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DOE OSTI2024

Gopakumar-Vafa invariants and the Emergent String Conjecture

Abstract The Emergent String Conjecture of Lee, Lerche, and Weigand holds that every infinite-distance limit in the moduli space of a quantum gravity represents either a decompactification limit or an emergent string limit in some duality frame. Within the context of 5d supergravities coming from M-theory compactifications on Calabi-Yau threefolds, we find evidence for this conjecture by studying (a) the gauge couplings and (b) the BPS spectrum, which is encoded in the Gopakumar-Vafa invariants of the threefold. In the process, we disuss a testable geometric consequence of the Emergent String Conjecture, and we verify that it is satisfied in all complete intersection Calabi-Yau threefolds in products of projective spaces (CICYs).

Physics↗
DOE OSTI2025

cymyc: $\underline{C}$alabi-$\underline{Y}$au $\underline{M}$etrics, $\underline{Y}$ukawas, and $\underline{C}$urvature

We introduce cymyc, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associated moduli spaces. We develop a well-defined geometric ansatz to numerically model tensor fields of arbitrary degree on a large class of Calabi-Yau manifolds. cymyc includes a machine learning component which incorporates this ansatz to model tensor fields of interest on these spaces by finding an approximate solution to the system of partial differential equations they should satisfy.

differential and algebraic geometry↗
DOE OSTI2023

Entanglement and topology in RG flows across dimensions: caps, bridges and corners

We quantitatively address the following question: for a QFT which is partially compactified, so as to realize an RG flow from a D-dimensional CFT in the UV to a d-dimensional CFT in the IR, how does the entanglement entropy of a small spherical region probing the UV physics evolve as the size of the region grows to increasingly probe IR physics? This entails a generalization of spherical regions to setups without full Lorentz symmetry, and we study the associated entanglement entropies holographically. We find a tight interplay between the topology and geometry of the compact space and the evolution of the entanglement entropy, with universal transitions from ‘cap’ through ‘bridge’ and ‘corner’ phases, whose features reflect the details of the compact space. As concrete examples we discuss twisted compactifications of 4d $\mathcal{N}$ = 4 SYM on T 2 , S 2 and hyperbolic Riemann surfaces.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

4-manifolds and topological modular forms

We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0, 1) supersymmetry and, possibly, a residual flavor symmetry. The equivariant topological Witten genus of this 2d theory then produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic (topological) modular forms. We describe basic properties of this map and present a few simple examples. As a byproduct, we obtain some new results on ’t Hooft anomalies of 6d (1, 0) theories and a better understanding of the relation between 2d (0, 1) theories and TMF spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Dark matter and dark radiation from the early universe with a modulus coupled to the PQMSSM

The supersymmetrized DFSZ axion model is especially compelling in that it contains 1. the SUSY solution to the gauge hierarchy problem, 2. the Peccei-Quinn (PQ) solution to the strong CP problem and 3. the Kim-Nilles solution to the SUSY μ problem. In a string setting, where a discrete R-symmetry ($Z$$^{R}_{24}$ for example) may emerge from the compactification process, a high-quality accidental axion (accion) can emerge from the accidental, approximate remnant global U(1) PQ symmetry where the decay constant f a is linked to the SUSY breaking scale, and is within the cosmological sweet zone. In this setup, one also expects the presence of stringy remnant moduli fields Φ i . Here, we consider the situation of a single light modulus Φ coupled to the PQMSSM in the early universe, with mixed axion plus higgsino-like WIMP dark matter. We evaluate dark matter and dark radiation production via nine coupled Boltzmann equations and assess the severity of the cosmological moduli problem (CMP) along with dark matter and dark radiation production rates. We find that typically the light modulus mass should be m Φ ≳ 10 4 TeV to avoid the moduli-induced dark matter overproduction problem. If one is able to (anthropically) tune the modulus field amplitude, we find a value of Φ 0 ≲ 10 –7 m P would be required to solve the overall CMP.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Moduli stabilisation and the statistics of axion physics in the landscape

