arXiv subjects

Roberta Angius

Publications and source records attributed to Roberta Angius.

15 recordsLinked to original sources

arXiv2026

The Art of Networking: Networks of Trivalent 10d Heterotic Junctions

We initiate the study of networks of 10d string theories connected by junctions implied by the cobordism conjecture. Focusing on the recently constructed junction of the three 10d non-tachyonic heterotic theories, we generalize its $(0, 1)$ heterotic worldsheet description to construct arbitrary networks. For one-dimensional networks, we formulate their topology in terms of graph theory and provide a simple worldsheet realization for general graphs. We then extend our analysis to higher-dimensional networks, describing e.g. nucleation in a theory of bubbles of pairs of other theories. We also discuss compact configurations, which define a novel class of compactifications in which different sectors propagate on different compact spaces, in a way reminiscent of compactifications on quantum geometries like $S^1 \vee S^1$.

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arXiv2026

Hodge Loci and Complex Multiplication via Generalized Symmetries in Calabi-Yau sigma models

We propose a sigma-model analogue of Hodge loci in the moduli space of geometric Calabi-Yau compactifications, characterized by the emergence of non-trivial rational Hodge endomorphisms, using generalized symmetries. In the CFT description, the complex cohomology is spanned by Ramond-Ramond ground states, the Hodge decomposition is determined by the $U(1)\times U(1)$ R-charges, and the rational structure is provided by BPS boundary states, with polarization induced by the open string Witten index. Hodge loci are identified by the existence of a non-trivial category $TDL$ of topological defects preserving the $N=(2,2)$ superconformal algebra and acting invertibly on the spectral-flow generators. At special points on these loci, the category $TDL$ exhibits additional arithmetic structure and admits embeddings of finite products of number fields with Complex Multiplication, leading to stronger constraints on the boundary states of the theory. Although the construction is general, we analyze in detail the cases of elliptic curves and $K3$ surfaces.

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arXiv2026

The Art of Branching: Cobordism Junctions of 10d String Theories

We describe the explicit construction of configurations of several 10d string theories joining at a 9d junction, providing a dynamical realization of cobordisms between multiple 10d string theories, predicted by the Cobordism Conjecture. We provide the microscopic worldsheet description of the configuration in a generalization of the `going up and down the RG flow' interpolations recently used in the description of IIA/IIB domain wall. The interpolations involve additional degrees of freedom, which are gapped except at the branch point, at which the gap closes and triggers the branching transition. The extra degrees of freedom admit an interpretation in terms of additional dimensions in a supercritical string theory, which reduces to the 10d junction configuration upon closed tachyon condensation. Quantum corrections of the 2d worldsheet theory turn the junction into a strongly coupled lightlike core whose UV resolution lies beyond worldsheet techniques. We construct explicit examples of junctions of 10d heterotic string theories, type 0, and type II theories and orientifolds thereof. Our explicit examples include junctions of 10d chiral theories whose chiral fields flow between different branches. One particularly nice configuration is a 4-branch junction of the IIB theory, with type I, the non-supersymmetric $USp(32)$ theory and the $U(32)$ orientifold of 0B theory, thus assembling the four non-tachyonic descendants of type 0B theory.

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arXiv2025

Non-invertible defects from the Conway SCFT to K3 sigma models II: duality and Fibonacci defects

We continue the study, initiated in [hep-th:2504.18619], of topological defect lines (TDLs) in the Conway module $V^{f \natural}$ and K3 non-linear sigma models (NLSMs). In the case of $V^{f \natural}$, we fully classify the potential $N=1$ (and $N=4$)--preserving duality defects for cyclic Tambara--Yamagami categories TY$(\mathbb{Z}_N)$, noting a curious relation to genus zero groups of monstrous moonshine. We use the correspondence with Leech lattice endomorphisms, discovered in [hep-th:2504.18619], to construct a number of non-trivial examples of TDLs in $V^{f \natural}$, including examples of irrational quantum dimension. In particular, we fully classify and construct defects for the TY$(\mathbb{Z}_2)$ and TY$(\mathbb{Z}_3)$ cases, and provide examples of duality defects for TY$(\mathbb{Z}_2\times \mathbb{Z}_2)$ and Fibonacci fusion categories as well. In the case of K3 NLSMs, we describe a duality defect of irrational quantum dimension $\sqrt{2}$ for the category TY$(\mathbb{Z}_2, -1)$ in a particular torus orbifold, which exists on a 16-dimensional slice of the moduli space. We also provide a detailed analysis of spectral flow--preserving TDLs in Gepner models of K3, of independent interest, and use this to construct non-invertible defects for Fibonacci and $Rep(S_3)$ categories in particular examples. Finally we provide evidence for our conjecture in [hep-th:2504.18619] that special subcategories of such TDLs in $V^{f \natural}$ correspond to $N=(4,4)$ and spectral flow--preserving defect lines in a corresponding K3 NLSM. In particular, we compute defect--twined elliptic genera for all non-invertible defects constructed in this article, demonstrating that for each defect found in a K3 NLSM, there is a corresponding defect in $V^{f \natural}$ with coincident twining genus, and making a prediction for a number of TDLs in K3 NLSMs yet to be found.

