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. PLEASE DO NOT USE THIS TAG for non-relativistic material strings, such as, e.g., a guitar string.

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Mathematician learning theoretical physics [duplicate]

EDIT: I was aware of the supposed duplicate. But I'm interested in a clear and focused path through the basics to theoretical physics, that avoids studying engineering physics, for a pure ...
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3answers
69 views

Calculating euler number of disk

I'm trying to do exercise 3.1 from Polchinski, which should be a rather easy differential geometry problem. I have to calculate the euler number defined by $$\chi = \frac{1}{4\pi}\int_{M}d^{2}\sigma ...
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25 views

Fourier transformation and mode expansions [duplicate]

Sorry as this is a rather trivial question, but I'm stuck with a certain implication. I'm working on exercise 1.7 from Polchinski where we are given an open string with boundary conditions ...
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1answer
28 views

Open string interactions implies closed string

I am currently reading Polchinski page 81, and am not 100% clear with the explanation given regarding why any open string theory necessarily contains closed strings. It is stated, quoted from page ...
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0answers
78 views

Fourier transformation and commutators

Sorry as this is a rather trivial question, but I'm stuck with a certain implication. I'm working on exercise 1.7 from Polchinski where we are given an open string with boundary conditions ...
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0answers
46 views

Extra dimensions in a black hole [on hold]

Could small extra dimensions predicted by string theory exist within a black holes singularity? I believe that these dimensions would not break down in a black hole as opposed to our three dimensional ...
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36 views

Is the Cauchy Horizon of Anti deSitter spacetime stable?

The Cosmic Censorship Conjecture are two mathematical conjectures about the structure of spacetime. In particular the so called Strong Cosmic Conjecture asserts heuristically that generically, ...
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86 views

Mode operators in the Virasoro algebra

This questions concerns Exercise 2.11 in Polchinski. We are asked to compute the commutator $$L_{m}(L_{-m}|0;0\rangle) - L_{-m}(L_{m} |0;0\rangle)$$ By plugging the mode expansions, we use the ...
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48 views

Calculation of OPE in Polchinski

Consider Exercise 2.8 in Polchinski's String Theory book. We are asked to compute the weight of $$f_{\mu \nu}:\partial X^{\mu} \bar{\partial}X^{\nu}e^{ik\cdot X}:$$ I have carried out the usual ...
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40 views

Projection that keeps graviton but gets rid of B-field

We consider the closed superstring and the massless states in the (NS,NS)-sector \begin{equation} \tilde{b}^i_{-\frac{1}{2}} |0\rangle_L \otimes b^j_{-\frac{1}{2}} |0\rangle_R. \end{equation} It is ...
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24 views

D-branes in type II string theory

D-branes, as I currently understand them, are submanifolds of spacetime on which open strings can end with Dirichlet boundary conditions. On the other hand, type II string theory is a theory of ...
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1answer
65 views

Operator product expansion energy momentum tensor

We have the following equation from Polchinski (2.4.6) $$ T(z)X^{\mu}(0) \sim \frac{1}{z}\partial X^{\mu}(0) , \tag{2.4.6} $$ where $T(z)$ is defined as $T(z) = -\frac{1}{\alpha'} :\partial X^{\mu} ...
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33 views

Do $p$-branes have curvature? [closed]

The metric in general relativity describes the curvature of space-time. A 4-manifold. Some people say that the Universe is contained on a 3-brane which is a 3-manifold and it's world sheet is a ...
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0answers
62 views

Why are there no branes in heterotic string theory?

Why does the heterotic string (or heterotic supergravity) have no brane solutions? According to David Tong's notes: the heterotic string doesn’t have (finite energy) D-branes. This is due to an ...
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0answers
41 views

What happens to M2 and M5 brane solutions upon orbifolding?

M-theory has M2 and M5 brane solutions. Suppose M-theory is compactified on $\mathbb{R}^{10} \times S^{1}/\mathbb{Z}_2$, what happens to the M2 and M5 brane solutions? How does one define the near ...
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28 views

When can a $k$-cycle wrap around a manifold?

According to the paper ``Heterotic and Type I String Dynamics from Eleven Dimensions'' (page 7): Even when the topology is wrong -- for instance on $\mathbb{R}^{11}$ where there is no two-cycle ...
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32 views

How to find de Sitter and almost de Sitter solutions in (super)string theory

From Cosmology, we have learned that we live in an almost de Sitter (positively accelerated!) Universe. It seems that dS space solutions in superstring/theory are problematic and there are some no-go ...
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14 views

Given the extension of a NS5-brane, can we find the extension of the T-dual KK5-brane?

