Abstract
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.
Highlights
In agreement with these field theory results, such a c-function was later defined from entanglement entropy via holography [3] and shown to be decreasing along the renormalization group (RG) flow when evaluated in the vacuum state, which corresponds to a domain-wall Anti-de Sitter (AdS) geometry [4] in the gravity dual theory [5,6,7,8,9]
Beginning with a review of entanglement entropy and c-functions in section 2, we introduce the holographic model in section 3, namely Einstein-Maxwell-Chern-Simons theory evaluated on charged magnetic black brane solutions, which are dual to charged anisotropic states subject to a strong external magnetic field in N = 4 Super-Yang-Mills theory (SYM)
The inset shows the difference, ∆s, between the thermal entropy with (γ = γSUSY) and without (γ = 0) the chiral anomaly taken into account, i.e. it visualizes the contribution of the chiral anomaly to the thermal entropy
Summary
Setting the stage for our investigative play, we first review selected aspects of the entanglement entropy from a field theory and from a holographic perspective. We remind ourselves how the c-function can be defined through the entanglement entropy. For a detailed review see [22]
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