Inverted c-functions in thermal states

2021/07/31 by Casey Cartwright, Matthias Kaminski
Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Condensed matter physics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Infrared #Mathematical physics #Monotonic function #Physics #Quantum #Quantum electrodynamics #Quantum entanglement #Quantum field theory #Quantum many-body systems #Quantum mechanics #Renormalization #Renormalization group #Thermal #Thermodynamics #Vacuum energy #hep-th

paper · pdf · doi:10.1007/jhep01(2022)161

published in Journal of High Energy Physics 2022(1) (Springer Nature) · 55 pgs, 26 figures. Comments welcome! (V2: New figure, minor update to discussion throughout, typos corrected)

openalex publication_date 2022/01/01 · arxiv created 2022/01/20 · arxiv updated 2022/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A bstract We first compute the effect of a chiral anomaly, charge, and a magnetic field on the entanglement entropy in N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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.

Citations

• Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
• Is there a c-theorem in four dimensions?
• Ac-theorem for entanglement entropy
• Detecting Topological Order in a Ground State Wave Function
• Entanglement as a probe of confinement
• Analogs of the c-theorem for four-dimensional renormalisable field theories
• Chaos and Quantum Thermalization
• Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence
• Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy
• Entropy and Area
• Holographic c-theorems in arbitrary dimensions
• Quantum statistical mechanics in a closed system
• Magnetic brane solutions in AdS
• The Holographic Bound in Anti-de Sitter Space
• Holographic entanglement entropy and renormalization group flow
• Entanglement entropy: Holography and renormalization group
• Replica Wormholes and the Entropy of Hawking Radiation
• The entropy of Hawking radiation