Swampland Constraints Research Articles

Fate of stringy noninvertible symmetries

Noninvertible 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 noninvertible gauge symmetries? In theories with gravity we find a new form of noninvertible gauge symmetry that emerges in the limit of fundamental, tensionless strings. These stringy noninvertible 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 noninvertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate noninvertible 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 subextremal states which fill in the gaps in the sublattice weak gravity conjecture. Published by the American Physical Society 2024

Finiteness of 3D higher spin gravity Landscape

Abstract We give Swampland constraints on the three dimensional Landscape of Anti-de Sitter higher spin gravity in the Chern-Simons formulation with connection valued in various split real forms of Lie algebras. We derive the finiteness conjecture by computing the upper bound on the rank of possible gauge groups then we refine it using the AdS distance conjecture. We discuss the implications of this Swampland constraint on the spectrum of higher spin gravity theories and we compare it with the gravitational exclusion principle required from BTZ black hole consideration to excerpt a constraint on the Chern-Simons level k.

Swampland constraints on the symmetry topological field theory of supergravity

We consider string/M-theory reductions on a compact space X=Xloc∪X∘, where Xloc contains the singular locus and X∘ is its complement. For the resulting supergravity theories, we construct a suitable symmetry topological field theory (SymTFT) associated with the boundary ∂Xloc∐∂X∘. We propose that boundary conditions for different Bogomol’nyi-Prasad-Sommerfield branes wrapping the same boundary cycles must be correlated for the SymTFT to yield an absolute theory consistent with quantum gravity. Using heterotic/M-theory duality, this constraint can be translated into a field-theoretic statement, which restricts the global structure of d≥7, N=1 supergravity theories to reproduce precisely the landscape of untwisted toroidal heterotic compactifications. Furthermore, for six-dimensional (2, 0) theories, we utilize a subtle interplay between gauged 0-, 2-, and 4-form symmetries to provide a bottom-up explanation of the correlated boundary conditions in K3 compactifications of type IIB. Published by the American Physical Society 2024

Intersecting end of the world branes

Dynamical cobordisms implement the swampland cobordism conjecture in the framework of effective field theory, realizing codimension-1 end of the world (ETW) branes as singularities at finite spacetime distance at which scalars diverge to infinite field space distance. ETW brane solutions provide a useful probe of infinity in moduli/field spaces and the associated swampland constraints, such as the distance conjecture.We construct explicit solutions describing intersecting ETW branes in theories with multiple scalars and general potentials, so that different infinite field space limits coexist in the same spacetime, and can be simultaneously probed by paths approaching the ETW brane intersection. Our class of solutions includes physically interesting examples, such as intersections of Witten’s bubbles of nothing in toroidal compactifications, generalizations in compactifications on products of spheres, and possible flux dressings thereof (hence including charged objects at the ETW branes). From the cobordism perspective, the intersections can be regarded as describing the end of the world for end of the world branes, or as boundary domain walls interpolating between different ETW brane boundary conditions for the same bulk theory.

Species entropy and thermodynamics

We analyse particle species and the species scale in quantum gravity from a thermodynamic perspective. In close analogy to black hole thermodynamics, we propose that particle species have an entropy and a temperature, which is determined by the species scale. This is identical to the Bekenstein-Hawking entropy of a corresponding minimal black hole and agrees with the number of species in a given tower of states. Through the species entropy, we find that certain entropy bounds are connected to recent swampland constraints. Moreover, the concept of species entropy and temperature allow us to formulate the laws of species thermodynamics, which are argued to govern the variations of moduli in string theory. They can be viewed as general rules that imply certain swampland conjectures, and vice versa.

Kination, meet Kasner: on the asymptotic cosmology of string compactifications

We study runaway, kination-dominated epochs in string cosmology. We show how the apparent classical decompactification runaway of the volume modulus, described by a kination epoch in the 4-dimensional EFT, can be uplifted to a classical Kasner solution in 10d in which the non-compact dimensions collapse towards a Big Crunch. This can also be generalised for arbitrary spacetime and compactification dimensions. We conclude with some comments on how this picture is modified by quantum effects, and the need for both dynamical and kinematical Swampland constraints.

