arXiv subjects

Markus Dierigl

Publications and source records attributed to Markus Dierigl.

At least 19 recordsLinked to original sources

arXiv2026

A missing link: Brane networks and the Cobordism Conjecture

The absence of global symmetries in a quantum gravity theory often requires the introduction of (new) symmetry-breaking defects, which appear as singular objects in the low-energy description. This has been formalized in the Cobordism Conjecture, which further relates the asymptotics of these defects to non-trivial deformation classes of the effective theory. In this work we investigate the symmetry-breaking defects for theories with a discrete symmetry $G$ encoded in the bordism groups $\Omega^{\xi}_2 (BG)$ and, in particular, its sub-class described in terms of the homology groups $H_2(BG;\mathbb{Z})$. Contrary to expectations we find that the defects are naturally described in terms of networks of codimension-two objects rather than isolated objects in codimension three. While in special situations linking configurations of defects are sufficient, our strategy generically predicts the existence of junctions, thus suggesting an extended applicability of the Cobordism Conjecture. We demonstrate the viability of this approach in four-dimensional supergravity theories originating from string and M-theory with a discrete Heisenberg group acting on its axionic degrees of freedom.

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arXiv2026

Modified Abelian Gauge Theories

The topological properties of field configurations in gauge theory contain important data about the (generalized) global symmetries of the theory as well as potential inconsistencies in the form of gauge anomalies. In this work we modify the topological classes of Abelian $p$-form fields, generating new global variants of gauge theories. These modifications implement constraints directly on the classifying space of the gauge field and its cohomology classes via homotopy fiber construction. This general approach allows us to investigate the universal effects of the constraints on the conserved global charges encoded in gauge characteristic classes. We further demonstrate that this procedure generically leads to new topological sectors introducing additional global charges and anomalies in the modified gauge theories.

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arXiv2025

Bounds on Discrete Gauge Symmetries in Supergravity

We place bounds on the order of enhanced discrete gauge symmetries that act on massless fields and thus arise at subloci of the moduli space in supergravity theories. We focus on supersymmetric theories with 8 or more supercharges which in some cases lead to sharp upper bounds realized by specific string constructions.

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arXiv2025

Exploring Pintopia: Reflection Branes, Bordisms, and U-Dualities

The U-dualities of maximally supersymmetric non-chiral supergravity (SUGRA) theories lead to strong constraints on the non-perturbative structure of quantum gravity. In this paper we determine Spin- and Pin-lifts of these dualities, which extend this action to fermionic degrees of freedom. Among other things, this allows us to access non-supersymmetric sectors of these low energy effective field theories in which bosonic and fermionic degrees of freedom are treated differently. We use this refinement of the duality groups, in tandem with the Swampland Cobordism Conjecture, to predict new codimension-two branes. These are a natural generalization of the recently discovered R7-branes of type II string theories. The first bordism groups for Spin-twisted duality bundles follow directly from the Abelianization of the duality groups. Viewing the SUGRA theory as the low energy limit of a toroidal compactification of M-theory, winding around these codimension-two defects enacts a reflection around one of the torus directions, which in the effective field theory appears as a charge conjugation symmetry. We establish some basic properties of such branes, including determining BPS objects which can end on it, as well as braiding rules and bound states realized by multiple reflection branes.

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arXiv2025

Cobordism Utopia: U-Dualities, Bordisms, and the Swampland

The U-dualities of maximally supersymmetric supergravity theories lead to celebrated non-perturbative constraints on the structure of quantum gravity. They can also lead to the presence of global symmetries since manifolds equipped with non-trivial duality bundles can carry topological charges captured by non-trivial elements of bordism groups. The recently proposed Swampland Cobordism Conjecture thus predicts the existence of new singular objects absent in the low-energy supergravity theory, which break these global symmetries. We investigate this expectation in two directions, involving the different choices of U-duality groups $G_U$, as well as $k$, the dimension of the closed manifold carrying the topological charge. First, we compute for all supergravity theories in dimension $3 \leq D \leq 11$ the bordism groups $\Omega_1^{\text{Spin}}(BG_U)$. Second, we treat in detail the case of $D = 8$, computing all relevant bordism groups $\Omega_k^{\text{Spin}}(BG_U)$ for $1 \leq k \leq 7$. In all cases, we identify corresponding string, M-, or F-theory backgrounds which implement the required U-duality defects. In particular, we find that in some cases there is no purely geometric background available which implements the required symmetry-breaking defect. This includes non-geometric twists as well as non-geometric strings and instantons. This computation involves several novel computations of the bordism groups for $G_U = \mathrm{SL}(2,\mathbb{Z}) \times \mathrm{SL}(3,\mathbb{Z})$, which localizes at primes $p=2,3$. Whereas an amalgamated product structure greatly simplifies the calculation of purely $\mathrm{SL}(2,\mathbb{Z})$ bundles, this does not extend to $\mathrm{SL}(3,\mathbb{Z})$. Rather, we leverage the appearance of product / ring structures induced from cyclic subgroups of $G_U$ which naturally act on the relevant bordism groups.

