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Prepotential and Instanton Corrections in N=2 Supersymmetric SU(N_1)xSU(N_2) Yang Mills Theories

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Marta Gomez-Reino

High Energy Physics - Theory · Submitted 16 Jan 2003

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

The authors' main claim As an application we develop a method to compute recursively the instanton corrections to the prepotential in a straightforward way.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-th/0301105 (version 2)
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CitationMarta Gomez-Reino. "Prepotential and Instanton Corrections in N=2 Supersymmetric SU(N_1)xSU(N_2) Yang Mills Theories." arXiv:hep-th/0301105 (2003). https://pith.science/paper/NMOABJQS
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,662 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.35 · compares with prior results 0.12 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper we analyse the non-hyperelliptic Seiberg-Witten curves derived from M-theory that encode the low energy solution of N=2 supersymmetric theories with product gauge groups. We consider the case of a SU(N_1)xSU(N_2) gauge theory with a hypermultiplet in the bifundamental representation together with matter in the fundamental representations of SU(N_1) and SU(N_2). By means of the Riemann bilinear relations that hold on the Riemann surface defined by the Seiberg--Witten curve, we compute the logarithmic derivative of the prepotential with respect to the quantum scales of both gauge groups. As an application we develop a method to compute recursively the instanton corrections to the prepotential in a straightforward way. We present explicit formulas for up to third order on both quantum scales. Furthermore, we extend those results to SU(N) gauge theories with a matter hypermultiplet in the symmetric and antisymmetric representation. We also present some non-trivial checks of our results.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we analyse the non-hyperelliptic Seiberg-Witten curves derived from M-theory that encode the low energy solution of N=2 supersymmetric theories with product gauge groups. contribution 0.90 0.79 0.07 asserted 0.97
s1 We consider the case of a SU(N_1)xSU(N_2) gauge theory with a hypermultiplet in the bifundamental representation together with matter in the fundamental representations of SU(N_1) and SU(N_2). contribution 0.64 0.46 0.04 asserted 0.92
s2 By means of the Riemann bilinear relations that hold on the Riemann surface defined by the Seiberg--Witten curve, we compute the logarithmic derivative of the prepotential with respect to the quantum scales of both gauge groups. method 0.97 0.95 0.16 asserted 1.00
s3 As an application we develop a method to compute recursively the instanton corrections to the prepotential in a straightforward way. contribution 0.69 0.96 0.27 asserted 1.00
s4 We present explicit formulas for up to third order on both quantum scales. result 0.94 0.96 0.15 asserted 1.00
s5 Furthermore, we extend those results to SU(N) gauge theories with a matter hypermultiplet in the symmetric and antisymmetric representation. contribution 0.97 0.95 0.08 asserted 1.00
s6 We also present some non-trivial checks of our results. contribution 0.63 0.91 0.05 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.79 · 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

In this paper we analyse the non-hyperelliptic Seiberg-Witten curves derived from M-theory that encode the low energy solution of N=2 supersymmetric theories with product gauge groups. We consider the case of a SU(N_1)xSU(N_2) gauge theory with a hypermultiplet in the bifundamental representation together with matter in the fundamental representations of SU(N_1) and SU(N_2). By means of the Riemann bilinear relations that hold on the Riemann surface defined by the Seiberg--Witten curve, we compute the logarithmic derivative of the prepotential with respect to the quantum scales of both gauge groups. As an application we develop a method to compute recursively the instanton corrections to the prepotential in a straightforward way. We present explicit formulas for up to third order on both quantum scales. Furthermore, we extend those results to SU(N) gauge theories with a matter hypermultiplet in the symmetric and antisymmetric representation. We also present some non-trivial checks of our results.

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