Entropic order parameters for the phases of QFT

Casini, Horacio; Huerta, Marina; Magán, Javier M.; Pontello, Diego

doi:10.1007/jhep04(2021)277

Cited by 37 publications

(142 citation statements)

References 75 publications

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“…Statements similar to ours have been discussed in the framework of algebraic QFT in[11]. In some cases, the underlying assumptions made there are significantly stronger than ours.…”

supporting

confidence: 75%

“…By Lemma 1, we see that the topological Gukov-Witten operators in pure G gauge theory correspond precisely to conjugacy classes [g] which act trivially on the adjoint representation. 11 This is in turn equivalent to the statement that gg 0 g −1 = g 0 for all g 0 in the identity component G 0 , i.e., the connected component of G containing the identity. (Note that if this holds for one representative g ∈ [g], it holds for all such representatives.)…”

Section: Jhep09(2021)203mentioning

confidence: 98%

See 1 more Smart Citation

Non-invertible global symmetries and completeness of the spectrum

Heidenreich

McNamara

Montero

et al. 2021

J. High Energ. Phys.

136

112

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It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings.

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“…Statements similar to ours have been discussed in the framework of algebraic QFT in[11]. In some cases, the underlying assumptions made there are significantly stronger than ours.…”

supporting

confidence: 75%

Section: Jhep09(2021)203mentioning

confidence: 98%

Non-invertible global symmetries and completeness of the spectrum

Heidenreich

McNamara

Montero

et al. 2021

J. High Energ. Phys.

136

112

View full text Add to dashboard Cite

show abstract

“…Results of a similar flavor have also been given by [39]. Interesting physical applications of the above "certainty relation" (16) involving Wilson-'t Hooft operators in four-dimensional quantum Yang-Mills theory have recently been pointed out by [12,30]. In such a situation, the algebras are expected to be of type III [9].…”

Section: Conditional Expectations Index and Relative Entropymentioning

confidence: 78%

Variational approach to relative entropies with an application to QFT

Hollands

2021

Lett Math Phys

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We define a new divergence of von Neumann algebras using a variational expression similar in nature to Kosaki’s formula for Umegaki’s relative entropy. Our divergence satisfies several of the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit. As an illustration, we use the formula in quantum field theory to compute our divergence between the vacuum in a bipartite system and an “orbifolded”—in the sense of a conditional expectation—system in terms of the Jones index. We take the opportunity to point out an entropic certainty relation associated with an inclusion of von Neumann factors related to the relative entropy. This certainty relation has an equivalent formulation in terms of error correcting codes.

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“…This uses on one hand known tools extracted from the DHR approach to global symmetries in QFT [10][11][12][13], and further developments in that direction by Longo and Rehren [14,15]. On the other hand, we resort to the entropic order and disorder parameters, together with the certainty relation satisfied by them [1][2][3].…”

Section: Jhep12(2021)100mentioning

confidence: 99%

“…The aim of this article is simple to state. By using the recently introduced entropic order parameters for global symmetries [1][2][3][4], we seek to prove a recent conjecture described in ref. [5] by Harlow and Ooguri, concerning the density of charged states in QFT.…”

Section: Introduction To the Conjecture And Its Different Facesmentioning

confidence: 99%

Proof of the universal density of charged states in QFT

Magán

2021

J. High Energ. Phys.

Self Cite

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We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups. An equivalent statement, based on the entropic order parameter associated with charged operators in the thermofield double state, was proven in a previous article by Casini, Huerta, Pontello, and the present author. Here we describe how the statement about the entropic order parameter arises, and how it gets transformed into the universal density of states. The use of the certainty principle, relating the entropic order and disorder parameters, is crucial for the proof. We remark that although the immediate application of this result concerns charged states, the origin and physics of such density can be understood by looking at the vacuum sector only. We also describe how these arguments lie at the origin of the so-called entropy equipartition in these type of systems, and how they generalize to QFT’s on non-compact manifolds.

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Entropic order parameters for the phases of QFT

Cited by 37 publications

References 75 publications

Non-invertible global symmetries and completeness of the spectrum

Non-invertible global symmetries and completeness of the spectrum

Variational approach to relative entropies with an application to QFT

Proof of the universal density of charged states in QFT

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