arXiv subjects

Cumrun Vafa

Publications and source records attributed to Cumrun Vafa.

At least 37 records · Page 2Linked to original sources

arXiv2024

The Dark Dimension and the Grand Unification of Forces

The dark dimension scenario, predicting one extra mesoscopic dimension in the micron range, has emerged by applying various Swampland principles to the dark energy. In this note we find that realizing the grand unification of gauge forces is highly constraining in this context. Without actually constructing any GUT models, we argue that the mere assumption of grand unification of forces in this scenario, together with the experimental bounds on massive replicas of the Standard Model gauge bosons, predicts an upper bound for the GUT scale, $M_{GUT}\lesssim 10^{16}\ {\rm GeV}$. Combined with the experimental bound on the proton lifetime, this predicts that the $X$ gauge boson mediating proton decay is a 5d solitonic string of Planckian tension stretched across a length scale $L\sim ({\rm 1-10\ TeV})^{-1}$ ending on gauge branes of the same diameter $\sim L$. This leads to a mass of $M_X\sim 10^{15}-10^{16}\ {\rm GeV}$. In particular assuming grand unification in the dark dimension scenario results in a tower of Kaluza-Klein excitations of Standard Model gauge bosons on the gauge branes in the 1-10 TeV range. This suggests that the diameter/separation $L$ of the gauge branes correlates with both the weak scale $\sim 1/L$ near a TeV {\it and} the GUT scale $\sim M_5^2 L$ at $10^{16}\ {\rm GeV}$.

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arXiv2024

The Tale of Three Scales: the Planck, the Species, and the Black Hole Scales

Quantum gravity (QG) has a natural cutoff given by the Planck scale $M_{\rm pl}$. However, it is known that the EFT of gravity can break down at a lower scale, the species scale $Λ_s\lesssim M_{\rm pl}$, if there are light species of particles. Here we point out that there is a third scale $Λ_{\rm BH}\lesssim Λ_s\lesssim M_{\rm pl}$, which marks the inverse length (or the temperature) of the smallest black hole where the EFT gives a correct description of its entropy and free energy. This latter scale is hard to detect from the viewpoint of EFT as it represents a phase transition to a state with lower free energy. We illustrate this using examples drawn from consistent QG landscape. In particular $Λ_{\rm BH}$ gets related to Gregory--Laflamme transition in the decompactification limits of quantum gravity and to the Horowitz--Polchinski solution in the light perturbative string limits. We propose the existence of $Λ_{\rm BH}$ marking the temperature at which neutral black holes undergo a phase transition, as a new Swampland condition for all consistent quantum theories of gravity. In the asymptotic regimes of field space $Λ_{\rm BH}$ is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.

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arXiv2024

Swampland and the Geometry of Marked Moduli Spaces

We define the notion of a marked moduli space as the parameter space of a physical theory together with all of its observables. In geometric examples, this coincides with the mathematical notion of Teichmüller space. We propose two new Swampland principles about the geometry of marked moduli spaces: We conjecture that a marked moduli space is always contractible, and moreover, that there is a unique shortest path connecting any pair of points in it with respect to its physical metric. We provide strong evidence for these conjectures for theories with 8 or more supercharges.

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arXiv2024

Exploring new constraints on Kahler moduli space of 6d N = 1 Supergravity

We propose new constraints for 6d (1, 0) supergravity theories based on consistency conditions on the Kahler moduli spaces of their 5d reductions. The requirement that both the metric and the BPS string tensions in the Kahler moduli space are positive imposes specific restrictions on the Chern-Simons coefficients in the 5d effective Lagrangians that are derived from the Kaluza-Klein reductions of 6d theories. Moreover, the emergence of local interacting 5d CFTs when the moduli space metric degenerates introduces additional constraints coming from the analysis of 5d SCFTs. Focusing on the moduli spaces of 6d supergravity theories without a tensor multiplet and their Higgsings, we show that these constraints require the presence of certain primary states in the 2d worldvolume CFTs on 1/2 BPS strings. We specifically analyze a class of SU(2) models and infinite families of U(1) models using these constraints, and demonstrate that the theories featuring a 1-form symmetry in their massless spectra, unless the 1-form symmetry is gauged, fail to satisfy the constraints and therefore belong to the Swampland.

