Errata for Introduction to Conformal Field Theory

This is a collection of errata for the lecture notes Introduction to Conformal Field Theory by R. Blumenhagen and E. Plauschinn. The authors would be grateful if further misprints and errors could be communicated to them.

Chapter 2

Page 8

In the second and third line of the formula between equations (2.5) and (2.6) the indices are not ordered properly. The correct expressions read

Thanks to A. Basu

Page 9

In the last equation on page 9, the exponent of the scale factor should be -2 instead of +2. The correct expression reads

Thanks to Y. Zhang

Page 11

Above equation (2.9), the indices should be in the range

Below equation (2.9), the metric for the case R^d-1,1 should be of the form

Thanks to Y. Zhang

Page 43

In the column "Field" of the table shown in equation (2.74), the order of the fields appearing in the normal-ordered products should be changed. In particular, it should read

Thanks to B. Zheng

Page 47

The definition of the energy-momentum tensor in equation (2.84) should contain the variation of the Lagrangian density L instead of the variation of the action S.

Thanks to N. Todoroki

Page 47

In equation (2.84) and in the expressions for the components of the energy-momentum tensor below, an overall minus sign should be included. This ensures consistency between the definition (2.80) and the formula above equation (2.85). In particular, the latter should read

Thanks to D. Thung

Page 47

In the second line from the bottom, it should read "Recalling the holomorphic part of the Laurent expansion (2.25) for j(z), ..."

Thanks to T. Feng

Page 49

In the last equation, the Laurent expansion for the anti-chiral current should involve the anti-holomorphic variable, that is

Thanks to T. Feng

Page 61

In equation (2.110), the conformal dimension in the second sum should be changed:

Thanks to T. Feng

Page 64

At the end of page 64, it should read "As mentioned above, because the fermions do in general not anti-commute, [...]".

Thanks to D. Thung

Page 66

In the middle of page 66 it should read

Thanks to D. Katsinis

Page 66

In the second half of page 66, the non-vanishing structure constants should be the following

However, since the constants p_ijk for i,j=1/2 are vanishing, the algebra of Laurent modes is unchanged.

Thanks to D. Katsinis

Page 68

At the end of page 68, the conformal dimension of the field c should read

Thanks to D. Katsinis

Page 74

In the first bullet point at the beginning of the page, it should read h>0.

Thanks to D. Thung

Page 74

In the third bullet point at the beginning of the page, it should read "A more careful analysis reveals that in fact negative-norm states are absent only on certain intersection points [...]"." .

Thanks to V. Larotonda

Page 75

In the conformal grid of the tri-critical Ising model, the second column is incorrect. The table should read:

Page 77

In the beginning of page 77, it should read "[...] we will now formalise the concept of descendants to some extent".

Thanks to D. Thung

Page 82

In the formula for the descendent fields, bars for the anti-holomorphic indices are missing. The formula should read

Thanks to D. Katsinis

Chapter 3

Page 89

In the last equation on that page, there is a wrong index on one of the Laurent modes. The correct expression reads

Thanks to T. Feng

Page 93

In the second formula of point 2, the last commutator has hats instead of tildes. It should read

Thanks to D. Katsinis

Page 95

In figure 3.1 the label q should be replaced by q/2. Corresponding replacements should be made on page 96.

Thanks to R. Álvarez-García

Page 105

In the decomposition of the Ising model, there should be a direct product in the last parenthesis of the last line. The correct expression reads

Thanks to P. Athanasopoulos

Page 101

Between equations (3.22) and (3.23), the reference to the OPE should be equation (3.17).

Thanks to R. Álvarez-García

Chapter 4

Page 121

In the computation at the beginning of page 121, there is a factor i missing, which however does not change the final result. The part which has to be changed is

Thanks to D. Thung

Page 128

The sentence below equation (4.31) should read "[...] since here we are considering characters and not modular invariant partition functions."

Thanks to N. Todoroki

Page 133

The first line in the first equation on that page should read

Thanks to T. Feng

Page 146

In the last line of that page, the reference should be to Section 4.2.3.

Thanks to P. Athanasopoulos

Page 158

In the equation in the middle of that page, there is an index i missing. The correct expression reads

Thanks to P. Athanasopoulos

Page 160

The definition of the delta-Funktion at the end of the page is missing a factor of 1/L.

Thanks to R. Álvarez-García

Page 163

Below equation (4.81) it should read

Thanks to N. Todoroki

Chapter 5

Page 171

In equation (5.3), at the end of the second line the "]" should be removed. The correct expression reads

Thanks to P. Athanasopoulos

Page 171

In the fourth line from the bottom it should read "normal ordered product."

Thanks to T. Feng

Page 174

In the boxed equation on page 174, the conformal weight h can be replaced by Δ. That means

Furthermore, the (anti-)commutators involving G_r should read

Thanks to D. Thung and N. Todoroki

Page 179

In equation (5.17), the following additional constraint should be imposed

Page 180

Above equation (5.22), it should be refered to the partition function in equation (5.20).

Thanks to P. Athanasopoulos

Page 186

In the last equation on that page, there is a comma missing in the anti-commutator in the second line. The correct expression reads

Thanks to P. Athanasopoulos

Page 189

In the framed formula, the summation should be changed from 1 to k

Thanks to M. Maio

Page 190

In equation (5.41) the delta-functions should be defined modulo 2(2+k) and 4, respectively. An easy way to see that is to recall from page 144 the fusion coefficients for u(1)k. The correct formula reads