All Questions
Tagged with quantum-anomalies string-theory
58
questions
0
votes
0
answers
38
views
How many dimensions are in string theory? [duplicate]
How many dimensions are in string theroy? I heard that there are 11 but to my understanding, there is an infinite, also can strings be on a 2D plane?
3
votes
1
answer
123
views
How is the dimensionful renornalization scale $\mu$ related to break of scale invariance in String Theory?
In the $7.1.1$ of David Tong's String Theory notes it is said the following about regularization of Polyakov action in a curved target manifold:
$$\tag{7.3} S= \frac{1}{4\pi \alpha'} \int d^2\sigma \ ...
1
vote
0
answers
60
views
Unitarity of Effective String Theory away from critical dimesions ($D=26$) , in the static gauge
Starting from compete UV description of QCD (in the confined phase), if we integrate out the quarks and Glueballs, in principle, we will get an effective theory of strings (QCD flux tube and not ...
4
votes
0
answers
131
views
Normalization of zero point energy in string theory
Following Joe Polchinski’s Little Book of String, page 12, he use the sum $$1+2+3+...=-1/12$$ to find the zero point energy of the bosonic string (and later used the result to argue that we must have ...
2
votes
1
answer
172
views
Light-cone quantization of open string as derived in Polchinski
Polchinski uses the following gauge conditions, but I don't follow this procedure of gauge fixing and quantization:
\begin{align}
X^+ = \tau, \tag{1.3.8a} \\
\partial_\sigma \gamma_{\sigma \sigma} = 0,...
0
votes
0
answers
32
views
Why M-theory has eleven dimensions? [duplicate]
Why M-theory has exactly 10+1 dimensions?
Some combinatorics with tensor indices will do.
2
votes
1
answer
150
views
Weyl Anomaly for Old Covariant Quantization in String Theory?
In the context of quantization in string theory, the modern approach is the path integral/modern covariant quantization approach. As known from QFT, we fix our gauge and represent the arising Fadeev-...
1
vote
1
answer
143
views
How did the two copies of the Witt algebra become two copies of the Virasoro algebra in the CFT?
The Virasoro algebra
\begin{equation}
[L_m,L_n]=(m-n) L_{m+n} +\frac{c}{12} (m^3-m) \delta_{m+n,0}
\end{equation}
of the stress energy tensor $T$ was said to follow from the witt algebra of the local ...
2
votes
0
answers
65
views
How does one arrive at the relation of commutator $\left[M^{-i}, M^{-j}\right]$ of Lorentz generators $M^i$ in terms of the string modes $\alpha_n^i$?
I am reading the book "String theory demystified" by David McMahon.
On page 149, the author discusses the "critical dimension" for superstrings.
the number of spacetime dimensions ...
2
votes
0
answers
129
views
How do I understand this conformal transformation?
I am learning conformal transformation, and this is by far the most confusing transformation for me.
For the 2D bc system
$$S=\frac{1}{2\pi}\int d^2 z b\overline{\partial}c,$$
we have the ghost ...
6
votes
1
answer
454
views
Polchinski's first derivation of the Weyl anomaly
So, i've been reading volume 1 of Polchinski's String Theory text book and have a doubt.
His first derivation of the Weyl anomaly goes as follows:
From dimensional analysis, we know that:
$$\begin{...
1
vote
0
answers
49
views
Existence of Weyl invariant regulator for bosonic string theory
In sec $(3.4)$ Polchinksi says
It is easy to preserve the diff- and Poincare invariances in the quantum theory. For example, one may define the gauge fixed path integral using a Pauli-Villars ...
3
votes
0
answers
112
views
Why are there only two 496-dim. gauge groups $E_8\times E_8$ and $SO(32)$ allowed in string theory? Why not $E_8\times U(1)^{248}$ or $U(1)^{496}$?
While constructing anomaly-free string theories with $\mathcal N=1$ supersymmetry (16 supercharges constituting a Majorana-Weyl spinor), we learn that the gauge group must be 496-dimensional in order ...
1
vote
1
answer
218
views
Is Weyl transformation part of diffeomorphism? Does a gravitational anomaly capture also the anomaly due to Weyl transformation? [duplicate]
Weyl transformation is a local rescaling of the metric tensor
$$
g_{ab}\rightarrow e^{-2\omega(x)}g_{ab}
$$
Diffeomorphism maps to a theory under arbitrary differentiable coordinate transformations
(...
4
votes
1
answer
189
views
Critical dimension of ${\cal N}=2$ strings
In "A tour through ${\cal N}=2$ strings" by Neil Marcus (https://arxiv.org/abs/hep-th/9211059) the following problem - among others - is noted:
The critical dimension of the ${\cal N}=2$ ...