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arXiv2025

(Quadratically) Refined Discrete Anomaly Cancellation

In this work we study the cancellation of non-perturbative anomalies of gravitational theories with gauge group $\mathbb{Z}_k$ in six dimensions. These subtle anomalies require a classification of deformation classes of manifolds with discrete gauge bundles known as bordism groups. The consistency of the theory demands a cancellation of the fermion anomalies, which can be done by the transformation properties of 2-form fields in the theory. Since the 2-forms in six dimensions are themselves chiral, their formulation needs subtle topological information encoded in a so-called quadratic refinement. A matching between the fermionic anomalies and the defining properties of the quadratic refinement, lead to strong consistency constraints on the charged fermion spectrum. We explicitly determine these consistency conditions for the case of a single chiral 2-form and various discrete gauge groups. Since we provide a model-independent formulation, these restrictions hold universally for theories of this type.

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arXiv2024

Frozen Generalized Symmetries

M-theory frozen singularities are (locally) $D$- or $E$-type orbifold singularities with a background fractional $C_3$-monodromy surrounding them. In this paper, we revisit such backgrounds and address several puzzling features of their physics. We first give a top-down derivation of how the $D$- or $E$-type 7D $\mathcal{N}=1$ gauge theory directly ``freezes" to a lower rank gauge theory due to the $C_3$-background. This relies on a Hanany--Witten effect of fractional M5 branes and the presence of a gauge anomaly of fractional D$p$ probes in the circle reduction. Additionally, we compute defect groups and 8D symmetry topological field theories (SymTFTs) of the 7D frozen theories in several duality frames. We apply our results to understanding the evenness condition of strings ending on $O7^+$-planes, and calculating the global forms of supergravity gauge groups of M-theory compactified on $T^4/\Gamma$ with frozen singularities. In an Appendix, we also revisit IIA $ADE$ singularities with a $C_1$-monodromy along a 1-cycle in the boundary lens space and show that this freezes the gauge degrees-of-freedom via confinement.

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arXiv2024

The Axion is Going Dark

In this work we explore the effect of a non-Abelian dark sector gauge group that couples to the axion field. In particular, we analyze effects that arise if the dark sector gauge group mixes topologically with the Standard Model. This is achieved by gauging a subgroup of the global center 1-form symmetries which embeds non-trivially in both the visible as well as the dark sector gauge groups. Leaving the local dynamics unchanged, this effect modifies the quantization conditions for the topological couplings of the axion, which enter the estimate of a lower bound on the axion-photon coupling. In the presence of a dark sector this lower bound can be reduced significantly, which might open up interesting new parameter regions for axion physics. We further determine the allowed exotic matter representations in the presence of topological mixing with a dark sector, explore the generalized categorical symmetries of such axion theories, and comment on other model-independent phenomenological consequences.

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arXiv2023

IIB Explored: Reflection 7-Branes

The Swampland Cobordism Conjecture successfully predicts the supersymmetric spectrum of 7-branes of IIB / F-theory. Including reflections on the F-theory torus, it also predicts the existence of new non-supersymmetric objects, which we dub reflection 7-branes (R7-branes). We present evidence that these R7-branes only exist at strong coupling. R7-branes serve as end of the world branes for 9D theories obtained from type IIB asymmetric orbifold and Dabholkar-Park orientifold backgrounds, and an anomaly inflow analysis suggests the existence of a gapless Weyl fermion, which would have the quantum numbers of a goldstino. Using general arguments, we conclude that different kinds of branes are able to end on the R7, and accounting for their charge requires exotic localized degrees of freedom, for which the simplest possibility is a massless 3-form field on the R7-brane worldvolume. We also show how to generalize the standard F-theory formalism to account for reflections.

