arXiv subjects

Mario De Marco

Publications and source records attributed to Mario De Marco.

12 recordsLinked to original sources

arXiv2026

5d Higgs Branches: Stratifications from Geometry

Higgs Branches of 5d SCFTs are hyperk\"ahler cones, symplectic varieties with interesting nested singularities governing the structure of possible Higgs branch RG flows. The main purpose of this note is to investigate 5d Higgs Branches via a geometric route: we study 5d SCFTs geometrically engineered from M-theory on non-compact Calabi-Yau threefolds, with non-isolated singularities. We match the (dynamical) complex structure deformations of the threefold with the symplectic leaves in the Higgs branch of the 5d SCFT, constructing its stratification purely relying on geometry. Consistency checks for our proposal are presented exploiting magnetic quivers.

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arXiv2026

5d Trinions and Tetraons

Recently, an atomic classification scheme of 5d SCFTs has been proposed, relying on the identification of indecomposable building blocks that can be fused together to produce large classes of 5d SCFTs. These novel SCFTs are known as bifundamental 5d conformal matter theories, and their fusion produces linear generalized quivers. We generalize such picture employing M-theory geometric engineering to construct trinions and tetraon 5d SCFTs with flavor symmetry of type D. They correspond to non-linear generalized quivers displaying novel patterns of instantonic symmetry enhancement, and their fusion produces singular geometries that often are non-toric non-complete intersections. Finally, within our setup, we rule out trinions and tetraons of type E.

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arXiv2026

From Quivers to Geometry: 5d Conformal Matter

We show that all 5d balanced (ADE-shaped) special unitary quivers with no Chern-Simons level admit a UV completion which is a 5d conformal matter SCFT. We give explicit local Calabi-Yau threefolds realizing each of these models in M-theory. This unified description enables a systematic exploration of their physical properties, such as their Higgs Branch, as well as connections to class-S constructions and the affine Grassmannian.

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arXiv2025

Non-toric 5d SCFTs from Reid's Pagoda

We construct new families of non-toric 5d SCFTs via abelian orbifolds of the Reid Pagoda, including a surprising infinite family of rank-1 theories, that evade all known classifications. Using the McKay correspondence, we derive their BPS quivers and superpotentials. The hallmark of these theories is a novel sector we dub Pagoda matter, whose vacuum expectation values obstruct the Kaehler moduli. This mechanism freezes the gauge coupling to infinite value, precluding a weak-coupling limit and rendering the theories intrinsically strongly coupled. Finally, we interpret these results as 5d SCFTs deformed by non-constant flavor backgrounds.

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arXiv2025

Symmetries Beyond Branes: Geometric Engineering and Isometries

In this work we consider the relation between finite isometries of the internal space and symmetries of the transverse field theory in Geometric Engineering. On top of the established relation between branes wrapping torsional cycles and topological defects, we study other symmetries of the field theory that are not captured by branes wrapped at infinity. Isometries of the engineering geometry have a representations on the field theory, encoded by their non-trivial actions on exceptional and torsional cycles. In this work we describe such action in general terms. As examples, we focus on three classes of geometric engineering spaces: Du Val singularities, toric Calabi-Yau threefolds and $G_2$ manifolds obtained as fibrations of Du Val singularities over $\mathbb S^3$. In the latter case, we check explicitly that M-theory on Calabi-Yau or $G_2$ manifold with finite isometries reproduces correctly the higher group structures and non-invertible symmetries of the transverse field theories.

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arXiv2025

Remarks on the Higgs Branch of 5d Conformal Matter

Among the elementary building blocks in the atomic classification of 5d SCFTs there are 5d bifundamental conformal matter theories of various kinds. In this work we study the Higgs branch of these models and of the corresponding molecules arising from their fusion. To this aim we use two complementary independent strategies. On the one hand for the type $A$ and $D$ conformal matter, we identify dual $(p,q)$ brane webs in IIB and exploit them to read off the corresponding magnetic quivers. On the other hand, we exploit circle reductions and study the resulting 4d $\mathcal N=2$ SCFTs, giving an alternative derivation of their Higgs branches which extend also to the $E$ types.

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arXiv2024

Disconnected gauge groups in the infrared

Gauging a discrete 0-form symmetry of a QFT is a procedure that changes the global form of the gauge group but not its perturbative dynamics. In this work, we study the Seiberg-Witten solution of theories resulting from the gauging of charge conjugation in 4d $\mathcal{N} = 2$ theories with $SU(N)$ gauge group and fundamental hypermultiplets. The basic idea of our procedure is to identify the $\mathbb{Z}_2$ action at the level of the SW curve and perform the quotient, and it should also be applicable to non-lagrangian theories. We study dynamical aspects of these theories such as their moduli space singularities and the corresponding physics; in particular, we explore the complex structure singularity arising from the quotient procedure. We also discuss some implications of our work in regard to three problems: the geometric classification of 4d SCFTs, the study of non-invertible symmetries from the SW geometry, and the String Theory engineering of theories with disconnected gauge groups.

