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Comments on the Morita Equivalence

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Kirill Saraikin

High Energy Physics - Theory · Submitted 16 May 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is known that noncommutative Yang-Mills theory with periodical boundary conditions on torus at the rational value of the noncommutativity parameter is Morita equivalent to the ordinary Yang-Mills theory with twisted boundary conditions on dual torus.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-th/0005138 (version 2)
Pith ID2T3PLBZI, Pith's permanent record of this paper and its review
CitationKirill Saraikin. "Comments on the Morita Equivalence." arXiv:hep-th/0005138 (2000). https://pith.science/paper/2T3PLBZI
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,593 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.46 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

It is known that noncommutative Yang-Mills theory with periodical boundary conditions on torus at the rational value of the noncommutativity parameter is Morita equivalent to the ordinary Yang-Mills theory with twisted boundary conditions on dual torus. We present simple derivation of this fact. We describe one-to-one correspondence between and gauge invariant observables in these two theories. In particular, we show that under Morita map Polyakov loops in the ordinary YM theory go to the open noncommutative Wilson loops discovered by Ishibashi, Iso, Kawai and Kutazawa.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 It is known that noncommutative Yang-Mills theory with periodical boundary conditions on torus at the rational value of the noncommutativity parameter is Morita equivalent to the ordinary Yang-Mills theory with twisted boundary conditions on dual torus. background 1.00 0.04 0.39 asserted 1.00
s1 We present simple derivation of this fact. contribution 0.94 0.94 0.08 asserted 0.99
s2 We describe one-to-one correspondence between and gauge invariant observables in these two theories. contribution 0.94 0.90 0.19 asserted 0.97
s3 In particular, we show that under Morita map Polyakov loops in the ordinary YM theory go to the open noncommutative Wilson loops discovered by Ishibashi, Iso, Kawai and Kutazawa. result 0.98 0.88 0.45 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.86 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

It is known that noncommutative Yang-Mills theory with periodical boundary conditions on torus at the rational value of the noncommutativity parameter is Morita equivalent to the ordinary Yang-Mills theory with twisted boundary conditions on dual torus. We present simple derivation of this fact. We describe one-to-one correspondence between and gauge invariant observables in these two theories. In particular, we show that under Morita map Polyakov loops in the ordinary YM theory go to the open noncommutative Wilson loops discovered by Ishibashi, Iso, Kawai and Kutazawa.

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