My question is about the relation between the Kaluza-Klein 5-brane and the NS5-brane and the effective dimensionality of the KK5 brane. To my knowledge, the KK5 is defined as the T-dual of the NS5, ...
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AdS/CFT-duality: How does the $U(1)$ decouple form the $U(N)$?

A stack of N coincident D3-branes on its world-volume describe, at the lowest order in $\alpha'$ and in absence of non-trivial background fields, a supersymmetric $U(N)$ gauge theory as explained in ...
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1answer
25 views

Polchinski, (0,0) picture vertex operator

I am currently working through chapter 12 of Polchinski and am confused as to how the equation $(12.3.39)$ for the (0,0) picture vertex operator arises. From the text: The state–operator mapping ...
2
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1answer
69 views

Canonical commutation relations in Light-cone gauge

It seems that when trying to identify the physical degrees of freedom for the string some authors$^1$ use: $$ q^-=\frac{1}{\ell}\int_0^{\ell} X^-(\tau,\sigma)d\sigma$$ Then, the commutation relation ...
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1answer
46 views

How many Dimension do we have? [duplicate]

I know that Einstein described three dimensions for space and one for time. But I also have heard something about a world with so many dimensions or 11 dimensions of space or ... On the whole due to ...
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54 views

Projector and delta function on a cycle $\Sigma$ of a manifold $\mathcal{M}_6$

In the paper ``Hierarchies from Fluxes in String Compactifications'' by Giddings, Kachru and Polchinski, the following example is considered for a localized source that may have negative tension (my ...
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28 views

What is $\mathcal{N}=2$ QED?

I would like to know is $\mathcal{N}=2$ QED is simply a $\mathcal{N}=2$ theory with gauge group $U(1)$ like in normal QED? If not, exactly what theory is it? Is there some reference for it?
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Charged black holes and AdS/CFT

People generalize the statements of AdS/CFT correspondence by adding black hole (charged black hole) in the gravity theory to provide the dual gauge theory finite temperature (finite density). I have ...
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1answer
51 views

Equations of motion for Polyakov action

In Polchinski 2.1.10 we have the action in terms of complex coordinates $$S = \frac{1}{2\pi \alpha'} \int d^{2}z \partial X^{\mu}\bar{\partial}X_{\mu}\tag{2.1.10}$$ This should be a rather trivial ...
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1answer
67 views

Question regarding moduli space of a Calabi-Yau manifold

On page 132 of "Introduction to Supergravity" by Horiatiu Nastase, the author says: On $M = CY_3$ (Calabi-Yau space) there are $b_3$ topologically nontrivial 3-surfaces, for which we can define a ...
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33 views

Ishibashi states and Cardy states in CFT

What are the Ishibashi states and Cardy states in CFTs? I am familiar with conformal field theory language. It would be great if someone can discuss about the basic idea of these states and their ...
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2answers
58 views

Topological strings: Why is the complex structure for $T^2$ denoted as $\tau$ in string theory?

In these notes by Vafa on topological string theory he says in page 7 that the moduli of the 2-torus can be repackaged into two quantities: $$A=iR_1/R_2 \,\,\,\,\,\,\,\,\, \tau=iR_2/R_1$$ where $A$ ...
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2answers
106 views

What laws are the same in all string theory compactifications?

In the string theory landscape, the set of particles we observe, their masses and interaction strengths originate from one of many different possible compactifications. What fundamental physical ...
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114 views

Monstrous Moonshine outside of String Theory

My question concerns applications of monstrous moonshine, which is the connection between the $j$-function and the monster group. Recently, physicists have applied it to string theory and, ultimately, ...
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1answer
60 views

Quark-gluon plasma: status [closed]

Can we say that a QGP has been observed or is there only suggestive evidence? Is the idea that string theory, through the AdS/CFT correspondence, could help to understand this new state of matter ...
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27 views

Why are closed strings with different perioidicities equivalent?

