arXiv subjects

Ralph Blumenhagen

Publications and source records attributed to Ralph Blumenhagen.

At least 19 recordsLinked to original sources

arXiv2026

A Novel Matrix Model for the M5-brane?

We provide a new formal extension of the BFSS matrix model by an additional 5-bracket. Maximal supersymmetry leads us to promote the BFSS 2-bracket structure constants to a dynamical field $H_{abc}$ governed by a Chern-Simons-like kinetic term. We first show that the full generic pseudo-action is invariant under maximal supersymmetry and that the associated supersymmetry algebra closes upon invoking a number of BPS-like quadratic constraints. We then present a special case based on the 5-Lie algebra $A_6$ that evades these additional constraints and allows for a Lagrangian description. These results hinge on a conspiracy of properties of the $SO(9)$ gamma matrices and the 2- and 5-brackets. Compellingly, the resulting model seems to realize some features expected of a theory containing M5-branes and opens up the possibility of further including higher brackets for the M6- and M9-branes.

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arXiv2026

Towards the Realization of the Dark Dimension Scenario in Ho\v{r}ava-Witten Theory

It has been suggested that Ho\v{r}ava-Witten theory could provide a concrete realization of the Dark Dimension Scenario. In this context, the observable Standard Model sector is naturally localized in the micron-sized large dimension, which is the interval in the eleventh direction. Considering Calabi-Yau manifolds supporting generic vector bundles including also abelian factors, we point out that symmetric tadpole cancellation on the $E_8$ walls has the potential to ameliorate some of the issues of such a realization, including too fast proton decay. By taking not only the hierarchically small value of the dark energy but also the size of the Standard Model gauge couplings into account, one is driven to a special infinite distance limit, which is the Ho\v{r}ava-Witten analogue of a limit recently at the focus of the M-theoretic Emergence Proposal. Extrapolating results obtained for BPS-saturated amplitudes, we speculate about the possibility of obtaining the moduli dependence of the scalar potential, the gauge couplings and the Planck scale by simple one-loop Schwinger integrals over towers of states.

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arXiv2026

Taxonomy of Instanton Corrections in Infinite Distance Limits

Using the BPS-protected higher derivative $R^4$-term as an exactly solvable example, we analyze which instanton corrections are generated by a one-loop Schwinger integral over the light towers of states that arise in infinite distance limits in moduli space. We find that the Schwinger integral fully captures precisely those instantons whose action lies parametrically in the window $(\Lambda_{\rm sp}/M_{\rm light})^{-1}\le {\rm S}_{\rm inst}\le \Lambda_{\rm sp}/M_{\rm light}$, that is, instantons whose action is bounded by the ratio of the gravity cutoff and the mass scale of the lightest tower. This proposal is supported by considering the entire moduli space of toroidal compactifications in eight dimensions, together with a number of limits in seven dimensions. In each case, integrating out the light towers via the Schwinger integral reproduces the complete contribution of the instantons within the above window. We further recast the proposal in terms of the taxonomy classification, allowing us to determine the emergent instantonic spectrum associated with any infinite distance limit.

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arXiv2026

Comments on the Emergence of 4D Topological Amplitudes in M-Theory

The M-theoretic Emergence Proposal claims that all of the terms in the low-energy action arise from quantum effects. After reviewing the current status of this proposal, we focus on four-dimensional compactifications with $N=2$ supersymmetry, where kinetic terms are encoded in topological string amplitudes, such as the prepotential $F_0$. Evidence for the emergence of such terms was provided recently, where in particular it was shown that the classical cubic term in $F_0$ can be obtained by integrating out the light towers of states in the M-theory limit, using a novel regularization of the infinite sum over Gopakumar/Vafa invariants. We address two issues that were left open. First, we show that the regularization can be equivalently performed in complex structure moduli space and in K\"ahler moduli space. Second, we extend the proposed regularization to the linear terms in the one-loop prepotential $F_1$.

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arXiv2025

Emergence of CY Triple Intersection Numbers in M-theory

To give more credence to the M-theoretic Emergence Proposal it is important to show that also classical kinetic terms in a low energy effective action arise as a quantum effect from integrating out light towers of states. We show that for compactifications of type IIA on Calabi-Yau manifolds, the classical weak coupling Yukawa couplings, which are the triple intersection numbers of the Calabi-Yau threefold, can be obtained from the 1/2-BPS protected one-loop Schwinger integral over $D2$-$D0$ bound states, after employing a novel regularization for the final infinite sum of Gopakumar-Vafa invariants. Approaching the problem in a consecutive manner from 6D decompactification over emergent string to the ultimate M-theory limits, we arrive at a mathematically concrete regularization that involves finite distance degeneration limits of Calabi-Yau threefolds in an intriguing way. We test and challenge this proposal by the concrete determination of the periods around such degeneration points for threefolds with one K\"ahler modulus and the two examples $\mathbb P_{1,1,1,6,9}[18]$ and $\mathbb P_{1,1,2,2,6}[12]$.

