Cluster capacity functionals and isomorphism theorems for Gaussian free fields

We investigate level sets of the Gaussian free field on continuous transient metric graphs $$\widetilde{{\mathcal {G}}}$$ G ~ and study the capacity of its level set clusters. We prove, without any further assumption on the base graph $${\mathcal {G}}$$ G , that the capacity of sign clusters on $$\widetilde{{\mathcal {G}}}$$ G ~ is finite almost surely. This leads to a new and effective criterion to determine whether the sign clusters of the free field on $$\widetilde{{\mathcal {G}}}$$ G ~ are bounded or not. It also elucidates why the critical parameter for percolation of level sets on $$\widetilde{{\mathcal {G}}}$$ G ~ vanishes in most instances in the massless case and establishes the continuity of this phase transition in a wide range of cases, including all vertex-transitive graphs. When the sign clusters on $$\widetilde{{\mathcal {G}}}$$ G ~ do not percolate, we further determine by means of isomorphism theory the exact law of the capacity of compact clusters at any height. Specifically, we derive this law from an extension of Sznitman’s refinement of Lupu’s recent isomorphism theorem relating the free field and random interlacements, proved along the way, and which holds under the sole assumption that sign clusters on $$\widetilde{{\mathcal {G}}}$$ G ~ are bounded. Finally, we show that the law of the cluster capacity functionals obtained in this way actually characterizes the isomorphism theorem, i.e. the two are equivalent.

Charging up the functional bootstrap

We revisit the problem of bootstrapping CFT correlators of charged fields. After discussing in detail how bounds for uncharged fields can be recycled to the charged case, we introduce two sets of analytic functional bases for correlators on the line. The first, which we call “simple”, is essentially a direct sum of analytic functionals for the uncharged case. We use it to establish very general bounds on the OPE density appearing in charged correlators. The second basis is dual to generalized free fields and we explain how it is related to a charged version of the Polyakov bootstrap. We apply these functionals to map out the space of correlators and obtain new improved bounds on the 3d Ising twist defect.

The reduced Dijkgraaf–Witten invariant of double twist knots in the Bloch group of 𝔽p

In 2004, Neumann showed that the complex hyperbolic volume of a hyperbolic 3-manifold [Formula: see text] can be obtained as the image of the Dijkgraaf–Witten invariant of [Formula: see text] by a certain 3-cocycle. After that, Zickert gave an analogue of Neumann’s work for free fields containing finite fields. The author formulated a geometric method to calculate a weaker version of Zickert’s analogue, called the reduced Dijkgraaf–Witten invariant, for finite fields and gave a formula for twist knot complements and [Formula: see text] in his previous work. In this paper, we show concretely how to calculate the reduced Dijkgraaf–Witten invariants of double twist knot complements and [Formula: see text], and give a formula of them for [Formula: see text].

Impact of Season, Region, and Traditional Agricultural Practices on Aflatoxins and Fumonisins Contamination in the Rice Chain in the Mekong Delta, Vietnam

The current study aimed to evaluate the impact of the crop season, cultivation region, and traditional pre- and post-harvest agricultural practices on mycotoxin contamination in the Mekong Delta rice chain of Vietnam. The results showed that aflatoxins (AFs) and fumonisins (FBs) were predominantly detected in both paddy (n = 91/184, 50%) and white rice (n = 9/46, 20%). Aflatoxin B1 (AFB1)-contaminated paddy samples (n = 3) exceeded the regulatory threshold (5 µg·kg−1). The contamination of paddy with AFs and FBs was not significantly different by growing seasons and cultivation localities. Evidently, in the winter–spring season, fumonisins frequently occurred in paddy planted in Can Tho, while AFs were found in paddy planted in regions Dong Thap and An Giang, and such toxins were absent in Can Tho. Furthermore, the selection of paddy varieties strongly impacted the occurrence of these toxins, especially AFs, for example, line DT8 and Jasmine were susceptible to AFs and FBs. In addition, poor pre- and post-harvest practices (such as crop residue-free fields, fertilizer application, unsanitary means of transport, delayed drying time) had an impact on the AFs and FBs contamination. Our findings can help to understand the dynamics of AFs and FBs in the rice chain in the Vietnamese Mekong Delta, leading to the mitigation of the contamination of AFs and FBs in rice.

Mutual information superadditivity and unitarity bounds

We derive the property of strong superadditivity of mutual information arising from the Markov property of the vacuum state in a conformal field theory and strong subadditivity of entanglement entropy. We show this inequality encodes unitarity bounds for different types of fields. These unitarity bounds are precisely the ones that saturate for free fields. This has a natural explanation in terms of the possibility of localizing algebras on null surfaces. A particular continuity property of mutual information characterizes free fields from the entropic point of view. We derive a general formula for the leading long distance term of the mutual information for regions of arbitrary shape which involves the modular flow of these regions. We obtain the general form of this leading term for two spheres with arbitrary orientations in spacetime, and for primary fields of any tensor representation. For free fields we further obtain the explicit form of the leading term for arbitrary regions with boundaries on null cones.

Dispersion relations and exact bounds on CFT correlators

We derive new crossing-symmetric dispersion formulae for CFT correlators restricted to the line. The formulae are equivalent to the sum rules implied by what we call master functionals, which are analytic extremal functionals which act on the crossing equation. The dispersion relations provide an equivalent formulation of the constraints of the Polyakov bootstrap and hence of crossing symmetry on the line. The built in positivity properties imply simple and exact lower and upper bounds on the values of general CFT correlators on the Euclidean section, which are saturated by generalized free fields. Besides bounds on correlators, we apply this technology to determine new universal constraints on the Regge limit of arbitrary CFTs and obtain very simple and accurate representations of the 3d Ising spin correlator.