Chern-Simons terms from thermal circles and anomalies

Abstract

Abstract:We compute the full contribution of flavor and (or) Lorentz anomalies to the thermodynamic partition function. Apart from the Wess-Zumino consistency condition the Euclidean generating function must satisfy an extra requirement which we refer to as 'consistency with the Euclidean vacuum'. The latter requirement fixes all Chern-Simons terms that arise in a particular Kaluza-Klein reduction of the theory. The solution to both conditions may be encoded in a 'thermal anomaly polynomial' which we compute. Our construction fixes all the thermodynamic response parameters of a hydrodynamic theory associated with anomalies.

Effective actions for anomalous hydrodynamics

“…The authors of [29] argued that this framework needs to be extended further before contribution from gravitational anomalies can be fully understood -the key point which they exploit is the fact that in equilibrium, characterized by a thermal partition function by considering the theory on a Euclidean time circle, one should be free to consider other cycles for thermal reduction, leading to further global constraints, which fix the contribution from the gravitational anomaly. These results have been recently extended in [30][31][32].…”

Supersymmetric Casimir energy and the anomaly polynomial

“…We hope to return to this question in future work. It should be noted that the equivariant integral seems similar to the "replacement rule" of [57][58][59][60]. It is tantalizing to explore this connection further.…”

Aspects of hot Galilean field theory

“…It turns out that the c 1 and c 2 terms can be described in a four-dimensional covariant way as outlined in [44], but to capture c 3 we need to lift to five dimensions. In fact, all three terms can be lifted to terms in five dimensions using the technology of [43,48] We begin with the four-dimensional version of c 1 and c 2 . From here until the end of this subsection, we will require the extensive use of differential forms.…”

“…To compute the currents, we use the machinery of [43,48] which we do not review here. Instead we refer the reader to appendix E of [43] which gives the basic idea.…”