pith. sign in

arxiv: 2606.23779 · v1 · pith:EL3KGMNRnew · submitted 2026-06-22 · ✦ hep-th · gr-qc· math-ph· math.MP· math.OA

Excitability of Gaussian states with VEVs

Jacqueline Caminiti , Federico Capeccia , Jonathan Sorce This is my paper

Pith reviewed 2026-06-26 07:09 UTC · model grok-4.3

classification ✦ hep-th gr-qcmath-phmath.MPmath.OA
keywords Gaussian statesvacuum expectation valuesexcitabilitytwo-point functionsanti-de Sitter spacetimeconformal field theoryKlein-Gordon vacuum
0
0 comments X

The pith

Gaussian states with nonzero vacuum expectation values can be excited from one another only if their connected two-point functions meet zero-mean criteria and the mean difference stays bounded by those functions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends prior criteria for exciting one Gaussian state from another in free field theories to the case where the states carry nonzero vacuum expectation values. It establishes that such excitation succeeds exactly when the connected two-point functions obey the same conditions as in the zero-mean setting and when the difference between the two means remains limited relative to those functions. This matters because many physical situations involve states with background values, and the result supplies a direct test for whether one such state can be reached from another by excitation. The work applies the criterion to anti-de Sitter spacetime and shows that a bulk mean shift is excitable from the Klein-Gordon vacuum precisely when the corresponding boundary shift is excitable from the dual conformal field theory vacuum.

Core claim

Excitability is possible exactly when the connected two-point functions satisfy criteria like those in the zero-mean case, and the difference of the VEVs is bounded relative to the two-point functions. As an application, in anti-de Sitter spacetime, a VEV shift can be excited from the Klein-Gordon vacuum if and only if its boundary extrapolation can be excited from the vacuum of the dual conformal field theory.

What carries the argument

The bound on the difference of vacuum expectation values relative to the connected two-point functions, which extends the zero-mean excitability conditions to states carrying nonzero means.

If this is right

  • Excitability checks reduce to verifying the two-point-function conditions plus verifying that the mean difference lies inside the allowed region.
  • In anti-de Sitter spacetime the bulk and boundary excitation problems become equivalent under the stated mapping of states.
  • The same pair of conditions applies to any generalized free field theory once the connected correlations are known.
  • Mean shifts introduce no independent obstructions beyond the size of the shift relative to the correlations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The criterion supplies a practical test that could be applied to other curved backgrounds once the relevant two-point functions are computed.
  • It suggests that nonzero means do not create fundamentally new barriers to state transitions beyond a simple size restriction.
  • Similar bounded-difference conditions might appear when extending excitability notions to interacting theories or to states that are only approximately Gaussian.

Load-bearing premise

That the states remain Gaussian after the VEV shift and that the connected two-point functions continue to obey the zero-mean excitability criteria without additional obstructions arising from the nonzero mean.

What would settle it

Finding a VEV difference in anti-de Sitter space that exceeds the bound set by the two-point functions yet still permits excitation from the Klein-Gordon vacuum to the shifted state would falsify the necessity of the bound.

read the original abstract

In arXiv:2604.19861, we gave general criteria for when one zero-mean Gaussian state can be excited out of another in a (generalized) free field theory. Here we extend this analysis to the case of nonzero mean, i.e., to Gaussian states with vacuum expectation values (VEVs). We prove that excitability is possible exactly when (i) the connected two-point functions satisfy criteria like those in arXiv:2604.19861, and (ii) the difference of the VEVs is bounded relative to the two-point functions. As an application, we give an explicit computation showing that in anti-de Sitter spacetime, a VEV shift can be excited from the Klein-Gordon vacuum if and only if its boundary extrapolation can be excited from the vacuum of the dual conformal field theory.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The paper extends the excitability criteria for zero-mean Gaussian states from arXiv:2604.19861 to Gaussian states with nonzero VEVs in generalized free field theories. It proves excitability is possible exactly when (i) the connected two-point functions satisfy the prior criteria and (ii) the VEV difference is bounded relative to the two-point functions. The AdS/CFT application shows a VEV shift is excitable from the Klein-Gordon vacuum iff its boundary extrapolation is excitable from the dual CFT vacuum.

Significance. If the result holds, the work completes the characterization of Gaussian-state excitability by adding an explicit boundedness condition derived directly from the definition for displaced Gaussians. The manuscript shows no further obstructions arise once the bound holds. The AdS/CFT application is obtained by specializing the general theorem to the bulk-to-boundary map and constitutes a concrete, falsifiable prediction in a holographic setting.

minor comments (1)
  1. [Abstract] The abstract could briefly note the precise definition of 'excitability' used, to aid readers unfamiliar with the prior work.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, accurate summary of the results, and recommendation to accept. No major comments were raised.

