I have been reading the Quantum Hall Effect from Prof. David Tong's notes. In the section on Chern-Simons theory, he describes the connection between the Thermal Partition Function and the Quantum partition function in section (5.1.2). He comments that the presence of $\epsilon_{\mu \nu \rho}$ symbol in (5.6) means that the action in Euclidean space picks up an extra i factor (in the last paragraph before section 5.1.3). I can't make sense of this statement. Why is there an extra factor of i because of epsilon symbol?

https://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf

I have been reading the Quantum Hall Effect from Prof. David Tong's notes. In the section on Chern-Simons theory, he describes the connection between the Thermal Partition Function and the Quantum partition function in section (5.1.2). He comments that the presence of $\epsilon_{\mu \nu \rho}$ symbol in (5.6) means that the action in Euclidean space picks up an extra i factor (in the last paragraph before section 5.1.3). I can't make sense of this statement. Why is there an extra factor of i because of epsilon symbol?

http://www.damtp.cam.ac.uk/user/tong/qhe.html