A class of theories that attempt to explain all existing particles (including force carriers) as vibrational modes of extended objects, such as the 1-dimensional fundamental string.
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votes
0answers
11 views
If the mankind was blind, would we think that we are living in a 3D world?
I know that this can be a little philosophical, but it is also a scientific question.
Let's consider the scenario where the mankind was not ever able to see.
Let's also consider that this limitation ...
3
votes
0answers
36 views
A question about Lorentz invariance of the Polyakov action
I have a super basic and stupid question about the Lorentz invariance of the Polyakov action (cannot skip the disclaimer..)
$$S_p[X,\gamma]=-\frac{1}{4 \pi \alpha'} \int_{-\infty}^{\infty} d \tau ...
2
votes
2answers
58 views
A question about surface term of ghost fields
(skip disclaimer)
Hi, I have a question in Polchinski's string theory vol I p 90, after introducing the ghost fields $b_{ab}$ and $c^a$, it is claimed
The equations of motion then provide a ...
8
votes
1answer
101 views
How are low energy effective actions derived in string theory?
For example the eq 2.1 here with regards to Type IIB.
Unless I am terribly missing/misreading something Polchinski doesn't ever seem to derive these low energy supergravity actions.
I would like to ...
1
vote
1answer
31 views
A question about variation of metric under Weyl and coordinate transformations
I have a question about deriving variation of metric under Weyl and coordinate transformations in Polchinski's string theory (3.3.16).
Under transformation $$\zeta: g \rightarrow g^{\zeta}, \,\,\, ...
5
votes
1answer
131 views
What does string theory say about the metric expansion?
Specifically, what happens to those small intertwined hidden dimensions? Do those expand too?
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votes
0answers
47 views
Mirror symmetry in String Theory?
From looking at the Wikipedia entry on string theory I gather that it is found that any given physical model implies two Calabi-Yau spaces.
Perhaps one space gives rise to a sector of particles with ...
3
votes
1answer
107 views
Classical theories and AdS/CFT
When I was editing the tag wiki for ads-cft, I initially wrote something on the lines of :
The AdS/CFT correspondence is a special case of the holographic principle. It states that a gravitating ...
3
votes
1answer
70 views
Euler number of the world sheet
I have a question in the section 3.2 "The Polyakov path integral" in Polchinski's string theory p. 83.
Given
$$ \chi=\frac{1}{4 \pi} \int_M d^2 \sigma g^{1/2} R + \frac{1}{2 \pi} \int_{\partial ...
3
votes
1answer
71 views
A question about vertex operator
(skip disclaimer)
I have a question about writing raising and lowering operators in the Schroedinger basis in the section of vertex operator in Polchinski's string theory vol 1 p.68.
It is given
...
3
votes
1answer
129 views
F=MA in String Theory
$F = M \Big|_{A(T^2) \rightarrow 0}$
The above equation is the duality equation between F-theory and M-Theory on a vanish 2-torus. What's the explanation for this equation?
Is there anything ...
2
votes
1answer
68 views
About the conserved charge for the ghost number current in $bc$ conformal field theory
(skip disclaimer)
I have a question about the conserved charge for the ghost number current in $bc$ conformal field theory in Polchinski's string theory p62. It is said
For the ghost number ...
2
votes
1answer
47 views
Anticommuting relation in $bc$ CFT
(skip disclaimer)
I have a question about conformal field theory in Polchinski's string theory vol 1 p. 61.
Given anticommuting fields $b$ and $c$ and the Laurent expansions
$$ b(z) = ...
4
votes
1answer
53 views
SL(2,R) to SL(2,Z) in Type IIB String Theory
I heard from Prof. Katrin Becker (in her "SUSY for Strings and Branes - Part 1" lecture) that the classical $SL(2,\mathbb{R})$ symmetry in type IIB String theory becomes $SL(2,\mathbb{Z})$ in Quantum ...
1
vote
0answers
35 views
one loop correlator in ads cft
Is there any example of explicit one loop computation for Witten diagrams?
It seems like it will be hard to compute for even for a simple $\phi^4$ theory in the bulk.
2
votes
2answers
84 views
A question about Virasoro algebra
(skip disclaimer)
I have a question in Polchinski's string theory book volume 1 p54, related to the Virasoro algebra.
Introducing complex coordinates
$$w=\sigma^1 + i \sigma^2 $$
$$z=\exp (-i ...
3
votes
0answers
72 views
Expressions of action and energy momentum tensor in bc conformal field with central charge equals one
I have a question with conformal field theory in Polchinski's string theory vol 1 p. 51.
For $bc$ conformal field theory
$$ S=\frac{1}{2\pi} \int d^2 z b \bar{\partial} c $$
$$ T(z)= :(\partial b) ...