String theory realisations of the QCD axion are often said to belong to the anthropic window where the decay constant is around the GUT scale and the initial misalignment angle has to be tuned close to zero. In this paper we revisit this statement by studying the statistics of axion physics in the string landscape. We take moduli stabilisation properly into account since the stabilisation of the saxions is crucial to determine the physical properties of the corresponding axionic partners. We focus on the model-independent case of closed string axions in type IIB flux compactifications and find that their decay constants and mass spectrum feature a logarithmic, instead of a power-law, distribution. In the regime where the effective field theory is under control, most of these closed string axions are ultra-light axion-like particles, while axions associated to blow-up modes can naturally play the role of the QCD axion. Hence, the number of type IIB flux vacua with a closed string QCD axion with an intermediate scale decay constant and a natural value of the misalignment angle is only logarithmically suppressed. In a recent paper we found that this correlates also with a logarithmic distribution of the supersymmetry breaking scale, providing the intriguing indication that most, if not all, of the phenomenologically interesting quantities in the string landscape might feature a logarithmic distribution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Semiclassics with ’t Hooft flux background for QCD with 2-index quarks

We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small $\mathbb{R}^2$× T 2 with a suitable magnetic flux. We first discuss the ’t Hooft anomaly of these theories and claim that discrete chiral symmetry should be spontaneously broken completely to satisfy the anomaly matching condition. The T 2 compactification with the magnetic flux preserves the ’t Hooft anomaly, and the 2d effective theory is constrained by the same anomaly of 4d QCD(Sym/ASym). We demonstrate the spontaneous breakdown of chiral symmetry using the dilute gas of center vortices, which confirms the prediction of the ’t Hooft anomaly. We also find that each vacuum maintains the charge conjugation symmetry, and this gives affirmative support for the nonperturbative large-N orientifold equivalence between QCD(Sym/ASym) and $\mathcal{N}$ = 1 supersymmetric SU(N) Yang-Mills theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Conformal symmetries for extremal black holes with general asymptotic scalars in STU supergravity

We present a construction of the most general BPS black holes of STU supergravity (N = 2 supersymmetric D = 4 supergravity coupled to three vector super-multiplets) with arbitrary asymptotic values of the scalar fields. These solutions are obtained by acting with a subset of the global symmetry generators on STU BPS black holes with zero values of the asymptotic scalars, both in the U-duality and the heterotic frame. The solutions are parameterized by fourteen parameters: four electric and four magnetic charges, and the asymptotic values of the six scalar fields. We also present BPS black hole solutions of a consistently truncated STU supergravity, which are parameterized by two electric and two magnetic charges and two scalar fields. These latter solutions are significantly simplified, and are very suitable for further explicit studies. We also explore a conformal inversion symmetry of the Couch-Torrence type, which maps any member of the fourteen-parameter family of BPS black holes to another member of the family. Furthermore, these solutions are expected to be valuable in the studies of various swampland conjectures in the moduli space of string compactifications.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Fine-tuned vs. natural supersymmetry: what does the string landscape predict?

A vast array of (metastable) vacuum solutions arise from string compactifications, each leading to different 4-d laws of physics. The space of these solutions, known as the string landscape, allows for an environmental solution to the cosmological constant problem. We examine the possibility of an environmental solution to the gauge hierarchy problem. We argue that the landscape favors softly broken supersymmetric models over particle physics models containing quadratic divergences, such as the Standard Model. We present a scheme for computing relative probabilities for supersymmetric models to emerge from the landscape. The probabilities are related to the likelihood that the derived value of the weak scale lies within the Agrawal et al. (ABDS) allowed window of values leading to atoms as we know them. This then favors natural SUSY models over unnatural (SUSY and other) models via a computable probability measure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Winding θ and destructive interference of instantons

While the θ dependence of field theories is 2π periodic, the ground-state wavefunctions at θ and θ + 2π often belong to different classes of symmetry-protected topological states. When this is the case, a continuous change of the θ parameter can introduce an interface that supports a nontrivial field theory localized on the wall. We consider the 2d CP N-1 sigma model as an example and construct a weak-coupling setup of this interface theory by considering the small S1 compactification with nonzero winding θ parameter and a suitable symmetry-twisted boundary condition. This system has N classical vacua connected by fractional instantons, but the anomaly constraint tells us that the fractional-instanton amplitudes should vanish completely to have N-fold degeneracy at the quantum level. We show how this happens in this purely bosonic system, uncovering that the integration over the zero modes annihilates the fractional instanton amplitudes, in sharp contrast to what happens when the θ angle is constant. Moreover, we provide another explanation of this selection rule by showing that the N perturbative vacua acquire different charges under the global symmetry with the activation of the winding θ angle. We also demonstrate a similar destructive interference between instanton effects in the CP N-1 quantum mechanics with the Berry phase.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Analytic bounds on late-time axion-scalar cosmologies