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arXiv2025

Emergence of $F^4$-couplings in Heterotic/Type IIA Dual String Theories

The M-theoretic emergence proposal claims that in an isotropic decompactification limit to M-theory the full effective action is generated via quantum effects by integrating out only the light towers of states of the theory. In the BPS particle sector, these include transversally wrapped $M2$- and $M5$-branes possibly carrying Kaluza-Klein momentum. This implies that a longitudinally wrapped $M5$-brane, i.e. a wrapped $D4$-brane, is not to be included in emergence computations. In this work we collect explicit evidence supporting this point by examining an $F^4$ gauge coupling in six dimensions, making use of the duality between heterotic string theory on $T^4$ and strongly coupled type IIA on K3. In this instance, the M-theoretic emergence proposal can be viewed as a tool for making predictions for the microscopic behavior of string theoretic amplitudes.

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arXiv2025

Non-associative Algebras of Cubic Matrices and their Gauge Theories

Motivated by M-theory, we define a new type of non-associative algebra involving usual and cubic matrices at the same time. The resulting algebra can be regarded as a two-term truncated $L_\infty$ algebra giving rise to a fundamental identity between the two- and the three-bracket. We provide a simple class of concrete examples of such algebras based on the structure constants of a Lie algebra. Connecting to previous results on higher structures, we generalize the construction of Yang-Mills theories, topological BF theory and generalized IKKT models and point out some appearing issues.

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arXiv2024

Reflections on an M-theoretic Emergence Proposal

In a pedagogical manner, we review recent developments in the investigation of the Emergence Proposal. Although it is fair to say that this idea is still at an exploratory level and a fully coherent picture has yet to be developed, we put it into perspective to previous work on the swampland program and on emergence in QG. In view of the emergent string conjecture, we argue and provide evidence that it is not the emergent string but rather the decompactification limit which is a natural candidate for the potential realization of the Emergence Proposal. This resonates in a compelling way with old ideas of emergence in M(-atrix) theory and gives rise to a number of further speculations.

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arXiv2024

Demystifying the Emergence Proposal

We revisit the Emergence Proposal in the vector multiplet moduli space of type IIA N=2 supersymmetric string vacua in four dimensions, for which the string tree-level prepotential and the string one-loop correction are exactly known via mirror symmetry. We argue that there exists an exact notion of emergence, according to which these four-dimensional couplings can be computed exactly in any asymptotic limit in field space. In such limits, a perturbative quantum gravity theory emerges, whose fundamental degrees of freedom include all complete infinite towers of states with typical mass scale not larger than the species scale. For a decompactification limit, this picture is closely related to and in fact motivated by the computation of Gopakumar-Vafa invariants. In addition, in the same limit our results suggest that the emergent theory will also contain asymptotically tensionless wrapped NS5-branes.

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arXiv2024

Emergence of $R^4$-terms in M-theory

It has been recently suggested that the strong Emergence Proposal is realized in M-theory limits by integrating out all light towers of states with a typical mass scale not larger than the species scale, i.e. the eleventh dimensional Planck mass. Within the BPS sector, these are transverse $M2$- and $M5$-branes, that can be wrapped and particle-like, carrying Kaluza-Klein momentum along the compact directions. We provide additional evidence for this picture by revisiting and investigating further the computation of $R^4$-interactions in M-theory \`a la Green-Gutperle-Vanhove. A central aspect is a novel UV-regularization of Schwinger-like integrals, whose actual meaning and power we clarify by first applying it to string perturbation theory. We consider then toroidal compactifications of M-theory and provide evidence that integrating out all light towers of states via Schwinger-like integrals thus regularized yields the complete result for $R^4$-interactions. In particular, this includes terms that are tree-level, one-loop and space-time instanton corrections from the weakly coupled point of view. Finally, we comment on the conceptual difference of our approach to earlier closely related work by Kiritsis-Pioline and Obers-Pioline, leading to a correspondence between two types of constrained Eisenstein series.

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arXiv2023

The Emergence Proposal and the Emergent String

We explore the Emergence Proposal for the moduli metric and the gauge couplings in a concrete model with 7 saxionic and 7 axionic moduli fields, namely the compactification of the type IIA superstring on a 6-dimensional toroidal orbifold. We show that consistency requires integrating out precisely the 12 towers of light particle species arising from KK and string/brane winding modes and one asymptotically tensionless string up to the species scale. After pointing out an issue with the correct definition of the species scale in the presence of string towers, we carry out the emergence computation and find that the KK and winding modes indeed impose the classical moduli dependence on the one-loop corrections, while the emergent string induces moduli dependent logarithmic suppressions. The interpretation of these results for the Emergence Proposal are discussed revealing a couple of new and still not completely settled aspects.

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arXiv2023

The Emergent M-theory Limit

It has been recently proposed that at each infinite distance limit in the moduli space of quantum gravity a perturbative description emerges with fundamental degrees of freedom given by those infinite towers of states whose typical mass scale is parametrically not larger than the ultraviolet cutoff, identified with the species scale. This proposal is applied to the familiar ten-dimensional type IIA and IIB superstring theories, when considering the limit of infinite string coupling. For type IIB, the light towers of states are given by excitations of the D1-brane, as expected from self-duality. Instead, for type IIA at strong coupling, which is dual to M-theory on $S^1$, we make the observation that the emergent degrees of freedom are bound states of transversal M2- and M5-branes with Kaluza-Klein momentum along the circle. We speculate on the interpretation of the necessity of including all these states for a putative quantum formulation of M-theory.