3
votes
1answer
22 views
String total cross sections at asymptotically high energy
I only have a vague understanding of string theory, but a solid understanding of particle physics. At asymptotically high energy (Regge limit), the string cross section is dominated by the exchange ...
2
votes
0answers
42 views
Deriving the critical dimension of bosonic string theory
I am going through the lecture note by Gleb Arutyunov on the derivation of critical dimension for bosonic string theory. I was able to reproduce all the results till the last step given on page 62.
...
1
vote
1answer
65 views
Compute the central charge of $bc$ conformal field theory
I have a s****d question, how to calculate the central charge of $bc$ conformal-field theory in Polchinski's string theory, Eq. (2.5.12)?
For a $bc$ CFT given by
$$S=\frac{1}{2\pi } \int d^2 z \,\,b ...
5
votes
1answer
62 views
The stability of D-Brane
In "String Theory and M-Theory: a modern introduction" by K.Becker, M. Becker and J.H.Schwarz, they say that BPS D-brane is stable as it preserves half of the Supersymmetry. I really want to ...
1
vote
1answer
82 views
How to derive Eq. (2.4.23) in Polchinski's string theory book
Given the Operator Product Expansion (OPE) of a product of the energy momentum tensors
$$T(z)T(0) = \frac{ \eta^{\mu}_{\mu} }{2z^4} - \frac{2}{\alpha' z^2} :\partial X^{\mu} \partial X_{\mu}(0): + ...
1
vote
1answer
40 views
Identify the weight of operator under conformal transformation
I have a stupid (homework tag may be suitable =_=) question about the problem 2.7 in Polchinski's string theory volume 1.
Why the weight of operator $:e^{ik\cdot X}:$ is $(\frac{\alpha'k^2}{4}, ...
1
vote
2answers
59 views
Identity of Operator Product Expansion (OPE)
I have one more s****d question in Polchinski's string theory book, Eqs. (2.3.14a)
$$ j^{\mu}(z) :e^{ik \cdot X(0,0)}:~ \sim~ \frac{k^{\mu}}{2 z} :e^{ik \cdot X(0,0)}:,$$
where $j^{\mu}_a ...
3
votes
3answers
106 views
Identify the coefficients of Operator Product Expansion (OPE)
Sorry I have a stupid question in Polchinski's string theory book vol 1, p46.
For a holomorphic function $T(z)$ with a general operator $\mathcal{A}$, there is a Laurent expansion
$$T(z) A(0,0) \sim ...
3
votes
1answer
74 views
A question about conformal transformation in Polchinski's string theory
I have one more stupid question in Polchinski's string theory book. P. 46,
it is said
It is convenient to take a basis of local operators that are eigenstates under rigid transformation (2.4.9)
...
1
vote
0answers
85 views
How to prove Eq. (2.4.5) in Polchinski's string theory book?
I got one more stupid question in Polchinski's string theory book. In p. 44, it is said
The currents
$$j(z)=i v(z) T(z), \tilde{j}(\bar{z}) = i v(z)^* \tilde{T}(\bar{z}) \tag{2.4.5}$$
are ...
2
votes
0answers
103 views
Is Electromagnetic Mass Possible?
If the sinusoidal electric component of a light wave were off-set to one side of the magnetic component and then the smaller "lobe" were to cancel out with much of the larger side, then where would ...
1
vote
1answer
108 views
How to derive Eq. (2.1.24) in Polchinski's string theory book
Excuse me, I got one more stupid question in Polchinski's string theory book :(
$$\partial \bar{\partial} \ln |z|^2 = 2 \pi \delta^2 (z,\bar{z}) (1) $$
I shall check this equation by integrating both ...
4
votes
1answer
112 views
Divergence theorem in complex coordinates
This question is related to Stokes' theorem in complex coordinates (CFT)
but, I still don't understand :(
Namely how to prove the divergence theorem in complex coordinate in Eq (2.1.9) in ...
3
votes
1answer
71 views
Some questions about the free Fermionic partition function on a circle (Ginsparg's CFT lectures)
The following questions are based on these lectures, http://arxiv.org/abs/hep-th/9108028
I would like to know what is the relationship between the last equation on page 82 ($(L_0)_{cyl} = L_0 - ...
6
votes
1answer
95 views
About the stability of the ground state of the bosonic string
In Polchinski's string theory vol 1, p. 23, it is said
"It is a complicated question whether the bosonic string has any stable vacuum, and the answer is not known."
The book was published on 1998. ...
6
votes
1answer
133 views
How exactly are Calabi-Yau compactifications done?
To compactify 2 open dimensions to a torus, the method of identification written down for this example as
$$
(x,y) \sim (x+2\pi R,y)
$$
$$
(x,y) \sim (x, y+2\pi R)
$$
can be applied.
What are the ...
2
votes
1answer
93 views
Where does $p^i/p^+$ come from in the EOM of an open string?