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arXiv2024

Axions in the Dark Dimension

The dark dimension scenario, which is motivated from Swampland principles and predicts a single micron scale extra dimension, suggests a consistent framework for the dark sector of the universe. We consider the implications of this scenario for the QCD axion. We find that in the scenario in which the axion is localized on the standard model brane (which we will argue is natural), a combination of theoretical (being bounded by the 5D Planck mass) and observational constraints forces it to have decay constant in a narrow range $f \sim 10^9 - 10^{10}$ GeV. This corresponds to a mass for the QCD axion of $m_a \sim (1 - 10)$ meV. The axion mass surprisingly coincides with the mass scale for the dark energy, the dark matter tower, and the neutrinos. In this scenario axions are not expected to form a large fraction of the dark matter but nevertheless this range of axion parameters is accessible to observations in near future experiments.

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arXiv2024

Swamplandish Unification of the Dark Sector

We provide a short overview of recent progress made in our understanding of the dark sector based on the Swampland program which in turn is rooted in lessons from string theory. We explain how the existence of one extra mesoscopic dimension (the ``dark dimension") in the micron range emerges and how this can lead to a unification of the dark energy and dark matter. In particular the smallness of the dark energy leads to the prediction of the existence of a tower of weakly interacting light particles which can naturally play the role of dark matter. Moreover this unifies dark matter with gravity as dark matter ends up being excitations of graviton in the dark dimension. We also explain how in combination with other Swampland principles one finds an explanation of the ``why now" and the ``cosmological coincidence" problems. This model is consistent with the cosmological bounds as well as the Newton's inverse square law, but makes predictions which differ from $Λ$CDM. It also gives rise to an appealing picture of hierarchy of scales in particle physics pegged to the dark energy, including a possible origin of the electroweak hierarchy and the prediction of masses of QCD axion and sterile neutrinos both in the 1-10 meV range. This review is intended for a broad audience of high energy theorists and cosmologists without prior knowledge of string theory and it explains the motivations and predictions of this program in a non-technical form.

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arXiv2024

Species Scale in Diverse Dimensions

In a quantum theory of gravity, the species scale $Λ_s$ can be defined as the scale at which corrections to the Einstein action become important or alternatively as codifying the "number of light degrees of freedom", due to the fact that $Λ_s^{-1}$ is the smallest size black hole described by the EFT involving only the Einstein term. In this paper, we check the validity of this picture in diverse dimensions and with different amounts of supersymmetry and verify the expected behavior of the species scale at the boundary of the moduli space. This also leads to the evaluation of the species scale in the interior of the moduli space as well as to the computation of the diameter of the moduli space. We also find evidence that the species scale satisfies the bound $\big|{\nabla Λ_s \over Λ_s} \big|^2\leq {1\over d-2}$ all over moduli space including the interior.

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arXiv2024

The Quasicrystalline String Landscape

In this work we investigate a largely unexplored non-geometric corner of the string landscape: the quasicrystalline orbifolds. These exist at special points of the Narain moduli leading to frozen moduli and large quantum symmetries. Here we complete the classification and construction of quasicrystalline Narain lattices and use this to explore supersymmetric compactifications in $4\leq D\leq 6$ and with $4\leq Q\leq 16$ supercharges, leading to novel theories including theories with large quantum symmetries at all points in the moduli space. We anticipate these constructions will have many applications and in subsequent papers we apply these techniques to construct non-geometric F-theory models as well as new non-supersymmetric tachyon free models. Similarly these constructions can lead to constructing exotic matter representations in the string landscape.

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arXiv2024

New Non-Supersymmetric Tachyon-Free Strings

In four decades of string theory research, only a handful of non-supersymmetric tachyon-free strings with only one neutral scalar at tree level were found. We construct new such non-supersymmetric tachyon-free string theories using asymmetric orbifolds that serve as the lower-dimensional counterparts to the $O(16) \times O(16)$ string in 4d, 6d, and 8d, each featuring only one neutral scalar at tree level, chiral matter and positive leading order cosmological constant. The 4d construction uses a quasicrystalline orbifold.