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arXiv2025

Towards a classification of topological defects in $K3$ sigma models

Given a $K3$ surface, a supersymmetric non-linear K3 sigma model is the internal superconformal field theory (SCFT) in a six dimensional compactification of type IIA superstring on $\mathbb{R}^{1,5} \times K3$. These models have attracted attention due to the discovery of Mathieu moonshine phenomena for the elliptic genera of K3 surfaces, and have played a pivotal role in extending Mukai's theorem on classification of symplectic automorphisms of $K3$ surfaces. We report on recent progress (arXiv:2402.08719 [hep-th]) in characterizing topological defects in $K3$ models, generalizing the notion of symmetries to categories of topological operators supported on arbitrary codimension submanifolds with possibly non-invertible fusion rules. Taking advantage of the interpretation of Mukai lattice as the D-brane charge lattice, we present a number of general results for the category of topological defect lines preserving the superconformal algebra and spectral flow, obtained by studying their fusion with boundary states. While for certain K3 models infinitely many simple defects, and even a continuum, can occur, at generic points in the moduli space the category is actually trivial, i.e. it is generated by the identity defect. Furthermore, if a K3 model is at the attractor point for some BPS configuration of D-branes, then all topological defects have integral quantum dimension. We also introduce a conjecture that a continuum of topological defects arises if and only if the K3 model is a (possibly generalized) orbifold of a torus model. These general results are confirmed by the analysis of significant examples. We also point out the connection to recent studies of topological defects in the Conway moonshine module theory (arXiv:2412.21141 [hep-th],arXiv:2504.18619 [hep-th]).

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arXiv2025

Wall crossing structure from quantum phenomena to Feynman Integrals

A growing body of evidence suggests that the complexity of Feynman integrals is best understood through geometry. Recent mathematical developments [Kontsevich and Soibelman, arXiv:2402.07343] have illuminated the role of exponential integrals as periods of twisted de Rham cocycles over Betti cycles, providing a structured approach to tackle this problem in many situations. In this paper, we apply these concepts to show how families of physically relevant integrals, ranging from exponentials to logarithmic multivalued functions, can be recast as twisted periods of differential forms over homology cycles. In the case of holomorphic exponents, we provide explicit decompositions as thimble expansions and reveal a geometric wall-crossing structure behind the analytic continuation in parameters. We then show that the generalization to multivalued functions provides the right framework to describe Feynman integrals in the Baikov representation, where the multivaluedness is governed by the logarithm of the Baikov polynomial. In this context, the thimble decomposition aligns with the decomposition into Master Integrals. We highlight how the wall-crossing structure allows for a sharp count of independent Master Integrals (or periods), circumventing complications arising from Stokes phenomena. Additionally, we study the large-parameter expansions of these integrals, whose coefficients correspond to periods of standard (co-)homology associated with families of algebraic varieties, and which reveal the dominant basis elements in different sectors of the wall crossing structure. This unifies perturbative expansions and geometric representation theory under a single cohomological framework.

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arXiv2025

Non-invertible defects from the Conway SCFT to K3 sigma models I: general results

We initiate the study of supersymmetry-preserving topological defect lines (TDLs) in the Conway moonshine module $V^{f \natural}$. We show that the tensor category of such defects, under suitable assumptions, admits a surjective but non-injective ring homomorphism into the ring of $\mathbb{Z}$-linear maps of the Leech lattice into itself. This puts strong constraints on possible defects and their quantum dimensions. We describe a simple construction of non-invertible TDLs from orbifolds of holomorphic (super)vertex operator algebras, which yields non-trivial examples of TDLs satisfying our main theorem. We conjecture a correspondence between four--plane--preserving TDLs in $V^{f\natural}$ and supersymmetry--preserving TDLs in K3 non-linear sigma models, which extends the correspondence between symmetry groups to the level of tensor category symmetry. We establish evidence for this conjecture by constructing non-invertible TDLs in special K3 non-linear sigma models.

