Inverted c-functions in thermal states

Journal Article · 26 January 2022 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep01(2022)161 · OSTI ID:1976437

Cartwright, Casey  ^[1]; Kaminski, Matthias  ^[2]

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1. University of Alabama, Tuscaloosa, AL (United States); Univ. of Alabama, Tuscaloosa, AL (United States)
2. University of Alabama, Tuscaloosa, AL (United States)

We first compute the effect of a chiral anomaly, charge, and a magnetic field on the entanglement entropy in $$\mathcal{N}$$ = 4 Super-Yang-Mills theory at strong coupling via holography. Depending on the width of the entanglement strip the entanglement entropy probes energy scales from the ultraviolet to the infrared energy regime of this quantum field theory (QFT) prepared in a given state. From the entanglement entropy, we compute holographic c-functions and demonstrate an inverted c-theorem for them. That is, these c-functions in generic thermal states monotonically increase towards the infrared (IR) energy regime. This is in contrast to the c-functions in vacuum states which decrease along the renormalization group flow towards the IR regime of a renormalizable QFT. Furthermore, in thermal states and in the IR limit, the c-functions behave thermally, growing proportionally to the value of the thermal entropy. The chiral anomaly affects the c-functions more in the IR regime, and its effect is peaked at an intermediate value of the magnetic field at a fixed chemical potential and temperature.

• Research Organization: University of Alabama, Tuscaloosa, AL (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0012447
• OSTI ID: 1976437
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2022; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English