Duality symmetry in softly broken N = 2 gauge theories

Mariño, Marcos; Zamora, Frederic

doi:10.1016/s0550-3213(98)00490-8

Cited by 7 publications

(6 citation statements)

References 47 publications

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“…For the asymptotically free theories, τ 0 is defined in terms of the dynamically generated scale Λ N f of the theory by [36]: 6) [36] -see also [37] for further details and extensions:…”

Section: The Integral For N = 4 Supersymmetrymentioning

confidence: 99%

“…, while for the finite theories N f = 4 and N = 4 it corresponds to the microscopic coupling. For the N = 4 theory one gets from (4.6) [36] -see also [37] for further details and extensions:…”

Section: The Integral For N = 4 Supersymmetrymentioning

confidence: 99%

“…As these duality transformations interchange the singularities, they induce a non-trivial monodromy transformation τ → (âτ + b)/(ĉτ + d) on the effective low-energy theory [13]. Under these combined duality transformations one has, for example, z → (cτ 0 + d) 2 z, (dz/da) → (cτ0+d) 2 ĉτ + d (dz/da), so that [37]:…”

Section: The Integral For N = 4 Supersymmetrymentioning

confidence: 99%

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Duality in twisted = 4 supersymmetric gauge theories in four dimensions

Labastida¹,

Lozano²

1999

Nuclear Physics B

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We consider a twisted version of the four-dimensional N = 4 supersymmetric Yang-Mills theory with gauge groups SU(2) and SO(3), and bare masses for two of its chiral multiplets, thereby breaking N = 4 down to N = 2. Using the wall-crossing technique introduced by Moore and Witten within the u-plane approach to twisted topological field theories, we compute the partition function and all the topological correlation functions for the case of simply-connected spin fourmanifolds of simple type. By including 't Hooft fluxes, we analyse the properties of the resulting formulae under duality transformations. The partition function transforms in the same way as the one first presented by Vafa and Witten for another twist of the N = 4 supersymmetric theory in their strong coupling test of S-duality. Both partition functions coincide on K3. The topological correlation functions turn out to transform covariantly under duality, following a simple pattern which seems to be inherent in a general type of topological quantum field theories.⋆

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“…For the asymptotically free theories, τ 0 is defined in terms of the dynamically generated scale Λ N f of the theory by [36]: 6) [36] -see also [37] for further details and extensions:…”

Section: The Integral For N = 4 Supersymmetrymentioning

confidence: 99%

Section: The Integral For N = 4 Supersymmetrymentioning

confidence: 99%

Section: The Integral For N = 4 Supersymmetrymentioning

confidence: 99%

See 1 more Smart Citation

Duality in twisted = 4 supersymmetric gauge theories in four dimensions

Labastida¹,

Lozano²

1999

Nuclear Physics B

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“…As ϑ 24 3 is a modular form of weight 12 for Γ(2), this shows that ∆ A has modular weight (0, 12) under Γ(2) τ × Γ(2) τ 0 . With the same reasoning as above, we find that ∆ A is a bimodular form of weight (0, 12) for the same triple (3.8).…”

Section: Case Amentioning

confidence: 84%

“…which act on the column vector m ∈ M := C 4 from the left [1,24,25]. The map T exchanges the two spinors keeping the vector fixed, while S exchanges the vector with the spinor, keeping the conjugate spinor fixed.…”

Section: Trialitymentioning

confidence: 99%

Four flavours, triality and bimodular forms

Aspman,

Furrer,

Manschot

2021

Preprint

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We consider N = 2 supersymmetric SU(2) gauge theory with N f = 4 massive hypermultiplets. The duality group of this theory contains transformations acting on the UV-coupling τ UV as well as on the running coupling τ . We establish that subgroups of the duality group act separately on τ UV and τ , while a larger group acts simultaneously on τ UV and τ . For special choices of the masses, we find that the duality groups can be identified with congruence subgroups of SL(2, Z). We demonstrate that in such cases, the order parameters are instances of bimodular forms with arguments τ and τ UV . Since the UV duality group of the theory contains the triality group of outer automorphisms of the flavour symmetry SO(8), the duality action gives rise to an orbit of mass configurations. Consequently, the corresponding order parameters combine to vector-valued bimodular forms with SL(2, Z) acting simultaneously on the two couplings.

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Topological twists of massive SQCD, Part I

Aspman,

Furrer,

Manschot

2024

Lett Math Phys

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We consider topological twists of four-dimensional $$\mathcal {N}=2$$ N = 2 supersymmetric QCD with gauge group SU(2) and $$N_f\le 3$$ N f ≤ 3 fundamental hypermultiplets. The twists are labelled by a choice of background fluxes for the flavour group, which provides an infinite family of topological partition functions. In this Part I, we demonstrate that in the presence of such fluxes the theories can be formulated for arbitrary gauge bundles on a compact four-manifold. Moreover, we consider arbitrary masses for the hypermultiplets, which introduce new intricacies for the evaluation of the low-energy path integral on the Coulomb branch. We develop techniques for the evaluation of these path integrals. In the forthcoming Part II, we will deal with the explicit evaluation.

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Duality symmetry in softly broken N = 2 gauge theories

Cited by 7 publications

References 47 publications

Duality in twisted = 4 supersymmetric gauge theories in four dimensions

Duality in twisted = 4 supersymmetric gauge theories in four dimensions

Four flavours, triality and bimodular forms

Topological twists of massive SQCD, Part I

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