kodama Wavefunctions
Edward Witten
Institute For Advanced Study, Princeton NJ 08540 USA
Yang-Mills theory in four dimensions formally admits an exact Chern-Simons wavefunction.
It is an eigenfunction of the quantum Hamiltonian with zero energy. It is known to be unphysical for a variety of reasons, but it is still interesting to understand what it describes.
We show that in expanding around this state, positive helicity gauge bosons have positive energy and negative helicity ones have negative energy. We also show that the Chern-Simons state is the supersymmetric partner of the naive fermion vacuum in which one
does not fill the fermi sea. Finally, we give a sort of explanation of “why” this state exists.
Similar properties can be expected for the analogous Kodama wavefunction of gravity.
Ed Witten:In the nonabelian case, and e are not invariant under homotopically non-trivial gauge
transformations. We ignore this. Along with the unnormalizability, lack of CPT invariance, etc., and additional properties that we will see below, this is one more reason that the Chern-Simons
state is formal and does not really correspond to a sensible physical theory.
arXiv:gr-qc/0306083 v1
yeah, that sounds like what CVJ says in his book. but that s the first part that i didn t follow. why is it natural to assign nondynamical degrees of freedom to the endpoints of a string? what does the phrase "nondynamical degrees of freedom" even mean? can you give me an example of a more pedestrian quantum theory where we do this? does anything like this ever happen in QED?Originally posted by jeff
In quantum systems it's natural to assign to distinguished points nondynamical internal degrees of freedom giving rise to global symmetries, i.e. conserved charges that don't contribute to the hamiltonian or ruin any pre-existing symmetry.
they have trivial world sheet dynamics because they don t appear in the lagrangian?
In string theory we can charge the endpoints of open strings with chan-paton degrees of freedom. Although these charges may interact with external gauge fields, during interactions of several open strings (open strings interact at their endpoints), they flow only along the world-sheet boundaries swept out by the endpoints and so are conserved. Since chan-paton charges have trivial world-sheet dynamics - that is, world-sheet interactions can't change them - consistency requires that only identically charged endpoints may interact.
Originally posted by jeff
If the chan-paton degrees of freedom in the 2D quantum conformal field theory governing the physics of open strings are to be useful, they must produce in the low energy limit the familiar yang-mills interactions of particles as they appear in the arena of QFT.
The main difference between open string field theory and closed string field theory is the type of strings that are considered. In open string field theory, the strings have two distinct endpoints, while in closed string field theory, the strings form a loop with no endpoints.
In open string field theory, the interactions between strings are described by the exchange of open strings with two endpoints. In closed string field theory, the interactions are described by the exchange of closed strings forming loops.
Both open string field theory and closed string field theory are considered equally fundamental in string theory. They are two different descriptions of the same underlying theory.
Yes, open string field theory and closed string field theory can be related through a process called closed string channelization. This allows for the translation of interactions between open strings to interactions between closed strings.
Both open string field theory and closed string field theory are used in string theory research, depending on the specific problem being studied. However, open string field theory is more commonly used in perturbative calculations, while closed string field theory is more often used in non-perturbative calculations.