Tagged Questions

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How can one calculate the central term of the conformal field theory algebra (and show it's really the virasoro algebra)?

So I'm following Szabo's book "An Introduction to String Theory and D-brane Dynamics (2nd ed, 2011); still on the canonical treatment in chapter 3. After doing a mode expansion, we get (up to a ...
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Conformal compatification of Minkowski and AdS

How do I show that the compactification of Minkowski is given by the quadric $$uv-\eta_{ij}x^{i}x^{j}=0$$ with an overall scale equivalence in the coordinates.I get that for $v \neq 0$, the surface ...
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Why is string theory a two dimensional quantum (conformal) field theory on its worldsheet?

In string theory, we quantize the two dimensional field theory on the string's worldsheet. I have a question about this kind of quantization of string theory: did we have similar theory for point-like ...
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What uniquely defines a CFT?

So, I am quite new to CFT (and a as descriptive answer as possible would be appreciated). I want to know what uniquely defines a CFT in 2D and otherwise. Firstly in 2D, What defines a CFT? So I ...
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Is integrability necessary for the Amplituhedron?

It is well known that there exist mappings between operators in N = 4 Super Yangâ€“Mills and spin chain states making the theory Bethe Ansatz integrable. Is integrability a necessity for the ...
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Expectation value of the stress-energy tensor in 2-D CFT

Due to a previous question, I am confused with the expectation value of the stress-energy tensor in a 2-D conformal field theory. Let's take the example of string theory, to sketch the problem. ...
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I have a question about the expressions for free field Green's functions in conformal field theory. It comes from three origins 1) In Polchinski's string theory volume I p36, it is given $$... 1answer 177 views The basic equation of bosonization [..quoting from Page 11 of Polchinski Vol2..] Given 1+1 conformal bosonic fields H(z) one has their OPE as, H(z)H(0) \sim -ln(z) Then from here how do the following identities come? ... 1answer 278 views About the general expression of trace anomaly and CFT partition functions I have put up a question here, http://mathoverflow.net/questions/139685/proof-of-the-general-expression-for-anomaly-in-a-cft-and-its-partition-function Here I am putting up a slightly different ... 1answer 73 views A question related to “old covariant quantization” of string theory I have a question about "old covariant quantization" in Polchinski's string theory p. 123. It is said The only nontrivial condition at this level is (L_0^{\rm m} + A) | \psi \rangle =0 , ... 1answer 92 views Virasoro operator in “old covariant quantization” I met some problem about the Virasoro operator in "old covariant quantization" in Polchinski's string theory vol I p 123. It is given$$L_0^{\rm m}=\alpha' p^2 + \alpha_{-1} \cdot \alpha_1 + \cdots ...
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(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 ...
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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 ...
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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) ...
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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 ...
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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 ...
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Symmetries in Wilsonian RG (2)

This question is related to the paper http://arxiv.org/abs/1204.5221 and is a continuation of the previous question Symmetries in Wilsonian RG In the liked paper why do the equalities in equation ...