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arXiv2025

Relative Quantum Gravity: Localized Gravity and the Swampland

We perform a systematic study of the applicability of swampland constraints to theories of localized gravity. We find that these gravity theories can violate swampland constraints, but can be reconciled with them when coupled to a higher-dimensional gravity theory. They realize what we call $\textit{relative quantum gravity}$: to become consistent at the quantum level, these gravity theories must be defined as $\textit{relative}$ to a host higher-dimensional gravity theory. We show that these theories can admit global symmetries, even anomalous ones; they can violate the cobordism, completeness, weak gravity, and distance conjectures; they may admit stable non-supersymmetric AdS vacua, or dS vacua. All swampland constraints are however satisfied when these gravity theories are regarded as relative and completed by coupling them to a higher-dimensional one. We discuss these properties in $d$-dimensional gravity theories localized on Karch-Randall End of the World (ETW) boundaries of AdS$_{d+1}$ spacetime. For AdS$_d$ ETW branes we use the formalism of double holography to describe the appearance of the species scale and the emergence of gauge dynamics from the quantum backreaction of CFT$_d$ modes. We also study microscopically the swampland constraints in localized gravity in explicit string theory models. Concretely, we exploit the 10d supergravity solutions describing AdS$_4$ ETW branes for AdS$_5\times\mathbf{S}^5$, holographically dual to semi-infinite D3-branes ending on NS5- and D5-brane configurations, realizing 4d $\mathcal{N}=4$ $SU(N)$ on half-space coupled to a 3d Gaiotto-Witten superconformal boundary CFT$_3$.

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arXiv2024

End of the World Boundaries for Chiral Quantum Gravity Theories

We describe the construction of large classes of explicit string theory backgrounds corresponding to 6d and 4d chiral theories with end of the world boundaries, and describe the strong coupling phenomena involved in gapping the chiral (but non-anomalous) sets of fields, such as strongly coupled phase transitions or symmetric mass generation. One class of 6d constructions is closely related to chirality changing phase transitions, such as those turning heterotic NS5-branes into gauge instantons, in flat space or orbifold singularities. A class of 4d models exploits systems of IIB D3-branes at toric CY3 singularities with an extra $\mathbf{Z}_2$ involution related to $G_2$ holonomy manifolds in the type IIB picture and its IIA mirror, which we explicitly describe in terms of dimer diagrams.

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arXiv2024

End of The World brane networks for infinite distance limits in CY moduli space

Dynamical Cobordism provides a powerful method to probe infinite distance limits in moduli/field spaces parameterized by scalars constrained by generic potentials, employing configurations of codimension-1 end of the world (ETW) branes. These branes, characterized in terms of critical exponents, mark codimension-1 boundaries in the spacetime in correspondence of finite spacetime distance singularities at which the scalars diverge. Using these tools, we explore the network of infinite distance singularities in the complex structure moduli space of Calabi-Yau fourfolds compactifications in M-theory with a four-form flux turned on, which is described in terms of normal intersecting divisors classified by asymptotic Hodge theory. We provide spacetime realizations for these loci in terms of networks of intersecting codimension-1 ETW branes classified by specific critical exponents which encapsulate the relevant information of the asymptotic Hodge structure characterizing the corresponding divisors.

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arXiv2024

Topological defects in K3 sigma models

We consider the topological defect lines commuting with the spectral flow and the $\mathcal{N}=(4,4)$ superconformal symmetry in two dimensional non-linear sigma models on K3. By studying their fusion with boundary states, we derive a number of general results for the category of such defects. We argue that while for certain K3 models infinitely many simple defects, and even a continuum, can occur, at generic points in the moduli space the category is actually trivial, i.e. it is generated by the identity defect. Furthermore, we show that if a K3 model is at the attractor point for some BPS configuration of D-branes, then all topological defects have integral quantum dimension. We also conjecture that a continuum of topological defects arises if and only if the K3 model is a (possibly generalized) orbifold of a torus model. Finally, we test our general results in a couple of examples, where we provide a partial classification of the topological defects.

