arXiv subjects

Johannes Aspman

Publications and source records attributed to Johannes Aspman.

21 records · Page 2Linked to original sources

arXiv2021

Four flavours, triality and bimodular forms

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

hep-th↗

arXiv2021

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

We consider the order parameter $u=\left<{\rm Tr}ϕ^2\right>$ as function of the running coupling constant $τ\in \mathbb{H}$ of asymptotically free $\mathcal{N}=2$ QCD with gauge group $SU(2)$ and $N_f\leq 3$ massive hypermultiplets. If the domain for $τ$ is restricted to an appropriate fundamental domain $\mathcal{F}_{N_f}$, the function $u$ is one-to-one. We demonstrate that these domains consist of six or less images of an ${\rm SL}(2,\mathbb{Z})$ 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 ${\rm SL}(2,\mathbb{Z})$ and the fundamental domain is $Γ\backslash\mathbb{H}$. For generic masses, however, branch points and cuts are present, and subsets of $\mathcal{F}_{N_f}$ 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.

hep-th↗

arXiv2021

Elliptic Loci of SU(3) Vacua

The space of vacua of many four-dimensional, $\mathcal{N}=2$ supersymmetric gauge theories can famously be identified with a family of complex curves. For gauge group $SU(2)$, this gives a fully explicit description of the low-energy effective theory in terms of an elliptic curve and associated modular fundamental domain. The two-dimensional space of vacua for gauge group $SU(3)$ parametrizes an intricate family of genus two curves. We analyze this family using the so-called Rosenhain form for these curves. We demonstrate that two natural one-dimensional subloci of the space of $SU(3)$ vacua, $\mathcal{E}_u$ and $\mathcal{E}_v$, each parametrize a family of elliptic curves. For these elliptic loci, we describe the order parameters and fundamental domains explicitly. The locus $\mathcal{E}_u$ contains the points where mutually local dyons become massless, and is a fundamental domain for a classical congruence subgroup. Moreover, the locus $\mathcal{E}_v$ contains the superconformal Argyres-Douglas points, and is a fundamental domain for a Fricke group.

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