Question

At finite temperature, anomaly is generally known to be contaminated, and thus the 't Hooft anomaly matching does not work after thermal compactification. Meanwhile, I have read paper saying that anomaly from higher-form symmetry can remains robust even at finite temperature, e.g.,

Circle compactification and ’t Hooft anomaly , by Yuya Tanizaki, Tatsuhiro Misumi, Norisuke Sakaic;
Theta, Time Reversal, and Temperature, by Davide Gaiotto, Anton Kapustin, Zohar Komargodski, and Nathan Seiberg.
However, I do not understand their derivations, can any one help to comment/explain on this?

Answer 1

Anomalies related to 't Hooft matching are typically considered unreliable at finite temperatures, but studies suggest that those from higher-form symmetries could be stable even after thermal compactification. This idea connects to broader physics concepts, including spontaneous symmetry breaking and the early universe's conditions, providing crucial knowledge for interpreting particle physics and cosmological data.

Step-by-step explanation:

The study of 't Hooft anomaly matching at finite temperatures involves exploring how certain symmetries and anomalies in quantum field theory behave under thermal conditions. In general, anomalies are thought to be unreliable at finite temperatures due to thermal effects, which can disrupt the connections assumed in anomaly matching. However, as mentioned in the works by Tanizaki, Misumi, Sakaic, Gaiotto, Kapustin, Komargodski, and Seiberg, anomalies arising from higher-form symmetries may remain stable even after thermal compactification, such as the circle compactification. This robustness at finite temperature signifies an exception to the general expectation that thermal effects would contaminate anomalies.

One of the core aspects to understand here is the idea of spontaneous symmetry breaking, an analogy to phase transitions in universal evolution described by Guth's inflationary scenario, which, though it took place at an energy scale beyond current experimental capabilities, provides insights into the conditions of the early universe. Moreover, these concepts are closely linked to our understanding of other phenomena such as high-temperature superconductors, which have transition temperatures (‘Te s’) well above the range we used to consider as achievable for superconducting materials.

Understanding how these anomalies persist at finite temperatures is critical for the theoretical framework that explains particle physics and cosmological observations, like the smoothness of the Cosmic Microwave Background Radiation (CMBR) and the history of the universe since the Big Bang.