The Scale of Supersymmetry Breaking and the Dark Dimension

We argue for a relation between the supersymmetry breaking scale and the measured value of the dark energy density Λ. We derive it by combining two quantum gravity consistency swampland constraints, which tie the dark energy density Λ and the gravitino mass M3/2, respectively, to the mass scale of a light Kaluza-Klein tower and, therefore, to the UV cut-off of the effective theory. Whereas the constraint on Λ has recently led to the Dark Dimension scenario, with a prediction of a single mesoscopic extra dimension of the micron size, we use the constraint on M3/2 to infer the implications of such a scenario for the scale of supersymmetry breaking. We find that a natural scale for supersymmetry signatures isM=OΛ18=OTeV.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ M=\\mathcal{O}\\left({\\Lambda}^{\\frac{1}{8}}\\right)=\\mathcal{O}\\left(\ extrm{TeV}\\right). $$\\end{document}This mass scale is within reach of LHC and of the next generation of hadron colliders. Finally, we discuss possible string theory and effective supergravity realizations of the Dark Dimension scenario with broken supersymmetry.

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.

Quantum gravity bounds on mathcal{N} = 1 effective theories in four dimensions

We propose quantum gravitational constraints on effective four-dimensional theories with mathcal{N} = 1 supersymmetry. These Swampland constraints arise by demanding consistency of the worldsheet theory of a class of axionic, or EFT, strings whose existence follows from the Completeness Conjecture of quantum gravity. Modulo certain assumptions, we derive positivity bounds and quantization conditions for the axionic couplings to the gauge and gravitational sector at the two- and four-derivative level, respectively. We furthermore obtain general bounds on the rank of the gauge sector in terms of the gravitational couplings to the axions. We exemplify how these bounds rule out otherwise consistent effective supergravity theories as theories of quantum gravity. Our derivations of the quantum gravity bounds are tested and further motivated in concrete string theoretic settings. In particular, this leads to a sharper version of the bound on the gauge group rank in F-theory on elliptic four-folds with a smooth base, which improves the known geometrical Kodaira bounds. We furthermore provide a detailed derivation of the EFT string constraints in heterotic string compactifications including higher derivative corrections to the effective action and apply the bounds to M-theory compactifications on G2 manifolds.

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 = ℤ3 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.

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 entropy- or 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 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.

At the end of the world: Local Dynamical Cobordism

The Cobordism Conjecture states that any Quantum Gravity configuration admits, at topological level, a boundary ending spacetime. We study the dynamical realization of cobordism, as spacetime dependent solutions of Einstein gravity coupled to scalars containing such end-of-the-world ‘branes’. The latter appear in effective theory as a singularity at finite spacetime distance at which scalars go off to infinite field space distance. We provide a local description near the end-of-the-world branes, in which the solutions simplify dramatically and are characterized in terms of a critical exponent, which controls the asymptotic profiles of fields and the universal scaling relations among the spacetime distance to the singularity, the field space distance, and the spacetime curvature. The analysis does not rely on supersymmetry. We study many explicit examples of such Local Dynamical Cobordisms in string theory, including 10d massive IIA, the 10d non-supersymmetric USp(32) theory, Bubbles of Nothing, 4d \U0001d4a9 = 1 cosmic string solutions, the Klebanov-Strassler throat, Dp-brane solutions, brane configurations related to the D1/D5 systems, and small black holes. Our framework encompasses diverse recent setups in which scalars diverge at the core of defects, by regarding them as suitable end-of-the-world branes. We explore the interplay of Local Dynamical Cobordisms with the Distance Conjecture and other swampland constraints.

Disorder averaging and its UV discontents

We present a stringy realization of quantum field theory ensembles in $D\ensuremath{\le}4$ spacetime dimensions, thus realizing a disorder averaging over coupling constants. When each member of the ensemble is a conformal field theory with a standard semiclassical holographic dual of the same radius, the resulting bulk can be interpreted as a single asymptotically anti--de Sitter space geometry with a distribution of boundary components joined by wormhole configurations, as dictated by the Hartle--Hawking wave function. This provides a UV completion of a recent proposal by Marolf and Maxfield that there is a high-dimensional Hilbert space for baby universes, but one that is compatible with the proposed swampland constraints of McNamara and Vafa. This is possible because our construction is really an approximation that breaks down both at short distances, but also at low energies for objects with a large number of microstates. The construction thus provides an explicit set of counterexamples to various claims in the literature that holographic and effective field theory considerations can be reliably developed without reference to any UV completion.

