arXiv subjects

Cumrun Vafa

Publications and source records attributed to Cumrun Vafa.

At least 55 records · Page 3Linked to original sources

arXiv2023

Bounds on Species Scale and the Distance Conjecture

The species scale $Λ_s\leq M_{pl}$ serves as a UV cutoff in the gravitational sector of an EFT and can depend on the moduli of the theory as the spectrum of the theory varies. We argue that the dependence of the species scale $Λ_s (ϕ)$ on massless (or light) modes $ϕ^i$ satisfies $M_{pl}^{d-2} |Λ_s'/Λ_s|^2< \mathcal{O}(1)$. This bound is true at all points in moduli space including also its interior. The argument is based on the idea that the short distance contribution of massless modes to gravitational terms in the EFT cannot dramatically affect the black hole entropy. Based on string theory arguments we expect the $\mathcal{O}(1)$ constant in this bound to be equal to ${1\over {d-2}}$ as we approach the boundary of the moduli space. However, we find that the slope of the species scale can approach its asymptotic value from above as we go from interior points to the boundaries, thereby implying that the constant in the bound must be larger than ${1\over {d-2}}$. The bound on the variation of the species scale also implies that the mass of towers of light modes cannot go to zero faster than exponential in field distance in accordance with the Distance Conjecture.

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arXiv2023

Lectures on the string landscape and the Swampland

We provide an overview of the string landscape and the Swampland program. Our review of the string landscape covers the worldsheet and spacetime perspectives, including vacua and string dualities. We then review and motivate the Swampland program from the lessons learned from the string landscape. These lecture notes are aimed to be self-contained and thus can serve as a starting point for researchers interested in exploring these ideas. These notes are an expanded version of two courses "The String Landscape and the Swampland" taught by C.~Vafa at Harvard University in 2018 with a focus on the landscape, written by M.~J.~Kang with additional material from N.~B.~Agmon, and in 2022 with a focus on the Swampland, written by A.~Bedroya.

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arXiv2023

The Dark Dimension and the Swampland

Motivated by principles from the Swampland program, which characterize requirements for a consistent UV completion of quantum gravity, combined with observational data, we are led to a unique corner of the quantum gravity landscape. In particular, using the Distance/Duality conjecture and the smallness of dark energy, we predict the existence of a light tower of states and a unique extra mesoscopic dimension of length $l\sim Λ^{-\frac{1}{4}}\sim 10^{-6}\, m$, with extra massless fermions propagating on it. This automatically leads to a candidate for a tower of sterile neutrinos, and an associated active neutrino mass scale $m_ν\sim \langle H\rangle^2\, Λ^{-\frac{1}{12}}M_{pl}^{-\frac{2}{3}}$. Moreover, assuming the mechanism for stabilization of this dark dimension leads to similar masses for active and sterile neutrinos we are led to the prediction of a Higgs vev $\langle H\rangle \sim Λ^{\frac{1}{6}}M_{pl}^{\frac{1}{3}}$. Another prediction of the scenario is a species scale ${\hat M} \sim Λ^ {\frac{1}{12}}M_{pl}^{\frac{2}{3}}\sim 10^{9}-10^{10} GeV$, corresponding to the higher-dimensional Planck scale. This energy scale may be related to the resolution of the instability of the Higgs effective potential present at a scale of $\sim 10^{11}\, GeV$. We also speculate about the interplay between this energy scale and the GZK limit on ultra-high energy cosmic rays.

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arXiv2022

Moduli-dependent Species Scale

The counting of the number of light modes in a gravitational theory is captured by the notion of the `species scale', which serves as an effective UV cutoff below the Planck scale. We propose to define a moduli-dependent species scale in the context of 4d, ${\cal N}=2$ theories, using the one loop topological free energy $F_1$, which we relate to a gravitational version of the $a$-function. This leads to $Λ_{\rm sp}\sim 1/\sqrt{F_1}$ from which we recover the expected scaling of the species scale in various corners of the moduli space. Moreover by minimizing $F_1$ we define the center of the moduli space (the `desert point') as a point where the species scale is maximal. At this point the number of light degrees of freedom is minimized.

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arXiv2022

Pure Supersymmetric AdS and the Swampland

We point out that pure supergravity theories in $AdS$ with enough supersymmetry lead, upon taking the large radius limit, to flat space quantum gravities with a nonperturbatively exact global symmetry, and are therefore in the Swampland. The argument applies to any $AdS$ supergravity with gauged R-symmetry group, including truncations of most well known examples, such as $AdS_5$ without the $S^5$ or $AdS_4$ without the $S^7$. This demonstrates that extreme scale separation, at least with enough supersymmetry, is not realizable. Moreover pure $AdS$ theories are also in conflict with some other Swampland principles including the Weak Gravity Conjecture and the (generalized) Distance Conjecture.

