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Vector $V^\mu$ vs the Lorentz contravariant components $V^a(x)$

This is just a choice of basis of vector fields in a smooth manifold really. Let $(M,g)$ be a $D$-dimensional smooth manifold with Lorentzian metric. Let $U\subset M$ be one open set and let $x:U\to \...
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Vector $V^\mu$ vs the Lorentz contravariant components $V^a(x)$

The $e^{a}_{\mu}$ objects are called vierbein field (or tetrads, or frame fields) and connect a general frame of coordinates (in which vectors are expressed as $V^{\mu}$) to a local frame of reference....
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4 votes

If mass in string theory is generated by string vibration, where does that leave the Higgs mechanism?

The massive states due to vibrations on the string have masses given as integer multiples of the string scale, which you should think of as a very large scale, near the Planck scale. (At least, nearer ...
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3 votes

Weyl Anomaly for Old Covariant Quantization in String Theory?

In lightcone quantization the mass of a level $N$ state is given by $m^2 \sim ( N - \frac{D-2}{24} )$. The $N=1$ transforms in a rep of $SO(D-2)$. This is because in lightcone quantization there are $...
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Why are we able to compare the open and closed string perspective in AdS/CFT?

String theories have two worldsheet co-ordinates and it can often be useful to interchange which ones we regard as space and time. I think the missing link you are looking for comes from exploiting ...
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1 vote

Kalb-Ramond current fall-offs at future null infinity

This will not be an answer, as I have some counter-questions regarding your post! However, hopefully it will lead to you answering my counter-questions (presumably in the comments) and me replying ...
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4 votes
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Does QFT Imply Strings the Same Way that String Theory Implies Branes?

When we take a good hard look at QFT, we don't see any particles (dimensionless points traveling on world lines). All we see are localized interactions. When we do our experiments to confirm these ...
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3 votes

In what way is String Theory "two-dimensional"?

A string worldsheet is 2D. One space dimension (how far you are along the string), one time dimension.
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4 votes
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Kaluza-Klein reducing the Chern-Simons term in 11D supergravity

$\newcommand{\d}{\mathrm{d}}\newcommand{\w}{\wedge}\newcommand{\R}{\mathbb{R}}$That integral vanishes because the differential form $\omega_i\w\omega_j\w\omega_k\in\Omega^6(S_4)$ vanishes (you cannot ...
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1 vote

Hamiltonian Open String

The orthogonality relations for sine and cosine functions should be proportional to the Kronecker $\delta$ symbol. Namely $$\int d\sigma \cos(m\sigma)\cos(n\sigma)\sim \delta_{mn}$$ $$\int d\sigma \...
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1 vote
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Worldsheet constraint Bosonic String

It is just a dummy variable change, from $p$ to $n:=m+p$. Since $m$ and $p$ run through all integers, $n$ also runs through all integers. $\newcommand{\ex}[1]{\mathrm{e}^{#1}}$ Stripping off the ...
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Asymmetry of the indices in a Weyl transformation for the Polyakov action

I think the asymmetry between the indices is a convention. We chose $\sigma^{\mu}=(\sigma, \tau)$ as the integration variables. This implies that the determinant of $h_{ab}$ will be the Jacobian. So ...
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3 votes

How (if) is the gauge group for gravity incorporated in the Calabi-Yau manifold of string theory?

The Yang-Mills type gauge groups of an effective theory in string theory do not arise solely from the compactification, but from "wrapping" D-branes (to which open strings can be attached) ...
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Covariant Quantisation and the Time Operator in String Theory

The difference between string theory and quantum field theory is that QFT is the theory of point excitation whereas string theory is the theory of 1d strings. When we talk about $[X^0 , H]=-i$ and ...
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