Swampland constraints on neutrino masses

Compactifying the Standard Model (SM) on a circle may lead to AdS 3D vacua, depending on the character (Majorana or Dirac) and the mass of the lightest neutrino. It has been shown that, imposing the Ooguri-Vafa conjecture that no stable non-SUSY AdS vacua are consistent with Quantum Gravity, one can obtain conditions on the mass of the lightest neutrino. This result has the shortcoming that it is in general sensitive to the UV structure of the theory. In the present paper we show that two other independent swampland conditions may yield constraints very similar to those. These other two conditions come from the AdS swampland distance conjecture and the dS conjecture as applied to AdS vacua by Lust, Palti and Vafa. Unlike the non-SUSY AdS constraints, for these conjectures the results require only local IR information of the radion potential. We consider both the case of an explicit cosmological 4D constant and the alternative of a simple quintessence 4D potential. Cosmological data in the next decade may falsify the results, giving us information on the constraints of particle physics from Quantum Gravity.

A stringy perspective on the coincidence problem

We argue that, for string compactifications broadly consistent with swampland constraints, dark energy is likely to signal the beginning of the end of our universe as we know it, perhaps even through decompactification, with possible implications for the cosmological coincidence problem. Thanks to the scarcity (absence?) of stable de Sitter vacua, dark energy in string theory is assumed to take the form of a quintessence field in slow roll. As it rolls, a tower of heavy states will generically descend, triggering an apocalyptic phase transition in the low energy cosmological dynamics after at most a few hundred Hubble times. As a result, dark energy domination cannot continue indefinitely and there is at least a percentage chance that we find ourselves in the first Hubble epoch. We use a toy model of quintessence coupled to a tower of heavy states to explicitly demonstrate the breakdown in the cosmological dynamics as the tower becomes light. This occurs through a large number of corresponding particles being produced after a certain time, overwhelming quintessence. We also discuss some implications for early universe inflation.

De Sitter quantum breaking, swampland conjectures and thermal strings

We argue that under certain assumptions the quantum break time approach and the trans-Planckian censorship conjecture both lead to de Sitter swampland constraints of the same functional form. It is a well known fact that the quantum energy-momentum tensor in the Bunch-Davies vacuum computed in the static patch of dS breaks some of the isometries. Proposing that this is a manifestation of quantum breaking of dS, we analyze some of its consequences. In particular, this leads to a thermal matter component that can be generalized to string theory in an obvious way. Imposing a censorship of quantum breaking, we recover the no eternal inflation bound in the low temperature regime, while the stronger bound from the dS swampland conjecture follows under a few reasonable assumptions about the still mysterious, presumably topological, high-temperature regime of string theory.

The swampland at large number of space-time dimensions

We discuss some aspects of swampland constraints — especially the swamp-land distance conjecture — in a large number of space-time dimensions D. We analyze Kaluza-Klein (KK) states at large D and find that some KK spectra possess an interesting dependence on D. On the basis of these observations we propose a new large dimension conjecture. We apply it to KK states of compactifications to anti-de Sitter backgrounds where it predicts an upper bound on the dimension of space-time as a function of its characteristic radius. We also apply our conjecture to black hole spacetimes, whose entropies have a D-dependence very similar to that of the KK spectrum.

Multi-field dark energy: Cosmic acceleration on a steep potential

We argue that dark energy with multiple fields is theoretically well-motivated and predicts distinct observational signatures, in particular when cosmic acceleration takes place along a trajectory that is highly non-geodesic in field space. Such models provide novel physics compared to ΛCDM and quintessence by allowing cosmic acceleration on steep potentials. From the theoretical point of view, these theories can easily satisfy the conjectured swampland constraints and may in certain cases be technically natural, potential problems which are endemic to standard single-field dark energy. Observationally, we argue that while such multi-field models are likely to be largely indistinguishable from the concordance cosmology at the background level, dark energy perturbations can cluster, leading to an enhanced growth of large-scale structure that may be testable as early as the next generation of cosmological surveys.

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.

Dynamical tadpoles and Weak Gravity Constraints

Non-supersymmetric string models are plagued with tadpoles for dynamical fields, which signal uncanceled forces sourced by the vacuum. We argue that in certain cases, uncanceled dynamical tadpoles can lead to inconsistencies with quantum gravity, via violation of swampland constraints. We describe an explicit realization in a supersymmetric toroidal Z2 × Z2 orientifold with D7-branes, where the dynamical tadpole generated by displacement of the D7-branes off its minimum leads to violation of the axion Weak Gravity Conjecture. In these examples, cancellation of dynamical tadpoles provides consistency conditions for the configuration, of dynamical nature (as opposed to the topological conditions of topological tadpoles, such as RR tadpole cancellation in compact spaces). We show that this approach provides a re-derivation of the Z-minimization criterion for AdS vacua giving the gravitational dual of a-maximization in 4d mathcal{N} = 1 toric quiver SCFTs.