Meromorphic scaling flow of supersymmetric Yang–Mills with matter

Dolan, Brian P.

doi:10.1016/j.nuclphysb.2005.12.027

Cited by 4 publications

(9 citation statements)

References 27 publications

(64 reference statements)

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“…We conclude with a brief discussion on our findings as well as some possible further directions in Section 7. As a by-product of our analyses we also propose an expression for the beta functions of the massive N f ≤ 3 theories, generalising the results of [42,43].…”

Section: Introductionmentioning

confidence: 72%

“…Another potential application is the N = 2 QCD beta function. In [42,43], Dolan gave a proposal for the beta function of the massless N f = 0, 1, 2, 3 theories, expanding on the work of [31,[102][103][104][105]. For the cases N f = 0, 2, 3 we can use the notation of the present paper to collect these conjectured expressions as 15 where ∆ is the reduced discriminant of (3.19).…”

Section: Discussionmentioning

confidence: 98%

“…For the cases N f = 0, 2, 3 we can use the notation of the present paper to collect these conjectured expressions as 15 where ∆ is the reduced discriminant of (3.19). In [43] a shift is also made for u in N f = 3. For N f = 1 the argument is revised, basically due to the square roots appearing in u and the spoilage of modularity.…”

Section: Discussionmentioning

confidence: 99%

“…We will start by including one hypermultiplet. The N f = 1 theory has been discussed in some detail in [32,43,[75][76][77].…”

Section: The N F = 1 Curvementioning

confidence: 99%

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Cutting and gluing with running couplings in $\mathcal{N}=2$ QCD

Aspman,

Furrer,

Manschot

2021

Preprint

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We consider the order parameter u = Trφ 2 as function of the running coupling constant τ ∈ H of asymptotically free N = 2 QCD with gauge group SU (2) and N f ≤ 3 massive hypermultiplets. If the domain for τ is restricted to an appropriate fundamental domain F N f , the function u is one-to-one. We demonstrate that these domains consist of six or less images of an SL(2, Z) keyhole fundamental domain, with appropriate identifications of the boundaries. For special choices of the masses, u does not give rise to branch points and cuts, such that u is a modular function for a congruence subgroup Γ of SL(2, Z) and the fundamental domain is Γ\H. For generic masses, however, branch points and cuts are present, and subsets of F N f are being cut and glued upon varying the mass. We study this mechanism for various phenomena, such as decoupling of hypermultiplets, merging of local singularities, as well as merging of non-local singularities which give rise to superconformal Argyres-Douglas theories.

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Section: Introductionmentioning

confidence: 72%

Section: Discussionmentioning

confidence: 98%

Section: Discussionmentioning

confidence: 99%

“…We will start by including one hypermultiplet. The N f = 1 theory has been discussed in some detail in [32,43,[75][76][77].…”

Section: The N F = 1 Curvementioning

confidence: 99%

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Cutting and gluing with running couplings in $\mathcal{N}=2$ QCD

Aspman,

Furrer,

Manschot

2021

Preprint

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“…and explicit forms of the corresponding modular β-functions are given in [49]. For N f = 1 and N f = 3 the group is the same as the symmetry group acting on the effective action while for N f = 0 and N f = 2 it is larger, due to the Z 2 action on the u-plane.…”

Section: Duality In Electromagnetismmentioning

confidence: 99%

Modular Symmetry and Fractional Charges in N = 2 Supersymmetric Yang-Mills and the Quantum Hall Effect

Dolan¹

2007

SIGMA

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Abstract. The parallel rôles of modular symmetry in N = 2 supersymmetric Yang-Mills and in the quantum Hall effect are reviewed. In supersymmetric Yang-Mills theories modular symmetry emerges as a version of Dirac's electric -magnetic duality. It has significant consequences for the vacuum structure of these theories, leading to a fractal vacuum which has an infinite hierarchy of related phases. In the case of N = 2 supersymmetric Yang-Mills in 3 + 1 dimensions, scaling functions can be defined which are modular forms of a subgroup of the full modular group and which interpolate between vacua. Infra-red fixed points at strong coupling correspond to θ-vacua with θ a rational number that, in the case of pure SUSY Yang-Mills, has odd denominator. There is a mass gap for electrically charged particles which can carry fractional electric charge. A similar structure applies to the 2 + 1 dimensional quantum Hall effect where the hierarchy of Hall plateaux can be understood in terms of an action of the modular group and the stability of Hall plateaux is due to the fact that odd denominator Hall conductivities are attractive infra-red fixed points. There is a mass gap for electrically charged excitations which, in the case of the fractional quantum Hall effect, carry fractional electric charge.

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