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arXiv2022

Holography and the KKLT Scenario

The KKLT scenario, one of the few ideas to realize dS vacua in string theory, consists of two steps: the first involves the construction of a supersymmetric AdS vacuum with a small negative cosmological constant, and the second involves breaking supersymmetry and uplifting the energy to achieve dS. In this paper we use conventional holography to argue why it is not possible to complete the first step. We obtain this by putting a bound on the central charge of the dual theory which involves branes wrapping special Lagrangian cycles in CY 4-folds. We find that $l_{\rm AdS}^2 \lesssim χ(CY_4)$. Since $l_{\rm species}^2\gtrsim χ(CY_4)$ this leads to $l_{\rm AdS}/l_{\rm species}\lesssim 1$ leading at best to a highly curved AdS which is beyond the validity of the EFT.

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arXiv2022

Dark Dimension Gravitons as Dark Matter

We consider cosmological aspects of the Dark Dimension (a mesoscopic dimension of micron scale), which has recently been proposed as the unique corner of the quantum gravity landscape consistent with both the Swampland criteria and observations. In particular we show how this leads, by the universal coupling of the Standard Model sector to bulk gravitons, to massive spin 2 KK excitations of the graviton in the dark dimension (the "dark gravitons") as an unavoidable dark matter candidate. Assuming a lifetime for the current de Sitter phase of our universe of order Hubble, which follows from both the dS Swampland Conjecture and TCC, we show that generic features of the dark dimenson cosmology can naturally lead to the correct dark matter density and a resolution of the cosmological coincidence problem, where the matter/radiation equality temperature ($T\sim$ 1 eV) coincides with the temperature where the dark energy begins to dominate. Thus one does not need to appeal to Weinberg's anthropic argument to explain this coincidence. The dark gravitons are produced at $T\sim$ 4 GeV, and their composition changes as they mainly decay to lighter gravitons, without losing much total mass density. The mass of dark gravitons is $m_{\text{DM}}\sim 1-100$ keV today.

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arXiv2022

On Upper Bounds in Dimension Gaps of CFT's

We consider CFT's arising from branes probing singularities of internal manifolds. We focus on holographic models with internal space including arbtirary Sasaki-Einstein manifolds coming from CY as well as arbitrary sphere quotients. In all these cases we show that there is a universal upper bound (depending only on the spacetime dimension) for the conformal dimension of the first non-trivial spin 2 operator in the dual CFT and a minimal diameter (in AdS units) for the internal space of the holographic dual and conjecture it holds for all CFT's.

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arXiv2021

Compactness of Brane Moduli and the String Lamppost Principle in $d>6$

We demonstrate the validity of the String Lamppost Principle-that all consistent theories of quantum gravity are in the String Landscape-for supersymmetric theories in $d>6$ using compactness and connectedness of the moduli space of small instantons, as well as the classification of the associated Coulomb branch.

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arXiv2021

The Desert and the Swampland

The most natural expectation away from asymptotic limits in moduli space of supergravity theories is the desert scenario, where there are few states between massless fields and the quantum gravity cutoff. In this paper we initiate a systematic study of these regions deep in the moduli space, and use it to place a bound on the number of massless modes by relating it to the black hole species problem. There exists a consistent sub-Planckian UV cutoff (the species scale) which resolves the black hole species problem without bounding the number of light modes. We reevaluate this in the context of supersymmetric string vacua in the desert region and show that even though heuristically the species scale is compatible with expectations, the BPS states of the actual string vacua lead to a stronger dependence of the cutoff scale on the number of massless modes. We propose that this discrepancy, which can be captured by the "BPS desert conjecture", resurrects the idea of a uniform bound on the number of light modes as a way to avoid the black hole species problem. This conjecture also implies a stronger form of the Tadpole Conjecture, which leads to an obstruction in stabilizing all moduli semi-classically for large number of moduli in flux compactifications.

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arXiv2021

Four Dimensional $\mathbf{\mathcal{N}=4}$ SYM and the Swampland

We consider supergravity theories with 16 supercharges in Minkowski space with dimensions $d>3$. We argue that there is an upper bound on the number of massless modes in such theories depending on $d$. In particular we show that the rank of the gauge symmetry group $G$ in $d$ dimensions is bounded by $r_G\leq 26-d$. This in particular demonstrates that 4 dimensional ${\cal N}=4$ SYM theories with rank bigger than 22, despite being consistent and indeed finite before coupling to gravity, cannot be consistently coupled to ${\cal N}=4$ supergravity in Minkowski space and belong to the swampland. Our argument is based on the swampland conditions of completeness of spectrum of defects as well as a strong form of the distance conjecture and relies on unitarity as well as supersymmetry of the worldsheet theory of BPS strings. The results are compatible with known string constructions and provide further evidence for the string lamppost principle (SLP): that string theory lamppost seems to capture ${\it all}$ consistent quantum gravitational theories.

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arXiv2021

Finiteness and the Swampland

We view and provide further evidence for a number of Swampland criteria, including the Weak Gravity Conjecture, Distance Conjecture and bounds on the finiteness of the quantum gravity vacua from the prism of the finiteness of black hole entropy. Furthermore we propose that at least all of these Swampland statements may be more fundamentally a consequence of the finiteness of quantum gravity amplitudes.

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arXiv2021

The FL bound and its phenomenological implications

Demanding that charged Nariai black holes in (quasi-)de Sitter space decay without becoming super-extremal implies a lower bound on the masses of charged particles, known as the Festina Lente (FL) bound. In this paper we fix the $\mathcal{O}(1)$ constant in the bound and elucidate various aspects of it, as well as extensions to $d>4$ and to situations with scalar potentials and dilatonic couplings. We also discuss phenomenological implications of FL including an explanation of why the Higgs potential cannot have a local minimum at the origin, thus explaining why the weak force must be broken. For constructions of meta-stable dS involving anti-brane uplift scenarios, even though the throat region is consistent with FL, the bound implies that we cannot have any light charged matter fields coming from any far away region in the compactified geometry, contrary to the fact that they are typically expected to arise in these scenarios. This strongly suggests that introduction of warped anti-branes in the throat cannot be decoupled from the bulk dynamics as is commonly assumed. Finally, we provide some evidence that in certain situations the FL bound can have implications even with gravity decoupled and illustrate this in the context of non-compact throats.

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arXiv2021

On The Finiteness of 6d Supergravity Landscape

We consider supergravity theories with 8 supercharges in $d=6$. We show that all the proposed anomaly free theories with unbounded number of massless modes are restricted to a finite subset and thus argue that there is an upper bound on the number of massless modes, consistent with the String Lamppost Principle.

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arXiv2021

8d Supergravity, Reconstruction of Internal Geometry and the Swampland

We sharpen Swampland constraints on 8d supergravity theories by studying consistency conditions on worldvolume theory of 3-brane probes. Combined with a stronger form of the cobordism conjecture, this leads to the reconstruction of the compact internal geometry and implies strong restrictions on the gauge algebra and on some higher derivative terms (related to the level of the current algebra on the 1-brane). In particular we argue that 8d supergravity theories with $\mathfrak{g}_2$ gauge symmetry are in the Swampland. These results provide further evidence for the string lamppost principle in 8d with 16 supercharges.

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arXiv2021

de Sitter Bubbles and the Swampland

A number of Swampland conjectures and in particular the Trans-Planckian Censorship Conjecture (TCC) suggest that de Sitter space is highly unstable if it exists at all. In this paper we construct effective theories of scalars rolling on potentials which are dual to a chain of short-lived dS spaces decaying from one to the next through a cascade of non-perturbative nucleation of bubbles. We find constraints on the effective potential resulting from various swampland criteria, including TCC, Weak Gravity Conjecture and Distance Conjecture. Surprisingly we find that TCC essentially incorporates all the other ones, and leads to a subclass of possible dual effective potentials. These results marginally rule out emergence of eternal inflation in the dual effective theory. We discuss some cosmological implications of our observations.

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arXiv2021

A CFT Distance Conjecture

We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in $d>2$ spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

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arXiv2021

Non-Holomorphic Cycles and Non-BPS Black Branes

We study extremal non-BPS black holes and strings arising in M-theory compactifications on Calabi-Yau threefolds, obtained by wrapping M2 branes on non-holomorphic 2-cycles and M5 branes on non-holomorphic 4-cycles. Using the attractor mechanism we compute the black hole mass and black string tension, leading to a conjectural formula for the asymptotic volumes of connected, locally volume-minimizing representatives of non-holomorphic, even-dimensional homology classes in the threefold, without knowledge of an explicit metric. In the case of divisors we find examples where the volume of the representative corresponding to the black string is less than the volume of the minimal piecewise-holomorphic representative, predicting recombination for those homology classes and leading to stable, non-BPS strings. We also compute the central charges of non-BPS strings in F-theory via a near-horizon $AdS_3$ limit in 6d which, upon compactification on a circle, account for the asymptotic entropy of extremal non-supersymmetric 5d black holes (i.e., the asymptotic count of non-holomorphic minimal 2-cycles).

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