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arXiv2023

Intersecting End of the World Branes

Dynamical cobordisms implement the swampland cobordism conjecture in the framework of effective field theory, realizing codimension 1 end of the world (ETW) branes as singularities at finite spacetime distance at which scalars diverge to infinite field space distance. ETW brane solutions provide a useful probe of infinity in moduli field spaces and the associated swampland constraints, such as the distance conjecture. We construct explicit solutions describing intersecting ETW branes in theories with multiple scalars and general potentials, so that different infinite field space limits coexist in the same spacetime, and can be simultaneously probed by paths approaching the ETW brane intersection. Our class of solutions includes physically interesting examples, such as intersections of Witten s bubbles of nothing in toroidal compactifications, generalizations in compactifications on products of spheres, and possible flux dressings thereof (hence including charged objects at the ETW branes). From the cobordism perspective, the intersections can be regarded as describing the end of the world for end of the world branes, or as boundary domain walls interpolating between different ETW brane boundary conditions for the same bulk theory.

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arXiv2023

Small Black Hole Explosions

Small black holes are a powerful tool to explore infinite distances in moduli spaces. However, we show that in 4d theories with a scalar potential growing fast enough at infinity, it is energetically too costly for scalars to diverge at the core, and the small black hole puffs up into a regular black hole, or follows a runaway behaviour. We derive a critical exponent characterizing the occurrence or not of such small black hole explosions, both from a 4d perspective, and in the 2d theory after an $\bf{S}^2$ truncation. The latter setup allows a unified discussion of fluxes, domain walls and black holes, solving an apparent puzzle in the expression of their potentials in the 4d $\cal{N}=2$ gauged supergravity context. We discuss the realization of these ideas in 4d $\cal{N}=2$ gauged supergravities. Along the way we show that many regular black hole supergravity solutions in the literature in the latter context are incomplete, due to Freed-Witten anomalies (or duals thereof), and require the emission of strings by the black hole. From the 2d perspective, small black hole solutions correspond to dynamical cobordisms, with the core describing an end of the world brane. Small black hole explosions represent obstructions to completing the dynamical cobordism. We study the implications for the Cobordism Distance Conjecture, which states that in any theory there should exist dynamical cobordisms accessing all possible infinite distance limits in scalar field space. The realization of this principle using small black holes leads to non-trivial constraints on the 4d scalar potential of any consistent theory; in the 4d $\cal{N}=2$ context, they allow to recover from a purely bottom-up perspective, several non-trivial properties of vector moduli spaces near infinity familiar from CY$_3$ compactifications.

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arXiv2022

Dynamical Cobordism and the Beginning of Time: Supercritical Strings and Tachyon Condensation

We describe timelike linear dilaton backgrounds of supercritical string theories as time-dependent Dynamical Cobordisms in string theory, with their spacelike singularity as a boundary defining the beginning of time. We propose and provide compelling evidence that its microscopic interpretation corresponds to a region of (a strong coupling version of) closed tachyon condensation. We argue that this beginning of time is closely related to (and shares the same scaling behaviour as) the bubbles of nothing obtained in a weakly coupled background with lightlike tachyon condensation. As an intermediate result, we also provide the description of the latter as lightlike Dynamical Cobordism.

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arXiv2022

At the End of the World: Local Dynamical Cobordism

The Cobordism Conjecture states that any Quantum Gravity configuration admits, at topological level, a boundary ending spacetime. We study the dynamical realization of cobordism, as spacetime dependent solutions of Einstein gravity coupled to scalars containing such end-of-the-world "branes". The latter appear in effective theory as a singularity at finite spacetime distance at which scalars go off to infinite field space distance. We provide a local description near the end-of-the-world branes, in which the solutions simplify dramatically and are characterized in terms of a critical exponent, which controls the asymptotic profiles of fields and the universal scaling relations among the spacetime distance to the singularity, the field space distance, and the spacetime curvature. The analysis does not rely on supersymmetry. We study many explicit examples of such Local Dynamical Cobordisms in string theory, including 10d massive IIA, the 10d non-supersymmetric $USp(32)$ theory, Bubbles of Nothing, 4d $ \mathcal{N}=1 $ cosmic string solutions, the Klebanov-Strassler throat, D$p$-brane solutions, brane configurations related to the D1/D5 systems, and small black holes. Our framework encompasses diverse recent setups in which scalars diverge at the core of defects, by regarding them as suitable end-of-the-world branes. We explore the interplay of Local Dynamical Cobordisms with the Distance Conjecture and other swampland constraints.

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