Modular anomaly equations and S-duality in N=2 conformal SQCD

Ashok, Sujay K.; Billó, Marco; Dell’Aquila, Eleonora; Frau, M.; Lerda, A.; Raman, Madhusudhan

doi:10.48550/arxiv.1507.07476

Cited by 11 publications

(33 citation statements)

References 32 publications

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“…Eq. ( 17) can be solved assuming that the coefficients f n in the mass expansion (7) of the quantum prepotential depend on τ only through quasi-modular forms of Γ 0 (n g ). The ring of these quasi-modular forms is generated by…”

Section: The Modular Anomaly Equationmentioning

confidence: 99%

“…This equation governs the appearance in the quantum prepotential of terms containing the second Eisenstein series E 2 , which is the only source of a quasi -modular behaviour. Using the mass expansion (7), this "modular anomaly" equation becomes a recursion relation…”

Section: The Modular Anomaly Equationmentioning

confidence: 99%

“…It is interesting to observe that for ng = 3, the matrices T and V 2 generate the subgroup Γ1(3), whose modular forms play a role in the N = 2 SYM theory with gauge group SU(3) and six fundamental hypermultiplets[7].…”

mentioning

confidence: 99%

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Resumming instantons in 𝒩 = 2^* theories with arbitrary gauge groups

Billó¹,

Frau²,

Fucito³

et al. 2017

The Fourteenth Marcel Grossmann Meeting

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We discuss the modular anomaly equation satisfied by the the prepotential of 4-dimensional N = 2 theories and show that its validity is related to S-duality. The recursion relations that follow from the modular anomaly equation allow one to write the prepotential in terms of (quasi)-modular forms, thus resumming the instanton contributions. These results can be checked against the microscopic multi-instanton calculus in the case of classical algebras, but are valid also for the exceptional E 6,7,8 , F 4 and G 2 algebras, where direct computations are not available.

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Section: The Modular Anomaly Equationmentioning

confidence: 99%

Section: The Modular Anomaly Equationmentioning

confidence: 99%

See 1 more Smart Citation

Resumming instantons in 𝒩 = 2^* theories with arbitrary gauge groups

Billó¹,

Frau²,

Fucito³

et al. 2017

The Fourteenth Marcel Grossmann Meeting

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show abstract

“…when the N = 2 ⋆ theory reduces to the pure N = 2 SYM theory 7 . In this case the 1-instanton prepotential is…”

Section: -Instantonmentioning

confidence: 99%

S-duality and the prepotential of N = 2 ⋆ $$ \mathcal{N}={2}^{\star } $$ theories (II): the non-simply laced algebras

Billó

Frau

Fucito

et al. 2015

J. High Energ. Phys.

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We derive a modular anomaly equation satisfied by the prepotential of the N = 2 ⋆ supersymmetric theories with non-simply laced gauge algebras, including the classical B r and C r infinite series and the exceptional F 4 and G 2 cases. This equation determines the exact prepotential recursively in an expansion for small mass in terms of quasi-modular forms of the S-duality group. We also discuss the behaviour of these theories under S-duality and show that the prepotential of the SO(2r + 1) theory is mapped to that of the Sp(2r) theory and viceversa, while the exceptional F 4 and G 2 theories are mapped into themselves (up to a rotation of the roots) in analogy with what happens for the N = 4 supersymmetric theories. These results extend the analysis for the simply laced groups presented in a companion paper.

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“…The modular anomaly is related to the holomorphic anomaly of topological string amplitudes through local Calabi-Yau embeddings of the SW curves [20] - [23]. It has been studied also in presence of an Ω-background [24]- [34], in the framework of the AGT correspondence [35]- [38] and in N = 2 conformal SQCD models with fundamental matter [30,31,39].…”

Section: Introductionmentioning

confidence: 99%

S-duality and the prepotential in N=2* theories (I): the ADE algebras

Billó¹,

Frau²,

Fucito³

et al. 2015

Preprint

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The prepotential of N = 2 ⋆ supersymmetric theories with unitary gauge groups in an Ω background satisfies a modular anomaly equation that can be recursively solved order by order in an expansion for small mass. By requiring that S-duality acts on the prepotential as a Fourier transform we generalise this result to N = 2 ⋆ theories with gauge algebras of the D and E type and show that their prepotentials can be written in terms of quasi-modular forms of SL(2, Z). The results are checked against microscopic multi-instanton calculus based on localization for the A and D series and reproduce the known 1-instanton prepotential of the pure N = 2 theories for any gauge group of ADE type. Our results can also be used to obtain the multi-instanton terms in the exceptional theories for which the microscopic instanton calculus and the ADHM construction are not available.

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Modular anomaly equations and S-duality in N=2 conformal SQCD

Cited by 11 publications

References 32 publications

Resumming instantons in 𝒩 = 2^* theories with arbitrary gauge groups

Resumming instantons in 𝒩 = 2^* theories with arbitrary gauge groups

S-duality and the prepotential of N = 2 ⋆ $$ \mathcal{N}={2}^{\star } $$ theories (II): the non-simply laced algebras

S-duality and the prepotential in N=2* theories (I): the ADE algebras

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Modular anomaly equations and S-duality in N=2 conformal SQCD

Cited by 11 publications

References 32 publications

Resumming instantons in 𝒩 = 2* theories with arbitrary gauge groups

Resumming instantons in 𝒩 = 2* theories with arbitrary gauge groups

S-duality and the prepotential of N = 2 ⋆ $$ \mathcal{N}={2}^{\star } $$ theories (II): the non-simply laced algebras

S-duality and the prepotential in N=2* theories (I): the ADE algebras

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Resumming instantons in 𝒩 = 2^* theories with arbitrary gauge groups

Resumming instantons in 𝒩 = 2^* theories with arbitrary gauge groups