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arXiv2024

Black Hole Entropy for M-theory on the Quintic Threefold via F-theoretic Strings

Microscopic black hole entropy calculations in string theory usually proceeds through identifying them as wrapped strings in one higher dimension. For M-theory on elliptic Calabi-Yau threefolds this proceeds via its relation to F-theory in one higher dimension. Here we show how this method can be extended to M-theory on non-elliptic Calabi-Yau threefolds such as the quintic via conifold transition to elliptic threefolds. This leads to the computation of the black hole entropy through elliptic genera of the strings. However the Cardy formula for the computation of the black hole entropy of these strings fails because the relevant momentum excitations on the string are much smaller than the central charge of the strings. We show how the black hole attractor entropy formula leads to predicting corrections to the Cardy formula in this regime.

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arXiv2024

Ray-Singer Torsion, Topological Strings and Black Holes

Genus one amplitude for topological strings on Calabi-Yau 3-folds can be computed using mirror symmetry: The partition function at genus one gets mapped to a holomorphic version of Ray-Singer torsion on the mirror Calabi-Yau. On the other hand it can be shown by a physical argument that this gives a curvature squared correction term to the gravitational action. This in paticular leads to an effective quantum gravity cutoff known as the species scale, which varies over moduli space of Calabi-Yau manifolds. This resolves some of the puzzles associated to the entropy of small black holes when there are a large number of light species of particles. Thus Ray-Singer torsion, via its connection to topological strings at genus one, provides a measure of light degrees of freedom of four dimensional N=2 supergravity theories. Based on a talk given on May 12th, 2023 at the Singer Memorial Conference, MIT.

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arXiv2024

On the Fate of Stringy Non-Invertible Symmetries

Non-invertible symmetries in quantum field theory (QFT) generalize the familiar product rule of groups to a more general fusion rule. In many cases, gauged versions of these symmetries can be regarded as dual descriptions of invertible gauge symmetries. One may ask: are there any other types of non-invertible gauge symmetries? In theories with gravity we find a new form of non-invertible gauge symmetry that emerges in the limit of fundamental, tensionless strings. These stringy non-invertible gauge symmetries appear in standard examples such as non-abelian orbifolds. Moving away from the tensionless limit always breaks these symmetries. We also find that both the conventional form of non-invertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate non-invertible symmetries have implications for Swampland constraints: in certain cases they can be used to prove the existence of towers of states related to the Distance Conjecture, and can sometimes explain the existence of slightly sub-extremal states which fill in the gaps in the sublattice Weak Gravity Conjecture.

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arXiv2024

Astrophysical Constraints on Decaying Dark Gravitons

In the dark dimension scenario, which predicts an extra dimension of micron scale, dark gravitons (KK modes) are a natural dark matter candidate. In this paper, we study observable features of this model. In particular, their decay to standard matter fields can distort the CMB and impact other astrophysical signals. Using this we place bounds on the parameters of this model. In particular we find that the natural range of parameters in this scenario is consistent with these constraints and leads to the prediction that the mean mass of the dark matter today is close to a few hundred keV and the effective size of the extra dimension is around $1 - 30 \;μ\mathrm{m}$.

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arXiv2023

Dark Dimension and Decaying Dark Matter Gravitons

We explore the cosmology of the Dark Dimension scenario taking into account perturbations in the linear regime. In the context of the Dark Dimension scenario, a natural candidate for dark matter in our universe is the excitations of a tower of massive spin-2 KK gravitons. These dark gravitons are produced in the early universe and decay to lighter KK gravitons during the course of cosmological evolution. The decay causes the average dark matter mass to decrease as the universe evolves. In addition, the kinetic energy liberated in each decay leads to a kick velocity for the dark matter particles leading to a suppression of structure formation. Using current CMB (Planck), BAO and cosmic shear (KiDS-1000) data, we put a bound on the dark matter kick velocity today $v_\mathrm{today} \leq 2.2 \times 10^{-4} c$ at 95\% CL. This leads to rather specific regions of parameter space for the dark dimension scenario. The combination of the experimental bounds from cosmology, astrophysics and table-top experiments lead to the range $l_5\sim 1- 10 \, μm$ for the size of the Dark Dimension. The Dark Dimension scenario is found to be remarkably consistent with current observations and provides signatures that are within reach of near-future experiments.