I was typing up some lecture notes the other day when I saw something unclear. While talking about bosonic open and closed strings and the Polyakov action, the notes say we don't need to distinguish ...
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1answer
67 views

Elementary question about global supersymmetry of a worldsheet [closed]

I'm reading chapter 4 of the book by Green, Schwarz and Witten. They consider an action $$ S = -\frac{1}{2\pi} \int d^2 \sigma \left( \partial_\alpha X^\mu \partial^\alpha X_\mu - i \bar \psi^\mu ...
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1answer
75 views

Facing a problem in Katrin Becker, Melanie Becker, John Schwarz's String Theory

In BBS's string theory book, in the equation (2.143), it says that $$\text{tr} \omega ^N=\prod _{n=1}^{\infty } \left(\prod _{i=1}^{24} \text{tr} \omega ^{\alpha _{-n}^i \:\alpha _n^i}\right)=\prod ...
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0answers
25 views

Polchinski equation 11.2.7

In Polchinski's string theory volume 2, when discussing the GSO projection for the heterotic string he says: In the IIA and IIB superstrings the GSO projection acted separately on the left- and ...
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2answers
50 views

What equation do we use to measure the energy level of a string, to determine it's “particle correlation”

If string theory happened to be correct, and a point-particle is replaced with a string, there is a direct correlation between the vibrating frequency of the string and the particle it produces. I was ...
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72 views

Branes at the conifold

Consider $N$ $D3$-branes at the singularity of the conifold. This particular example can be viewed as a $AdS_{5} \times T^{1,1}$ in the near horizon limit, where the Einstein manifold has isometry ...
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1answer
111 views

Does Conformal Invariance of the Polyakov Action in Conformal Gauge imply Conformal Invariance of the Pre-gauge-fixed Polyakov Action?

In bosonic string theory the Polyakov action can be put in into conformal gauge. It is then possible to show that the resulting gauge fixed action is conformally invariant. Actually it's shown that ...
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17 views

Dirac Matrix property suitable to finding sets of intersecting branes

So, 11 dimensional supergravity has four oft-studied half-BPS states, the KK1 plane wave, the M2 brane, the M5 brane and the KK6 monopole. To figure out if we can find more solutions in the form of ...
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46 views

String theory book comparision : Polchinski and Blumenhagen,Lust & Theisen [closed]

I have studied Quantum Field Theory and General Relativity, and now wish to study string theory. I have gone through the book recommendation questions on this site (1, 2) which are very helpful. ...
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1answer
205 views

Reduction of Nambu Goto action to true degrees of freedom

First consider the particle $$S=m\int\sqrt{-\dot{X}^2}d\tau$$ if you choose the static gauge $\tau=X^0$ and replace it in the action you get $$=m\int\sqrt{1-\dot{X}^j\dot{X}^j}d\tau$$ So now, you ...
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1answer
120 views

Could M-Theory explain dark matter as well as dark energy?

Is it possible that M-Theory provides a solution to the mystery of dark matter and dark energy? The idea of dark matter and dark energy is that there is some inexplicable source affecting our ...
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2answers
158 views

How to find the rank of the matrix $\frac{\partial ^2\mathcal{L}}{\partial \dot{X^\mu} \partial \dot{X^\nu} }$ for the Nambu-Goto string Lagrangian?

In this case $$\mathcal{L}~=~-T\sqrt{-\dot{X^2}X'^2+(\dot{X}\cdot X')^2}.$$ I was reading some books and papers about the constraints in the Nambu-Goto action, and all of them say something like ...
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1answer
116 views

Polchinski Equation (7.2.4)

On page 209 of Polchinski's string theory book he writes down the expectation value of a product of vertex operators on the torus; equation $(7.2.4)$. The derivation is analogous to an earlier ...
2
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1answer
53 views

Standard derivation of Witt algebra

I have been studying Conformal field theory for the past one week from the books by Blumenhagen and Di Francesco etal. If I understand correctly, whenever one talks of 'local (infinitesimal) ...
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1answer
53 views

Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap?

Quantum chromodynamics, or QCD, is the theory describing the strong nuclear force. Carried by gluons, it binds quarks into particles like protons and neutrons. According to the theory, the tiny ...
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0answers
135 views

Chiral Scale and Conformal Invariance in 2D QFT

I am reading a paper by Hofman and Strominger. In the appendix A, I have reproduced the equations (A10). Now they made a statement that "The Jacobi identity can be used to show that $O_h$ and $O_p$ ...
3
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0answers
56 views

Branes wrapping curves in M-theory. What does it mean?

What does it mean that a M5-branes wraps a holomorphic curve in M-theory? In specific a lot of Vafa's paper involve various branes (not only M5) wrapping some cycles. What does this really mean ...
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2answers
102 views

Understanding the AdS/CFT Correspondence [duplicate]

I am beginning to learn about the AdS/CFT correspondence, but I can't find a comprehensive introduction that includes the relevant gravitational/string theory physics. What specific areas of general ...