Circularity Check

0 steps flagged

No significant circularity; extension derives new boundedness condition independently

full rationale

The manuscript extends the zero-mean excitability criteria from the cited prior work by proving an additional explicit boundedness condition on VEV differences, which is derived directly from the definition of excitability applied to displaced Gaussian states. This new condition is shown to be necessary and sufficient alongside the connected two-point criteria, with no further obstructions. The AdS/CFT application is obtained by direct specialization of the general theorem to the bulk-to-boundary correspondence. The self-citation supports only the base case and is not load-bearing for the novel derivation or application; the argument remains internally consistent without reducing any central claim to a fit, self-definition, or unverified chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities. The result appears to rest on standard definitions of Gaussian states, connected correlators, and the prior excitability criteria.

pith-pipeline@v0.9.1-grok · 5674 in / 1125 out tokens · 27865 ms · 2026-06-26T07:09:42.295766+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

19 extracted references · 6 linked inside Pith

  1. [1]

    Caminiti, F

    J. Caminiti, F. Capeccia, and J. Sorce,Excitability in quantum field theory, arXiv:2604.19861

    Pith/arXiv arXiv

  2. [2]

    Gel’fand and M

    I. Gel’fand and M. Na˘ ımark,On the imbedding of normed rings into the ring of operators in Hilbert space,Mat. Sb., Nov. Ser.12(1943) 197–213

    1943

  3. [3]

    I. E. Segal,Irreducible representations of operator algebras,

  4. [4]

    R. T. Powers and E. Størmer,Free states of the canonical anticommutation relations, Commun. Math. Phys.16(1970) 1–33

    1970

  5. [5]

    Araki,On quasifree states of the canonical commutation relations: II.,

    H. Araki,On quasifree states of the canonical commutation relations: II.,

  6. [6]

    Van Daele,Quasi-equivalence of quasi-free states on the weyl algebra,Commun

    A. Van Daele,Quasi-equivalence of quasi-free states on the weyl algebra,Commun. Math. Phys.21(1971) 171–191

    1971

  7. [7]

    Araki and S

    H. Araki and S. Yamagami,On quasi-equivalence of quasifree states of the canonical commutation relations,Publications of the Research Institute for Mathematical Sciences18 (1982), no. 2 703–758

    1982

  8. [8]

    S. L. Woronowicz,On the purification of factor states,Commun. Math. Phys.28(1972) 221–235

    1972

  9. [9]

    Sorce,Continuum canonical purifications,arXiv:2512.17014

    J. Sorce,Continuum canonical purifications,arXiv:2512.17014

    arXiv

  10. [10]

    Ashtekar,ASYMPTOTIC QUANTIZATION: BASED ON 1984 NAPLES LECTURES

    A. Ashtekar,ASYMPTOTIC QUANTIZATION: BASED ON 1984 NAPLES LECTURES. 1987

    1984

  11. [11]

    Honegger and A

    R. Honegger and A. Rieckers,The general form of non-fock coherent boson states, Publications of The Research Institute for Mathematical Sciences26(1990) 397–417. – 21 –

    1990

  12. [12]

    Witten,Anti de Sitter space and holography,Adv

    E. Witten,Anti de Sitter space and holography,Adv. Theor. Math. Phys.2(1998) 253–291, [hep-th/9802150]

    Pith/arXiv arXiv 1998

  13. [13]

    S. S. Gubser, I. R. Klebanov, and A. M. Polyakov,Gauge theory correlators from noncritical string theory,Phys. Lett. B428(1998) 105–114, [hep-th/9802109]

    Pith/arXiv arXiv 1998

  14. [14]

    Balasubramanian, P

    V. Balasubramanian, P. Kraus, and A. E. Lawrence,Bulk versus boundary dynamics in anti-de Sitter space-time,Phys. Rev. D59(1999) 046003, [hep-th/9805171]

    Pith/arXiv arXiv 1999

  15. [15]

    I. R. Klebanov and E. Witten,AdS / CFT correspondence and symmetry breaking,Nucl. Phys. B556(1999) 89–114, [hep-th/9905104]

    Pith/arXiv arXiv 1999

  16. [16]

    C. J. Fewster and K. Rejzner,Algebraic Quantum Field Theory – an introduction, arXiv:1904.04051

    arXiv 1904

  17. [17]

    Breitenlohner and D

    P. Breitenlohner and D. Z. Freedman,Stability in Gauged Extended Supergravity,Annals Phys.144(1982) 249

    1982

  18. [18]

    Duetsch and K.-H

    M. Duetsch and K.-H. Rehren,Generalized free fields and the AdS - CFT correspondence, Annales Henri Poincare4(2003) 613–635, [math-ph/0209035]

    Pith/arXiv arXiv 2003

  19. [19]

    Verch,Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved space-time,Commun

    R. Verch,Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved space-time,Commun. Math. Phys.160(1994) 507–536. – 22 –

    1994