Momentum-space entanglement in scalar field theory on fuzzy spheres

Abstract

Quantum field theory defined on a noncommutative space is a useful toy model of quantum gravity and is known to have several intriguing properties, such as nonlocality and UV/IR mixing. They suggest novel types of correlation among the degrees of freedom of different energy scales. In this paper, we investigate such correlations by the use of entanglement entropy in the momentum space. We explicitly evaluate the entanglement entropy of scalar field theory on a fuzzy sphere and find that it exhibits different behaviors from that on the usual continuous sphere. We argue that these differences would originate in different characteristics; non-planar contributions and matrix regularization. It is also found that the mutual information between the low and the high momentum modes shows different scaling behaviors when the effect of a cutoff becomes important.

1+35 pages, 35 figures; Ver.2, minor changes; Ver. 3, added some explanation in Section 4, some paragraphs in Section 5, and some references. Version to appear in JHEP

References in corpus (3)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models

Cited by in corpus (4)

• Momentum Space Entanglement from the Wilsonian Effective Action
• Momentum space entanglement of interacting fermions
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality