arXiv subjects

Cumrun Vafa

Publications and source records attributed to Cumrun Vafa.

At least 19 recordsLinked to original sources

arXiv2026

The Phenomenology of the Dark Dimension and Non-Supersymmetric Strings

Swampland principles, combined with the smallness of dark energy $Λ$, lead to the dark dimension scenario, with one extra dimension of micron size. We review this scenario and its predictions: KK graviton dark matter (or the KK tower of the quintessence field into which the gravitons convert), neutrino masses tied to $Λ^{1/4}$ via a bulk $B-L$ gauge symmetry, QCD axion decay constant $f_a\sim Λ^{1/12}\sim 10^9-10^{10}$ GeV at the 5d Planck scale $M_5$, connecting electroweak hierarchy to $Λ^{1/6}$, and a relation between the GUT and weak scales with $M_5$ as the geometric mean. The dark dimension also provides a concrete realization of an evolving dark sector: the evolution of its diameter correlates the variation of dark energy with that of the dark matter mass, fitting the recent DESI DR2 (+CMB+supernovae) data while avoiding the phantom crossing that the $w_0w_a$CDM parametrization would suggest---the apparent phantom behavior instead arises from the evolving dark matter mass. The fits suggest that the dark energy field sits in the interior of moduli space, near an unstable critical point. Motivated by this, we review recent progress on non-supersymmetric string vacua: isolated critical points protected by duality symmetries, in non-geometric flux compactifications and in Scherk--Schwarz compactifications of M-theory, and an emerging duality web for non-supersymmetric strings. This note is based on two talks given by the author at String Phenomenology 2026 (Paris) and Strings 2026 (Shanghai).

hep-th↗

arXiv2026

M-theory on $S^1\vee S^1$ as Type 0A

We propose an exotic geometric M-theory dual for the weak coupling Type 0A string: compactification on a sub-Planckian $S^1\vee S^1$ (two circles connected at a point), where strong quantum effects lead to fields living on distinct resolutions of that space. Moreover we argue that tachyon condensation of the 0A theory corresponds to shrinking of one of the two circles leading to the IIA supersymmetric string. We use this and other dualities to provide an F-theoretic description of the axio-dilaton and the tachyonic field of Type 0B and argue for the existence of a strong coupling critical point of the potential using the resulting duality symmetry $Γ_0(2)\subset SL(2,\mathbb{Z})$ when tachyon field vanishes. The existence of this critical point can also be argued using conventional M-theory dualities. If this critical point is unique it is an unstable dS vacuum. Using this we propose a strong coupling conformal fixed point for a non-supersymmetric gauge theory in four dimensions living on coincident $D3^+-D3^-$branes of 0B. More generally we conjecture that the tachyon field can be identified with a pair of points on the torus parameterized by $z$ leading to the full duality group $SL(2,\mathbb{Z})$ acting on $(z,τ)$. We find tantalizing hints that for both 0A and 0B the tachyon fields can be identified with the holonomy of a flat $SU(2)$ gauge field suggesting that we have two copies of the universe interacting with one another as if they are D-branes!

hep-th↗

arXiv2026

A Type IIB Dualifold

We present evidence that ten-dimensional type IIB string theory orbifolded by the $\mathbb{Z}_3$ duality symmetry at the strong-coupling fixed point $τ=\exp(2πi/3)$ defines a consistent theory. Motivated by its F-theory dual description and its duality with M-theory in nine dimensions and type IIA string theory in eight dimensions, we argue that the resulting theory is a ten-dimensional chiral non-supersymmetric theory with a discrete gauge symmetry whose bosonic part is the automorphism group of the Narain lattice $Γ^{2,2}(A_2)$ ($S_3 \times S_3 \times \mathbb{Z}_2$). We further identify the ten-dimensional tachyon fields with the corresponding Narain moduli. Gauge anomalies cancel nontrivially through a topological Green-Schwarz mechanism involving a $\mathbb{Z}_3$-valued two-form gauge symmetry: the ten-dimensional lift of the familiar zero-form orbifold quantum symmetry in the eight-dimensional type IIA description.

