{"arxiv_id":"hep-th/0108007","incoming":{"papers":4,"sentences":9,"groups":[{"kind":"comparison","label":"Compares with it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1109.3703","title":"Noncommutative Vortices and Instantons from Generalized Bose Operators","url":"/paper/1109.3703","section":"$ℝ^2_NC×ℝ^2_C$:","sentence":"Usually the single instanton solution in $ℝ_NC^2 ×ℝ_C^2$ with $U(1)$ gauge group is normalized as [ref] [equation] But in our solution this technique cannot be used because in this case $Ψ_0^†Ψ_0=N_1-Λ_-/N_1-1δ(δ-1)$ vanishes when it operates on the state $|0⟩$ and the inverse of $Ψ_0^†Ψ_0$ does not exist.","intent_p":0.86,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":4,"sentences":5,"quotes":[{"arxiv_id":"1109.3703","title":"Noncommutative Vortices and Instantons from Generalized Bose Operators","url":"/paper/1109.3703","section":"Noncommutative ADHM Construction","sentence":"Let us first discuss the usual single anti-self-dual $U(1)$ instanton solutions ($k=1, N=1$) in $ℝ^2_NC×ℝ^2_C$ [ref] and in $ℝ^2_NC×ℝ^2_NC$ [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"1301.4051","title":"Topics in Noncommutative Gauge Theories and Deformed Relativistic Theories","url":"/paper/1301.4051","section":"Noncommutative ADHM Construction","sentence":"Let us first discuss the usual single anti-self-dual $U(1)$ instanton solutions ($k=1, N=1$) in $R^2_NC×R^2_C$ [ref] and in $R^2_NC×R^2_NC$ [ref] .","intent_p":0.89,"contests_p":null},{"arxiv_id":"0805.1917","title":"Fayet-Iliopoulos Terms in AdS/CFT with Flavour","url":"/paper/0805.1917","section":"Noncommutative U(1) Instantons and modified ADHM Construction","sentence":"In this subsection we briefly review the noncommutative ADHM construction, as explained in e.g. [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"0711.3059","title":"Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories","url":"/paper/0711.3059","section":"Introduction","sentence":"Thus, not only as the simplest field theories in quantum spacetime but also as toy models of string theory, various perturbative and non-perturbative aspects such as unitarity [ref] , causality [ref] , UV-IR mixing [ref] , renormalizability [ref] , scalar solitons [ref] , instantons [ref] , monopoles [ref] , and other solitonic solutions [ref] have extensively been analyzed.","intent_p":0.96,"contests_p":null}]}],"unlabelled_sentences":3},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/hep-th/0108007"}}