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arXiv2023

R7-Branes as Charge Conjugation Operators

R7-branes are a class of recently discovered non-supersymmetric real codimension-two duality defects in type IIB string theory predicted by the Swampland Cobordism Conjecture. For type IIB realizations of 6D SCFTs with $\mathcal{N} = (2,0)$ supersymmetry, wrapping an R7-brane "at infinity" leads to a topological operator associated with a zero-form charge conjugation symmetry that squares to the identity. Similar considerations hold for those theories obtained from further toroidal compactification, but this can be obstructed by bundle curvature effects. Using some minimal data on the topological sector of the R7-branes, we extract the associated fusion rules for these charge conjugation operators. More broadly, we sketch a top down realization of various topological operators / interfaces associated with $\mathsf{C}$, $\mathsf{R}$, and $\mathsf{T}$ transformations. We also use holography to provide strong evidence for the existence of the R7-brane which is complementary to the Cobordism Conjecture. Similar considerations apply to other string-realized QFTs with symmetry operators constructed via non-supersymmetric branes which carry a conserved charge.

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arXiv2023

The Chronicles of IIBordia: Dualities, Bordisms, and the Swampland

In this work we investigate the Swampland Cobordism Conjecture in the context of type IIB string theory geometries with non-trivial duality bundle. Quite remarkably, we find that many non-trivial bordism classes with duality bundles in Mp$(2,\mathbb{Z})$, a double cover of SL$(2,\mathbb{Z})$ related to fermions, correspond to asymptotic boundaries of well-known supersymmetric F-theory backgrounds. These include $[p,q]$-7-branes, non-Higgsable clusters, S-folds, as well as various lower-dimensional generalizations. These string theoretic objects break the global symmetries associated to the non-trivial bordism groups, providing a strong test of the Cobordism Conjecture. Further including worldsheet orientation reversal promotes the duality group to the Pin$^+$ cover of GL$(2,\mathbb{Z})$. The corresponding bordism groups require a new non-supersymmetric "reflection 7-brane" and its compactifications to ensure the absence of global symmetries, thus providing an interesting prediction of the Cobordism Conjecture for non-supersymmetric type IIB backgrounds. A major component of the present work is the explicit derivation of the involved bordism groups as well as their generators, which correspond to asymptotic boundaries of explicit string theory backgrounds. The main tool is the Adams spectral sequence, to which we provide a detailed introduction. We anticipate that the same techniques can be applied in a wide variety of settings.

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arXiv2022

The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings

We study global anomalies of discrete gauge symmetries in six-dimensional supergravities and their realizations in F-theory. We explicitly construct a discrete Green-Schwarz mechanism that depends on the choice of a coupling constant and on a certain quadratic refinement in differential cohomology. By geometrically engineering theories with $G=\mathbb{Z}_3$ gauge symmetry and no tensor multiplets, we observe that a particular choice of the quadratic refinement is singled out in F-theory. This implies new Swampland constraints on the discrete charge spectra of 6d supergravities. On the other hand, the discrete Green-Schwarz coupling depends on the geometry of the Calabi-Yau. We use anomaly inflow to relate this to a 't Hooft anomaly of the induced global symmetry in the worldsheet theories of non-critical strings. Using topological symmetry lines, we further relate this anomaly to the modular properties of twisted-twined elliptic genera. We then argue that the latter are encoded in the A-model topological string partition functions on different torus fibrations that are equipped with a flat torsional B-field. This allows us to derive a geometric expression for the global discrete anomaly in terms of the height-pairing of a multi-section on a genus one fibered Calabi-Yau.

