S-duality and the prepotential in N = 2 ⋆ $$ \mathcal{N}={2}^{\star } $$ theories (I): the ADE algebras

Self Cite

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.

Section: Introductionsupporting

confidence: 53%

Section: Jhep11(2015)026mentioning

confidence: 80%

Section: Jhep11(2015)026mentioning

confidence: 80%

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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

Self Cite

“…1 As a consequence of this structure, it is possible to encode the mass expansion of the prepotential in terms of quasi-modular functions of the gauge coupling and the vacuum expectation ϕ of the scalar in the gauge multiplet. The construction is general and holds for arbitrary gauge groups [37][38][39].…”

Section: Introduction and Resultsmentioning

confidence: 99%

Chiral trace relations in Ω-deformed N = 2 $$ \mathcal{N}=2 $$ theories

Beccaria

Fachechi

Macorini

2017

We consider N = 2 SU(2) gauge theories in four dimensions (pure or mass deformed) and discuss the properties of the simplest chiral observables in the presence of a generic Ω-deformation. We compute them by equivariant localization and analyze the structure of the exact instanton corrections to the classical chiral ring relations. We predict exact relations valid at all instanton number among the traces Trϕ n , where ϕ is the scalar field in the gauge multiplet. In the Nekrasov-Shatashvili limit, such relations may be explained in terms of the available quantized Seiberg-Witten curves. Instead, the full two-parameter deformation enjoys novel features and the ring relations require non trivial additional derivative terms with respect to the modular parameter. Higher rank groups are briefly discussed emphasizing non-factorization of correlators due to the Ω-deformation. Finally, the structure of the deformed ring relations in the N = 2 theory is analyzed from the point of view of the Alday-Gaiotto-Tachikawa correspondence proving consistency as well as some interesting universality properties.

“…It would be interesting to study the Nahm construction of the monopoles [39] for the construction of the solutions with higher charges and their moduli space. It is also interesting to study S-duality [8][9][10][40][41][42][43] of the Ω-deformed N = 4 theory as well as the relation to the integrable systems [15][16][17].…”

Section: Jhep11(2015)152mentioning

confidence: 99%

BPS equations in Ω-deformed N = 4 $$ \mathcal{N}=4 $$ super Yang-Mills theory

Ito¹,

Kanayama²,

Nakajima³

et al. 2015

We study supersymmetry of N = 4 super Yang-Mills theory in four dimensions deformed in the Ω-background. We take the Nekrasov-Shatashvili limit of the background so that two-dimensional super Poincaré symmetry is recovered. We compute the deformed central charge of the superalgebra and study the 1/2 and 1/4 BPS states. We obtain the Ω-deformed 1/2 and 1/4 BPS dyon equations from the deformed supersymmetry transformation and the Bogomol'nyi completion of the energy.