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Pseudo Entropy in $U(1)$ gauge theory

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arxiv 2205.08179 v1 pith:IZAKHY3E submitted 2022-05-17 hep-th

Jyotirmoy Mukherjee This is my paper · ORCID
classification hep-th
keywords entropypseudoboundarydifferencefieldgroundnearstate
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We study the properties of pseudo entropy, a new generalization of entanglement entropy, in free Maxwell field theory in $d = 4$ dimension. We prepare excited states by the different components of the field strengths located at different Euclidean times acting on the vacuum. We compute the difference between the pseudo R\'{e}nyi entropy and the R\'{e}nyi entropy of the ground state and observe that the difference changes significantly near the boundary of the subsystems and vanishes far away from the boundary. Near the boundary of the subsystems, the difference between pseudo R\'{e}nyi entropy and R\'{e}nyi entropy of the ground state depends on the ratio of the two Euclidean times where the operators are kept. To begin with, we develop the method to evaluate pseudo entropy of conformal scalar field in $d=4$ dimension. We prepare two states by two operators with fixed conformal weight acting on the vacuum and observe that the difference between pseudo R\'{e}nyi entropy and ground state R\'{e}nyi entropy changes only near the boundary of the subsystems. We also show that a suitable analytical continuation of pseudo R\'{e}nyi entropy leads to the evaluation of real-time evolution of R\'{e}nyi entropy during quenches.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Imaginary pseudo entropy encodes temporal orientation

    quant-ph 2026-06 unverdicted novelty 7.0 of 10

    The calibrated pseudo-Rényi phase and replica visibility exactly equal the Helstrom trace distance between forward and backward ancilla states, giving a bounded operational meaning to imaginary pseudo entropy.

  2. Linear Growth of Holographic Time-like Entanglement Entropy and Kasner exponents

    hep-th 2026-06 unverdicted novelty 6.5 of 10

    Late-time TEE growth in asymptotically AdS black holes with space-like singularities is governed by a critical extremal surface inside the horizon, with real/imaginary growth rates bounded by Schwarzschild-AdS under e...

  3. Entanglement first law for timelike entanglement entropy and linearized Einstein's equation

    hep-th 2025-11 conditional novelty 6.0 of 10

    For timelike boundary regions, the entanglement first law ΔS = Δ⟨H⟩ is equivalent, by the paper's proof, to the linearized Einstein equations around AdS.

  4. Thermal Pseudo-Entropy

    hep-th 2024-11 conditional novelty 5.0 of 10

    Thermal pseudo-entropy is the analytic continuation S(β+it) of thermal entropy, equals the pseudo-entropy of a Thermofield Double transition matrix, and its averaged real part tracks the spectral form factor.

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