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arXiv2023

On the String Landscape Without Hypermultiplets

In this work we study interesting corners of the quantum gravity landscape with 8 supercharges pushing the boundaries of our current understanding. Calabi-Yau threefolds compactifications of F/M/type II theories to 6, 5 and 4 dimensions are the most prominent examples of this class, and these always lead to a universal hypermultiplet coming from the volume/string coupling constant. We find that there are asymmetric orbifold constructions which have no hypermultiplets in 4 or 5 dimensions and no neutral hypers in 6d. We argue that these theories can also be obtained by going to strong coupling/small volume regions of geometric constructions where a new Coulomb branch opens up and moving in this direction freezes the volume/string coupling constant. Interestingly we find that the Kodaira condition encountered in geometric limits of F-theory compactifications to 6 dimensions is violated in these corners of the landscape due to strong quantum corrections. We also construct a theory in 3 dimensions which if it were to arise by toroidal compactifications from 5d, it would have to come from pure ${\mathcal N}=1$ supergravity with no massless scalar fields.

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arXiv2023

Trans-Planckian Censorship and the Swampland

In this paper, we propose a new Swampland condition, the Trans-Planckian Censorship Conjecture (TCC), based on the idea that in a consistent quantum theory of gravity sub-Planckian quantum fluctuations should remain quantum and never become larger than the Hubble horizon and freeze in an expanding universe. TCC leads to conditions that are similar to the refined dS Swampland conjecture. For example, applied to the case of cosmologies driven only by a scalar field, the TCC imposes an upper bound of $2/\sqrt{d-2}$ on the asymptotic value of $|V'|/V$. Additionally, it implies that a monotonically decreasing potential across $[ϕ_1,ϕ_2]$ satisfies $V(ϕ_2)\leq A\cdot\exp(-2(ϕ_2-ϕ_1))/\sqrt{(d-1)(d-2)})$ for some $\mathcal{O}(1)$ constant $A$. Like the dS Swampland conjecture, the TCC forbids long-lived meta-stable dS spaces, but allows sufficiently short-lived ones.

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arXiv2023

Bounds on Field Range for Slowly Varying Positive Potentials

In the context of quantum gravitational systems, we place bounds on regions in field space with slowly varying positive potentials. Using the fact that $V<Λ_s^2$, where $Λ_s(ϕ)$ is the species scale, and the emergent string conjecture, we show this places a bound on the maximum diameter of such regions in field space: $Δϕ\leq a \log(1/V) +b$ in Planck units, where $a\leq \sqrt{(d-1)(d-2)}$, and $b$ is an $\mathcal{O}(1)$ number and expected to be negative. The coefficient of the logarithmic term has previously been derived using TCC, providing further confirmation. For type II string flux compactifications on Calabi--Yau threefolds, using the recent results on the moduli dependence of the species scale, we can check the above relation and determine the constant $b$, which we verify is $\mathcal{O}(1)$ and negative in all the examples we studied.

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arXiv2023

Black Holes as Probes of Moduli Space Geometry

We argue that supersymmetric BPS states can act as efficient finite energy probes of the moduli space geometry thanks to the attractor mechanism. We focus on 4d $\mathcal{N}=2$ compactifications and capture aspects of the effective field theory near the attractor values in terms of physical quantities far away in moduli space. Furthermore, we illustrate how the standard distance in moduli space can be related asymptotically to the black hole mass. We also compute a measure of the resolution with which BPS black holes of a given mass can distinguish far away points in the moduli space. The black hole probes may lead to a deeper understanding of the Swampland constraints on the geometry of the moduli space.

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