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Complexity, scaling, and a phase transition
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abstract
We investigate the holographic complexity of CFTs compactified on a circle with a Wilson line, dual to magnetized solitons in AdS$_4$ and AdS$_5$. These theories have a confinement-deconfinement phase transition as a function of the Wilson line, and the complexity of formation acts as an order parameter for this transition. Through explicit calculation, we show that proposed complexity functionals based on volume and action obey a scaling relation with radius of the circle and further prove that a broad family of potential complexity functionals obeys this scaling behavior. As a result, we conjecture that the scaling law applies to the complexity of conformal field theories on a circle in more general circumstances.
Forward citations
Cited by 3 Pith papers
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Krylov Complexity, Confinement and Universality
Holographic calculations show the proper-momentum proxy for Krylov complexity oscillates in every confining geometry with a smooth infrared cap, with frequency set by the confinement scale.
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Holographic Subregion Complexity and Fidelity Susceptibility in Noncommutative Yang--Mills Theory
In the noncommutative Yang–Mills dual, holographic subregion complexity acquires a lower bound and a minimum-length scale, and strong subadditivity fails exactly at that scale.
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CFT Complexity and Penalty Factors
A submersion-based method turns weighted generator costs into state-complexity metrics for CFTs, giving analytic formulas in simple limits and constraints on which weight choices are viable.
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