3
votes
0answers
39 views

Structure of Hilbert Space in Bosonic String Theory

My question is about the canonical quantization of free bosonic string theory as described by Green, Schwarz & Witten. There they use spurious states to calculate a value for the ambiguity ...
6
votes
1answer
81 views

Quantized coefficients of Chern-Simons action and F $\wedge$ F $\wedge \dots$

We know that for U(1) gauge field Chern-Simons action in 2+1 Dim(ension), we have an action $$ S=\alpha \int A \wedge dA $$ with $\alpha=k/(4\pi)$ for a proper level quantization. Here $k$ is the ...
5
votes
1answer
197 views

String theory in the context of quantization prescriptions

My new question here: has string theory been analyzed somewhere in the context of various quantization prescriptions formulated in a mathematically sound way? I mean something like geometric ...
0
votes
1answer
216 views

Does string/M-theory address higher-dimensional membrane vibration modes?

A loop is a 1-sphere that can vibrate in increasingly complex ways as it is embedded in higher dimensional spaces. Does string theory assume that 1-spheres are the only possible vibrating ...
6
votes
1answer
170 views

Critical dimension in quantization of p-branes

So I have what might be a fairly basic question, but my understanding that in the quantization of the the string, or the 1-brane, there are conditions on the number of spacetime dimensions to ensure ...
12
votes
2answers
700 views

Why one-dimensional strings, but not higher-dimensional shells/membranes?

One way that I've seen to sort-of motivate string theory is to 'generalize' the relativistic point particle action, resulting in the Nambu-Goto action. However, once you see how to make this ...
5
votes
2answers
157 views

Quantization of strings on a curved backgrond

usually when people want to quantize the string on flat background, they will try to find the the OPE of embeddings (by solving a green function in a 2D space) and use them to find the energy-momentum ...
3
votes
1answer
288 views

Quantization of Nambu–Goto action in multiples of Planck's constant?

Isn't it possible? Quantization of Nambu–Goto action $$\mathcal{S} ~=~ -\frac{1}{2\pi\alpha'} \int \mathrm{d}^2 \Sigma \sqrt{{\dot{X}} ^2 - {X'}^2}~=~nh\qquad n \in\mathbb{Z}.$$
8
votes
0answers
71 views

Pohlmeyer reduction of string theory for flat and AdS spaces

The definition of Pohlmeyer invariants in flat-space (as per eq-2.16 in Urs Schreiber's DDF and Pohlmeyer invariants of (super)string) is the following: $ Z^{\mu_1...\mu_N} (\mathcal{P}) = ...
3
votes
0answers
89 views

Pohlmeyer reduction of string theory for flat- and AdS- spaces

The definition of Pohlmeyer invariants in flat-space (as per eq-2.16 in Urs Schreiber's DDF and Pohlmeyer invariants of (super)string) is the following: $ Z^{\mu_1...\mu_N} (\mathcal{P}) = ...
10
votes
2answers
374 views

Virasoro constraints in quantization of the Polyakov action

The generators of the Virasoro algebra (actually two copies thereof) appear as constraints in the classical theory of the Polyakov action (after gauge fixing). However, when quantizing only "half" of ...
22
votes
1answer
1k views

How does classical GR concept of space-time emerge from string theory?

First, I'll state some background that lead me to the question. I was thinking about quantization of space-time on and off for a long time but I never really looked into it any deeper (mainly because ...