Four flavors, triality, and bimodular forms

Johannes Aspman, Elias Furrer, Jan Manschot

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We consider 𝒩 = 2 supersymmetric SU(2) gauge theory with Nf = 4 massive hypermultiplets. The duality group of this theory contains transformations acting on the UV coupling τUV as well as on the running coupling τ. We establish that subgroups of the duality group act separately on τUV and τ, while a larger group acts simultaneously on τUV 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 τUV . Since the UV duality group of the theory contains the triality group of outer automorphisms of the flavor 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.
Original languageEnglish
Article number025017
Number of pages23
JournalPhysical Review D
Issue number2
Publication statusPublished - 15 Jan 2022


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