- #1

- 1,344

- 32

1. the stress-energy tensor is defined as the matrix

of conserved currents which arise from translational invariance,

$$\delta\sigma^{a} = \epsilon^{a},$$

where ##\sigma^{a}## are the worldsheet coordinates, and that

2. in flat spacetime, a translation is a special case of a conformal transformation.

This I understand. But then he goes on to say that

*we can derive conserved currents by promoting the constant parameter ##\epsilon## that appears in the symmetry to a function of the spacetime coordinates.*

I do not follow this.

**If the translational invariance of the worldsheet coordinates under ##\delta\sigma^{a} = \epsilon^{a}## give us the stress-energy tensor of the theory, why do we need to gauge the symmetry in order to derive the stress-tensor of the theory?**

**How do you then go ahead to show that the change in the action must then be of the form,**

$$\delta S = \int d^{2}\sigma J^{\alpha}\partial_{\alpha}\epsilon$$

for some function of the fields, ##J^{\alpha}##?

$$\delta S = \int d^{2}\sigma J^{\alpha}\partial_{\alpha}\epsilon$$

for some function of the fields, ##J^{\alpha}##?