hep-th↗

arXiv2026

Cosmology & Astrophysics of the Dark Dimension with Bulk Majorana Neutrinos

Recently, the possibility of having sterile Majorana neutrinos charged under $B-L$ gauge symmetry in the bulk of the dark dimension has been explored. We point out a cosmological restriction on the Majorana mass of bulk neutrinos leading to mass $\gtrsim 100~{\rm GeV}$. This avoids the over-production of Kaluza-Klein neutrino towers in the early universe thus resolving the cosmological neutrino catastrophe of extra dimension scenarios. If the mass of the bulk neutrino is at the lower end of this bound, it can potentially also explain the recently observed Fermi halo excess on gamma rays through the evaporation of long-lived 5d (i.e. dark) black holes through Hawking radiation to bulk neutrinos, which promptly decay into standard model particles.

hep-ph↗

arXiv2026

Neutrinos, B-L Symmetry and the Dark Dimension

We consider realizations of a gauged B-L symmetry in the context of the Dark Dimension scenario, where the SM lives on a codimension one brane in 5d spacetime. The B-L can naturally be a bulk gauge symmetery leading to a global symmetry on the SM brane, and have its gauge anomaly canceled by charged bulk modes. This naturally leads to the existence of 3 right-handed neutrinos propagating in the dark dimension. Allowing for spontaneous breaking of B-L in the bulk results in a massive gauge field with a very weak coupling $g_{B-L}\sim 10^{-10}$; for instance, B-L breaking at the weak scale gives $m_{B-L}\sim 100$ GeV, which is allowed by current bounds, as is a wide range of other values of the B-L breaking scale. The bulk sterile neutrinos are expected to have a mass of the order of the B-L breaking scale. Once the full Kaluza-Klein tower of bulk neutrinos is taken into account, the active neutrino masses turn out to be insensitive to the sterile neutrino mass, and reproduce the original Dark Dimension estimate $m_ν\sim y^2\langle H\rangle^2/M_5$, which leads to the observed neutrino mass scale for Yukawa couplings $y\sim 10^{-3}$.

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arXiv2026

Symmetries and M-theory-like Vacua in Four Dimensions

Non-geometric flux vacua have recently been revisited, leading to the remarkable discovery of isolated 4D ${\mathcal N}=1$ supersymmetric Minkowski vacua. These constructions rely on the non-renormalization of the superpotential, which is supported by heuristic arguments. Given the significance of verifying the existence of these isolated M-theory-like vacua, we present alternative symmetry-based arguments that arrive at the same conclusion. Additionally, we leverage these symmetries to argue for the existence of unstable dS solutions as well as supersymmetric AdS solutions.

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arXiv2026

On BPS Branes

We study supersymmetric BPS branes (BPS-B) in supergravity theories. Some of these states are anticipated by BPS black-brane (BPS-BB) solutions of supergravity. In particular, we define and distinguish the cone generated by BPS branes from the subcone of charges that admit BPS black-brane attractor solutions in the infrared limit of the supergravity effective field theory. We denote these cones by $C_{\rm BPS-B}$ and $C_{\rm BPS-BB}$, respectively. We conjecture that, in any supersymmetric theory of quantum gravity, every integrally charged state lying in $C_{\rm BPS-BB}$ is realized by a BPS state in the spectrum. Furthermore, we conjecture and present evidence that when $C_{\rm BPS-B}$ is moduli independent, it can be determined as the cone dual to the $C_{\rm BPS-BB}$ under the electric-magnetic pairing.