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arXiv2023

5d Conformal Matter

Six-dimensional superconformal field theories (SCFTs) have an atomic classification in terms of elementary building blocks, conformal systems that generalize matter and can be fused together to form all known 6d SCFTs in terms of generalized 6d quivers. It is therefore natural to ask whether 5d SCFTs can be organized in a similar manner, as the outcome of fusions of certain elementary building blocks, which we call 5d conformal matter theories. In this project we begin exploring this idea and we give a systematic construction of 5d generalized ``bifundamental'' SCFTs, building from geometric engineering techniques in M-theory. In particular, we find several examples of $(\mathfrak {e}_6,\mathfrak {e}_6)$, $(\mathfrak {e}_7,\mathfrak {e}_7)$ and $(\mathfrak {e}_8,\mathfrak {e}_8)$ 5d bifundamental SCFTs beyond the ones arising from (elementary) KK reductions of the 6d conformal matter theories. We show that these can be fused together giving rise to 5d SCFTs captured by 5d generalized linear quivers with exceptional gauge groups as nodes, and links given by 5d conformal matter. As a first application of these models we uncover a large class of novel 5d dualites, that generalize the well-known fiber/base dualities outside the toric realm.

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arXiv2023

5d Higgs Branches from M-theory on quasi-homogeneous cDV threefold singularities

We classify rank zero 5d SCFTs geometrically engineered from M-theory on quasi-homogeneous compound Du Val isolated threefold singularities. For all such theories, we characterize the Higgs Branch, by computing the dimension, the continuous and discrete symmetry groups, as well as more refined details such as the charges of the hypermultiplets under these groups. We derive these data by means of a gauge-theoretic method, that we have recently introduced, based on establishing a correspondence between an adjoint Higgs field and the M-theory geometry. As a byproduct, this further allows us to construct several T-brane backgrounds, that yield inequivalent 5d spectra but are associated with the same geometry.

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arXiv2022

Flops of any length, Gopakumar-Vafa invariants, and 5d Higgs Branches

The conifold is a basic example of a noncompact Calabi-Yau threefold that admits a simple flop, and in M-theory, gives rise to a 5d hypermultiplet at low energies, realized by an M2-brane wrapped on the vanishing sphere. We develop a novel gauge-theoretic method to construct new classes of examples that generalize the simple flop to so-called length l=1,...,6. The method allows us to naturally read off the Gopakumar-Vafa invariants. Although they share similar properties to the beloved conifold, these threefolds are expected to admit M2-bound states of higher degree. We demonstrate this through our computations of the GV invariants. Furthermore we fully characterize the associated Higgs branches by computing their dimensions and flavor groups. With our techniques we extract more refined data such as the charges of the hypers under the flavor group.

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arXiv2021

Higgs Branches of rank-0 5d theories from M-theory on $(A_j,A_l)$ and $(A_k,D_n)$ singularities

We study the dynamics of M-theory on isolated non-toric Calabi-Yau threefold singularities of type $(A_j,A_l)$ and $(A_k,D_n)$, engineering five-dimensional rank-zero SCFTs. Our approach consists in mapping these backgrounds to type IIA string theory with D6 branes at angles and O6$^{-}$ planes, computing the five-dimensional open string modes located at the brane intersections. This permits us to characterize the Higgs Branches of these theories as algebraic varieties, determine the flavour and gauge group and inspect subtleties related to T-branes. Our methods apply for all the considered singularities: we give a closed formula for the $(A_j,A_l)$ Higgs Branches, and tables for the Higgs Branches of the $(A_k,D_n)$ series.

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arXiv2021

Higgs branches of 5d rank-zero theories from geometry

We study the Higgs branches of five-dimensional N=1 rank-zero theories obtained from M-theory on two classes non-toric non-compact Calabi-Yau threefolds: Reid's pagodas, and Laufer's examples. Our approach consists in reducing to IIA with D6-branes and O6-planes, and computing the open-string spectra giving rise to hypermultiplets. Starting with the seven-dimensional worldvolume theories, we switch on T-brane backgrounds to give rise to bound states with angles. We observe that the resulting partially Higgsed 5d theories have discrete gauge groups, from which we readily deduce the geometry of the Higgs branches as orbifolds of quaternionic varieties.

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