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arXiv2023

Dimensional Reduction of Cobordism and K-theory

It has been proposed that cobordism and K-theory groups, which can be mathematically related in certain cases, are physically associated to generalised higher-form symmetries. As a consequence, they should be broken or gauged in any consistent theory of quantum gravity, in accordance with swampland conjectures. We provide further support to this idea by showing that cobordism and K-theory groups of a general manifold $X$ reproduce the pattern of symmetries expected from the dimensional reduction of the theory on $X$, as well as their breaking and gauging. To this end, we employ the Atiyah-Hirzebruch spectral sequence to compute such groups for common choices of $X$ in string compactifications.

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arXiv2023

Dynamical Cobordism Conjecture: Solutions for End-of-the-World Branes

We analyze finite size solutions for a generalized $D$-dimensional Dudas-Mourad (DM) model featuring dynamical cobordism with neutral and charged end-of-the-world (ETW) defect branes. Confirming a dynamical version of the Cobordism Conjecture, we explicitly construct non-isotropic solutions for the latter codimension one branes and show the appearance of a lower bound $δ\ge 2\sqrt{(D-1)/(D-2)}$ for the critical exponent in the scaling behavior of the distance and the curvature close to the wall. This allows us to make a connection to the (sharpened) Swampland Distance Conjecture and the (Anti-) de Sitter Distance Conjecture. Moreover, BPS orientifold planes appear as special cases in our analysis and the whole picture is consistent with dimensional reduction from ten to $D$ dimensions. An analogous analysis is performed for a generalized Blumenhagen-Font (BF) model featuring neutral codimension two ETW-branes where the same lower bound for the scaling parameter $δ$ arises.

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arXiv2023

The Dark Dimension in a Warped Throat

By combining swampland conjectures with observational data, it was suggested that our universe should lie in an asymptotic region of the quantum gravity landscape. The generalized distance conjecture for dS, the smallness of the cosmological constant and astrophysical constraints led to a scenario with one mesoscopic large dimension of size $\ell\sim Λ^{-1/4}\sim 10^{-6}$m. We point out that a strongly warped throat with its redshifted KK tower provides a natural string theoretic mechanism that realizes the scaling $m\sim Λ^α$ with the factor $α=1/4$, the dark dimension being the one along the throat. We point out that in string theory it could be challenging to keep other KK towers heavy enough to avoid a conflict with astrophysical constraints on the number of extra large dimensions.

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arXiv2022

Mass Hierarchies and Quantum Gravity Constraints in DKMM-refined KKLT

We carefully revisit the mass hierarchies for the KKLT scenario with an uplift term from an anti D3-brane in a strongly warped throat. First, we derive the bound resulting from what is usually termed "the throat fitting into the bulk" directly from the Klebanov-Strassler geometry. Generating the small value of the superpotential $W_{0}$ via the mechanism proposed by Demirtas, Kim, McAllister and Moritz (DKMM), we identify two possible DKMM-refined KKLT scenarios for stabilizing the light axio-dilaton modulus. The first scenario spoils the expected hierarchy between the bulk and the throat mass scales and implies that the energy scale of the uplift is larger than the species scale of the effective theory in the throat. Moreover it requires an unnaturally large tadpole $N\sim 10^{7-8}$ that is certainly in conflict with tadpole cancellation. For the less restricted second scenario, the hierarchy can be controlled at the expense of, under the most optimistic assumptions, an only moderately large tadpole $N\sim 10^{2-3}$.

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arXiv2022

Dynamical Cobordism of a Domain Wall and its Companion Defect 7-brane

Starting from an already known solution in the literature, we study the dynamical cobordism induced by the backreaction of a non-supersymmetric, positive tension domain wall in string theory. This could e.g. be a non-BPS D8-brane of type I or a $\overline{D8}/O8$ stack of a non-supersymmetric type IIA orientifold. The singularities which typically appear indicate either an inherent inconsistency of this background or the required presence of a suitable defect, as predicted by the cobordism conjecture. We provide evidence that this end-of-the-world $7$-brane is explicitly described by a new kind of non-isotropic solution of the dilaton-gravity equations of motion. Intriguingly, on the formal level this solution turns out to be closely related to the initial solution for the non-supersymmetric domain wall.

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arXiv2022

Open-Closed Correspondence of K-theory and Cobordism

Non-trivial K-theory groups and non-trivial cobordism groups can lead to global symmetries which are conjectured to be absent in quantum gravity. Inspired by open-closed string duality, we propose a correspondence between the two groups, which can be considered as the physical manifestation of a generalisation of the classic Conner--Floyd isomorphism. The picture is exemplified by the relations between KO-groups and Spin-cobordisms and between K-groups and Spin$^c$-cobordisms. Global symmetries related by such isomorphism are eventually gauged. By combining K-theory and cobordism, we recover then tadpole cancellation conditions in type I string theory and F-theory from a bottom-up perspective.

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