hep-th↗

arXiv2026

Evolving Dark Sector and the Dark Dimension Scenario

String theory naturally leads to the expectation that dark energy is not stable, and may be evolving as captured by the Swampland de Sitter conjectures. Moreover, motivated by the distance conjecture, a unification of dark sector has been proposed, where the smallness of dark energy leads to one extra dimension of micron size with dark matter being the Kaluza--Klein graviton excitations in this extra dimension. We consider the natural possibility that the radius of the dark dimension varies as the energy decreases, leading to the variation of the dark matter mass. This correlates the variation of the dark energy with the variation of the dark matter mass as they depend on the variations of a scalar field $ϕ$ controlling the radius of the extra dimension. A simple realization of this idea for small range of $ϕ$ is adequately captured by choosing a potential which is locally of the form $V=V_0\ {\rm exp}(-cϕ)$ and dark matter mass $m_{\rm DM}=m_0\ {\rm exp}(-c' ϕ)$ as was proposed in Agrawal et al. (2019). We find excellent agreement with recent experimental data from DESI DR2 combined with SN measurements (from DES, Union3 or Pantheon+) and reproduces the same significance as CPL parametrization with the added benefit of providing a natural explanation for the apparent phantom behavior ($w<-1$) reported by DESI and DES based on a physical model. DESI and SN datasets independently favor non-zero values of $c'$ and $c$, respectively, both lying within the expected $\mathcal{O}(1)$ range suggested by the Swampland criteria. Moreover, our best fit value $c'\simeq 0.05 \pm 0.01$ is remarkably consistent with the experimental upper bound of $c'\lesssim 0.2$ demanded by the lack of detection of fifth force in the dark sector.

astro-ph.CO↗

arXiv2026

Isolated Critical Points for Scherk-Schwarz Compactifications of M-theory

We consider Scherk-Schwarz compactifications of M-theory (toroidal compactifications with a non-trivial spin structure) in various dimensions and find isolated critical points of the potential on the moduli space. We demonstrate this by identifying the unbroken duality group and finding isolated points on the moduli spaces which are fixed by elements of the unbroken duality group. We work out concrete examples involving compactifications down to $d=8,6, 5$ and $4$ spacetime dimensions. We also conjecture a duality covariant anomaly cancellation condition for M-theory on $T^n$ orbifolded by discrete $\mathbb Z_N$ symmetries acting as phases on the charge lattice. This anomaly cancellation condition generalizes the level matching requirement for perturbative string orbifolds.

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arXiv2026

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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arXiv2026

A Duality Web for Non-Supersymmetric Strings

Motivated by the recently proposed geometric descriptions of 0A and 0B in M-theory and F-theory, we propose a web of duality among non-supersymmetric strings. In particular we argue that the distinct $\mathbb{Z}_2$ quotients of M-theory on $S^1\vee S^1$ lead to both 0A orientifolds as well as non-supersymmetric 10d heterotic vacua of the E-type, including the tachyon-free $SO(16)\times SO(16)$ strings. Moreover we identify certain $\mathbb{Z}_2$ quotients of F-theory on $(S^1\vee S^1)\times S^1$ with 0B orientifolds (including a tachyon-free model) as well as others with dual to non-supersymmetric heterotic strings of the D-type. Moreover using this picture we resolve some puzzles and provide further evidence for the Bergman-Gaberdiel duality between a particular 0B orientifold in 10 dimensions and the Narain compactification of 26-dimensional bosonic strings on a 16-dimensional torus, as well as the DMS conjecture of a 0A orientifold duality in 10d with a bosonic string orientifold of a Narain compactification to 10d.

hep-th↗

arXiv2026

Symmetry Points of $\mathcal{N}=1$ Modular Geometry

We consider 4d $\mathcal{N}=1$ supergravity theories with modular symmetry, where the modulus $τ$ is the upper half-plane modulo $SL(2,\mathbf{Z})$ action. We focus on enhanced discrete gauge symmetry points $τ=i, \exp(2πi/3)$, and argue that, if there are no new additional massless fields at these points, they will always be critical points of the scalar potential. Moreover, we show that whether these correspond to dS, AdS, or Minkowski vacua can be generically determined simply by the weight of the superpotential under modular transformations. We also analyze the asymptotics of the scalar potential and find that compatibility with the Swampland principles implies that, if nonvanishing, the scalar potential decays either exponentially or double-exponentially, and that the asymptotic slope is bounded. The slope is governed by the superpotential weight as well as by real-analytic modular contributions to the Kähler potential.

hep-th↗

arXiv2026

Counting AdS Vacua

We study the 'number' $\mathfrak{N}(μ)$ of AdS vacua with a UV cut off $ μ$. It has been proposed that this number is finite. We find evidence that $\mathfrak{N}(μ)\sim a \ μ^{-b}$ as $μ\rightarrow 0$ for some constants $a$ and $b$ of $O(1)$ in Planck units that may depend on dimension and the number of supercharges. For this result to hold it is crucial to integrate over the volume of massless and tachyonic directions of AdS which corresponds to the volume of the space of marginal and relevant deformations of the dual CFT. We are led to the surprising prediction that theories with large number of light moduli contribute very little to the volume measure among all theories. We also speculate about the dS case leading to the number of quasi-dS vacua of the order of $Λ^{-α}$ for some $O(1)$ parameter $α$.