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arXiv2022

Large and Small Non-extremal Black Holes, Thermodynamic Dualities, and the Swampland

In this paper we discuss black hole solutions parametrized by their entropy $\mathcal{S}$ and temperature $\mathcal{T}$ in gravitational effective theories. We are especially interested in the analysis of the boundary regions in the $\mathcal{T}-\mathcal{S}$ diagram, i.e. large/small values of entropy and temperature, and their relation to Swampland constraints. To explore this correlation, we couple the gravitational theories to scalar fields and connect limits of thermodynamic quantities of black holes to scalar field excursions in the corresponding solutions. Whenever the scalar fields traverse an infinite field distance, the Swampland Distance Conjecture allows for a reformulation in terms of {\it entropy-} or {\it temperature-distance}. The effective theories with scalars we investigate are Einstein-Maxwell-dilaton theory as well as $\mathcal{N} = 2$ supergravity in four dimensions. The relation of the latter to type II string theory compactified on Calabi-Yau 3-folds often allows for a direct identification of the corresponding light tower of states. These setups also point towards various dualities between asymptotic regions of the black hole solution. In the context of $\mathcal{N} = 2$ supergravity black holes, these {\it thermodynamic dualities} have an interpretation in terms of T- and S-dualities along the internal directions and their natural action on Kaluza-Klein and winding states.

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arXiv2022

One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions

String and 5-brane junctions are shown to succinctly classify all known 8d ${\cal N}$=1 string vacua. This requires an extension of the description for ordinary $[p,q]$-7-branes to consistently include O7$^+$-planes, which then naturally encodes the dynamics of $\mathfrak{sp}_n$ gauge algebras, including their higher-form center symmetries. Central to this analysis are loop junctions, i.e., strings/5-branes which encircle stacks of 7-branes and O7$^+$'s. Loop junctions further signal the appearance of affine symmetries of emergent 9d descriptions at the 8d moduli space's boundaries. Such limits reproduce all 9d string vacua, including the two disconnected rank (1,1) moduli components.

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arXiv2022

The Fate of Discrete 1-Form Symmetries in 6d

Recently introduced generalized global symmetries have been useful in order to understand non-perturbative aspects of quantum field theories in four and lower dimensions. In this paper we focus on 1-form symmetries of weakly coupled 6d supersymmetric gauge theories coupled to dynamical tensor multiplets. We study the consistency of global 1-form symmetries corresponding to the center of the gauge groups, or subgroups thereof, by activating their background fields, which makes the instanton density fractional. In 6d, an instanton background for a given gauge theory sources BPS strings via tadpole cancellation. The non-trivial 1-form symmetry background configurations contribute to the charge of the BPS strings. However, Dirac quantization imposes restrictions on the consistent 1-form backgrounds, since they can in general lead to and induce fractional charges, thus making (part of) the putative higher-form symmetry inconsistent. This gives explicit criteria to determine whether the discrete 1-form symmetries are realized. We implement these criteria in concrete examples originating from string compactifications. We also corroborate this by finding that a non-trivial fractional contribution is related to states which explicitly break the global 1-form symmetry appearing as massive excitations of the 6d BPS strings. For 6d theories consistently coupled to gravity, this hints at a symmetry breaking tower of states. When the fractional contributions are absent, the F-theory realization of the theories points to the gauging of the 1-form symmetry via the presence of non-trivial Mordell--Weil torsion.

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arXiv2021

Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality

We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations of the gauge group topology in F-theory via Mordell--Weil torsion and string junctions. We further study dimensional reductions of the 11d Chern--Simons term in the presence of torsional boundary $G_4$-fluxes, which encode background gauge fields of center 1-form symmetries in the lower-dimensional effective gauge theory. We find contributions that can be interpreted as 't Hooft anomalies involving the 1-form symmetry which originate from a fractionalization of the instanton number of non-Abelian gauge theories in F-/M-theory compactifications to 8d/7d and 6d/5d.

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arXiv2021

The anomaly that was not meant IIB

Type IIB supergravity enjoys a discrete non-Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F-theory. Remarkably, a subtle modification of the standard 10d Chern-Simons term cancels these anomalies, a fact which relies on the ***specific*** field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green-Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.

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arXiv2021

On the Gauge Group Topology of 8d CHL Vacua

Compactifications of the CHL string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice $Λ_M$, the so-called Mikhailov lattice. Based on this data, we devise a method to determine the global gauge group structure including all $U(1)$ factors. The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual. Interpreting a non-trivial $π_1(G) \equiv {\cal Z}$ for the non-Abelian gauge group $G$ as having gauged a ${\cal Z}$ 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly (arXiv:2008.10605) that would obstruct this gauging. We verify this by explicitly computing ${\cal Z}$ for all 8d CHL vacua with rank$(G)=10$. Since our method applies also to $T^2$ compactifications of heterotic strings, we further establish a map that determines any CHL gauge group topology from that of a "parent" heterotic model.

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