I have a stupid question about Eq. (1.3.22) in Polchinski's string theory volume 1.
In the equation of motion for an open string, Eq. (1.3.22),
$$X^i (\tau, \sigma) = x^i + \frac{ p^i}{p^+} \tau + ...
4
votes
0answers
95 views
Poincare recurrence and the multiverse
In this paper Susskind claims that a stable de Sitter universe is problematic (among other things) due to the existence of Poincare recurrence, which happen because of finite entropy. I disagree that ...
3
votes
1answer
60 views
IIA and IIB Compact on 8D
How can compactifying IIA (non-Chiral) and IIB (Chiral) Superstring on $T^2$ (2-torus) gives rise to ($2$ dual descriptions of) the same $N = 2$ supergravity in $8$ dimensions? I don't see it. Could ...
13
votes
5answers
478 views
String Theory and Standard Model in CERN
I don't know how to say it, but in the TV dominatrices and the popular science books we see the string theory as "the best theory to explain everything", and as "the only game in town"... etc. And ...
-2
votes
1answer
102 views
String theory and the SM spectrum [closed]
Long ago, I realized this: (super)string theory can NOT give a well-defined/unique prediction of why the electron (muon, tau) or the neutrino (any flavor) masses have the masses we measure. String ...
9
votes
1answer
193 views
What is the relationship between string theory and quantum field theory?
Please forgive a string theory novice asking a basic question.
Over at this question Luboš Motl gave an excellent answer, but he made a side comment that I've heard before and really would want to ...
2
votes
1answer
67 views
Deriving the transformation under Weyl rescaling in Polchinski eq. (1.2.31)
I have another question in Polchinski's string theory book volume 1, namely how to derive Eq. (1.2.32)?
$$(-\gamma')^{1/2} R'=(-\gamma)^{1/2} (R-2 \nabla^2 \omega) (1.2.32)$$
I have awared his Eq. ...
2
votes
1answer
39 views
Weyl symmetry and Polyakov action
I have a question in reading Polchinski's string theory volume 1.
p12-p13
Given the Polyakov action
$S_P[X,\gamma]= - \frac{1}{4 \pi \alpha'} \int_M d \tau d \sigma (-\gamma)^{1/2} \gamma^{ab} ...
2
votes
1answer
114 views
How to derive Eq. (1.2.17) in Polchinski?
I have a super stupid question about deriving Eq. (1.2.17) in Polchinski's string theory, vol 1.
The book seems to derive from
$$\tag{1.2.16} h_{ab}=\frac{1}{2} \gamma_{ab} \gamma^{cd} h_{cd} $$
...
3
votes
1answer
114 views
Why does tachyon arise in bosonic string theory?
I am looking for precise mathematical and physical reasons which cause the presence of tachyon in bosonic string theory(specially closed bosonic string theory). Has it to do with the specific form of ...
6
votes
2answers
219 views
The General Relativity from String Theory Point of View [duplicate]
I have a hard time understand the statement that
When you only look at the classical limit or classical physics, string
theory exactly agrees with general relativity
Because from what I know, ...
5
votes
1answer
125 views
Why can the Euler beta function be interpreted as a scattering amplitude?
The Wikipedia article on the Veneziano Amplitude claims that the Euler beta function can be interpretted as a scattering amplitude. Why is this?
In another word, when the Euler beta function is ...
8
votes
1answer
233 views
Is String Theory proven to be finite?
I read Lee Smolin's book "The trouble with physics" and the book says that the finiteness of string theory ( or string pertubative theory) is by no means a proven mathematical fact, despite that the ...
2
votes
0answers
21 views
boundary conditions Faddeev-Popov ghosts bosonic string
I have a question concerning the Faddeev-Popov ghost boundary conditions in the path integral quantization of bosonic strings. My ghost action is:
$S_g= - \frac{i}{2\pi} \int d^2 \xi \sqrt{-h} \; ...
5
votes
1answer
75 views
Decomposition of Representation Multiplication
How can the multiplication of spinor representations (of $SO(8)$) $8_+ \otimes 8_-$ be decomposed into $8_v \oplus 56_v$? Where can I read more about the decomposition rule of different ...
5
votes
1answer
174 views
Energy-momentum tensor of Bosonic Ghost Action in String Theory
When quantizing bosonic string theory by means of the path integral, one inverts the Fadeev-Popov determinant by going to Grasmann variables, yielding:
$$
S_{\mathrm{ghosts}} = ...
2
votes
0answers
91 views
What is the physical meaning of equivalence of 1st and 2nd quantization formalism?
Ref (Superstring theory (Green, Schwarz, Witten))
Take an $n$ dimensional euclidean space-time $x_0,x_1...x_{n -1}$, a relativist real scalar field, with a propagator $G_E(x,y)$.
The propagator ...