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arXiv2025

Elementary Constituents Conjecture

In this note, we conjecture and provide evidence that quantum gravity cobordism classes are trivialized by elementary generators with tension at most order 1 in Planck units. Motivated by the attractor mechanism and a number of key examples, we propose that there is always a regime in the field space of the EFT in which the intrinsic tension of such an object is at most Planckian. This work brings together kinematic and dynamical aspects of cobordism defects in the context of the Swampland program.

hep-th↗

arXiv2025

Finite Landscape of 6d N=(1,0) Supergravity

We present a bottom-up argument showing that the number of massless fields in six-dimensional quantum gravitational theories with eight supercharges is uniformly bounded. Specifically, we show that the number of tensor multiplets is bounded by $T\leq 193$, and the rank of the gauge group is restricted to $r(V)\leq 480$. Given that F-theory compactifications on elliptic CY 3-folds are a subset, this provides a bound on the Hodge numbers of elliptic CY 3-folds: $h^{1,1}({\rm CY_3})\leq 491$, $h^{1,1}({\rm Base})\leq 194$ which are saturated by special elliptic CY 3-folds. This establishes that our bounds are sharp and also provides further evidence for the string lamppost principle. These results are derived by a comprehensive examination of the boundaries of the tensor moduli branch, showing that any consistent supergravity theory with $T\neq0$ must include a BPS string in its spectrum corresponding to a "little string theory" (LST) or a critical heterotic string. From this tensor branch analysis, we establish a containment relationship between SCFTs and LSTs embedded within a gravitational theory. Combined with the classification of 6d SCFTs and LSTs, this then leads to the above bounds. Together with previous works, this establishes the finiteness of the supergravity landscape for $d\geq 6$.

hep-th↗

arXiv2025

Finiteness and the Emergence of Dualities

We argue that the finiteness of quantum gravity amplitudes in fully compactified theories (at least in supersymmetric cases) leads to a bottom-up prediction for the existence of non-trivial dualities. In particular, finiteness requires the moduli space of massless fields to be compactifiable, meaning that its volume must be finite or at least grow no faster than that of Euclidean space. Moreover, we relate the compactifiability of moduli spaces to the condition that the lattice of charged objects transform in a semisimple representation under the action of the duality group. These ideas are supported by a wide variety of string theory examples.

hep-th↗

arXiv2025

Chern-Simons Theory, Holography and Topological Strings

In this note we present a brief overview of connections between Chern-Simons theory and topological strings. A prominent role in this link has been played by large N dualities and holography. We demystify this by explaining why the Kahler form should be viewed as dual to the field strength associated with a 3-form gauge potential, sourced by Lagrangian D-branes. We explain how this leads to the computation of topological string amplitudes in terms of topological vertex for toric Calabi-Yau threefolds. Furthermore, applications of topological strings to a conceptual derivation of Skein relations for link invariants as well as some of its physical applications to black hole physics are also reviewed.

math.AG↗

arXiv2025

On Measuring Distances in the Quantum Gravity Landscape

In this note, we propose a generalized notion of distance between vacua in the theory of a scalar field $ϕ$ with scalar potential $V(ϕ)$ coupled to gravity. We propose the normalized tension of domain wall connecting different field values, with a varying normalization relative to a local energy scale, as the distance. We show this definition reproduces the usual moduli space distance for zero potential, as well as the $d\propto |\log Λ|$ behavior with the vacuum energy $Λ$ in the AdS case, previously proposed in the literature. In the case of large AdS we also obtain the expected exponent of mass versus distance in one particular case, when the mass of the light tower is $m\sim \sqrt Λ$ and there is a single extra dimension decompactifying. We also discuss the features and shortcomings of alternative but related proposals.

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