S-duality in N = 4 Yang-Mills theories with general gauge groups

Girardello, L.; Giveon, Amit; Porrati, Massimo; Zaffaroni, Alberto

doi:10.1016/0550-3213(95)00177-t

Cited by 45 publications

(58 citation statements)

References 51 publications

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“…Its easy to see that ord Ψ L = 2r , ord Ψ S = 2r 2 − 2r , (A. 10) so that the total number of roots is 2r 2 which is the order of Ψ. According to (A.1), we have where h = 2r is the Coxeter number and h ∨ = r + 1 is the dual Coxeter number for C r .…”

Section: Discussionmentioning

confidence: 95%

“…The presence of long and short roots in these algebras implies several important differences with respect to the ADE case, even if the overall picture remains similar. In particular, the notion of S-duality, originally formulated in [8][9][10][11][12][13] for the N = 4 theories, can be also extended to the N = 2 ⋆ models with nonsimply laced gauge algebras where the strong/weak coupling symmetry requirement takes the form of a relation between the S-dual prepotential and the Legendre transform of its dual [3,4,14]. However, differently from the ADE case, one finds that S-duality is not a true symmetry since it maps a theory with gauge algebra g to a theory with a dual gauge algebra g ∨ , obtained by exchanging (and rescaling) the long and short roots [9].…”

Section: Jhep11(2015)026mentioning

confidence: 99%

“…The correspondence between g and g ∨ is given in table 1, where for F 4 and G 2 , the ′ in the second column means that the dual root systems are equivalent to the original ones up to a rotation. Note that according to this definition, which is simply the N = 2 version of the N = 4 S-duality rule [8][9][10][11][12][13], the electric variables of the g theory are dual to the magnetic variables of the g ∨ theory. Moreover, using the roots given in appendix A, from (2.8) it is easy to check that, up to a-independent terms, 2…”

Section: S-dualitymentioning

confidence: 99%

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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

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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Section: Discussionmentioning

confidence: 95%

Section: Jhep11(2015)026mentioning

confidence: 99%

Section: S-dualitymentioning

confidence: 99%

See 1 more Smart Citation

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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show abstract

“…Recall that for N 4 super-Yang-Mills theory with a simply-laced simple Lie algebra g the duality group is conjectured to be SL2; Z, while for nonsimply-laced Lie algebras it is a subgroup of SL2; Z denoted ÿ 0 q, where q 2 for g so, sp, F 4 and q 3 for g G 2 (see Refs. [17,18]). We remind that the group ÿ 0 q is a subgroup of SL2; Z consisting of the matrices of the form The group SL2; Z is generated by three elements S, T, C where C ÿ1 is central and the following relations hold:…”

Section: S-dualitymentioning

confidence: 99%

Wilson-’t Hooft operators in four-dimensional gauge theories andS-duality

2006

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We study operators in four-dimensional gauge theories which are localized on a straight line, create electric and magnetic flux, and in the UV limit break the conformal invariance in the minimal possible way. We call them Wilson-'t Hooft operators, since in the purely electric case they reduce to the wellknown Wilson loops, while in general they may carry 't Hooft magnetic flux. We show that to any such operator one can associate a maximally symmetric boundary condition for gauge fields on AdS 2 E S 2 . We show that Wilson-'t Hooft operators are classified by a pair of weights (electric and magnetic) for the gauge group and its magnetic dual, modulo the action of the Weyl group. If the magnetic weight does not belong to the coroot lattice of the gauge group, the corresponding operator is topologically nontrivial (carries nonvanishing 't Hooft magnetic flux). We explain how the spectrum of Wilson-'t Hooft operators transforms under the shift of the -angle by 2. We show that, depending on the gauge group, either SL2; Z or one of its congruence subgroups acts in a natural way on the set of Wilson-'t Hooft operators. This can be regarded as evidence for the S-duality of N 4 super-Yang-Mills theory. We also compute the one-point function of the stress-energy tensor in the presence of a Wilson-'t Hooft operator at weak coupling.

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“…Sen then went on to construct explicitly a dyonic solution with charges (1, 2) in complete agreement with the conjecture. Further evidence was supplied by Vafa and Witten [10], by studying partition functions of the twisted N = 4 theory on various 4-manifolds, and also by Girardello et al [9].…”

Section: Monopoles Of N = 4 and N = Yang-millsmentioning

confidence: 96%