The cosmological dynamics of multiple scalar/pseudoscalar fields are difficult to solve, especially when the field-space metric is curved. This presents a challenge in determining whether a given model can support cosmic acceleration, without solving for the on-shell solution. In this work, we present bounds on late-time FLRW-cosmologies in classes of theories that involve arbitrary numbers of scalar and pseudoscalar fields coupled both kinetically (leading to a curved field space metric) and through scalar potentials. Such bounds are proven analytically, independently of initial conditions, with no approximation in the field equations and without referring to explicit solutions. Besides their broad applications to cosmological model building, our bounds can be applied to studying asymptotic cosmologies of certain classes of string compactifications.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs

Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge C T , we clarify the properties of stress tensor composite primary operators of minimal twist, [ T m ], using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling $\left\langle {\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^m\right]\right\rangle$, where ${\mathcal{O}}_L$ is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling $\left\langle TT{\mathcal{O}}_L\right\rangle$, the three-point coupling $\left\langle {\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^2\right]\right\rangle$ is modified at large C T if $\left\langle TT{\mathcal{O}}_L\right\rangle \sim \sqrt{C_T}$. This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to ${\mathcal{O}}_L $ can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin- ℓ ≥ 2 bulk field at tree level, or any spin ℓ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Brill-Noether-general limit root bundles: absence of vector-like exotics in F-theory Standard Models

Root bundles appear prominently in studies of vector-like spectra of 4d F-theory compactifications. Of particular importance to phenomenology are the Quadrillion F-theory Standard Models (F-theory QSMs). In this work, we analyze a superset of the physical root bundles whose cohomologies encode the vector-like spectra for the matter representations ($3$, $2$) 1/6 , ($\overline{3}$, $1$) -2/3 and ($1$, $1$) 1 . For the family B 3 (Δ$^{°}_{4}$) consisting of $\mathcal{O}$(10 11 ) F-theory QSM geometries, we argue that more than 99.995% of the roots in this superset have no vector-like exotics. This indicates that absence of vector-like exotics in those representations is a very likely scenario in the O(10 11 ) QSM geometries B 3 (Δ$^{°}_{4}$). The QSM geometries come in families of toric 3-folds B 3 (Δ°) obtained from triangulations of certain 3-dimensional polytopes Δ°. The matter curves in X Σ $\large{ϵ}$ B 3 (Δ°) can be deformed to nodal curves which are the same for all spaces in B 3 (Δ°). Therefore, one can probe the vector-like spectra on the entire family B 3 (Δ°) from studies of a few nodal curves. We compute the cohomologies of all limit roots on these nodal curves. In our applications, for the majority of limit roots the cohomologies are determined by line bundle cohomology on rational tree-like curves. For this, we present a computer algorithm. The remaining limit roots, corresponding to circuit-like graphs, are handled by hand. The cohomologies are independent of the relative position of the nodes, except for a few circuits. On these jumping circuits, line bundle cohomologies can jump if nodes are specially aligned. This mirrors classical Brill-Noether jumps. B 3 (Δ°) admits a jumping circuit, but the root bundle constraints pick the canonical bundle and no jump happens.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Unitarization from geometry

We study the perturbative unitarity of scattering amplitudes in general dimensional reductions of Yang–Mills theories and general relativity on closed internal manifolds. For the tree amplitudes of the dimensionally reduced theory to have the expected high-energy behavior of the higher-dimensional theory, the masses and cubic couplings of the Kaluza–Klein states must satisfy certain sum rules that ensure there are nontrivial cancellations between Feynman diagrams. These sum rules give constraints on the spectra and triple overlap integrals of eigenfunctions of Laplacian operators on the internal manifold and can be proven directly using Hodge and eigenfunction decompositions. One consequence of these constraints is that there is an upper bound on the ratio of consecutive eigenvalues of the scalar Laplacian on closed Ricci-flat manifolds with special holonomy. This gives a sharp bound on the allowed gaps between Kaluza–Klein excitations of the graviton that also applies to Calabi–Yau compactifications of string theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Sharpening the Distance Conjecture in diverse dimensions

The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field distance ||$\phi$|| as m ~ exp(–λ||$\phi$||), where λ is order-one in Planck units. While the evidence for this conjecture is formidable, there is at present no consensus on which values of λ are allowed. In this paper, we propose a sharp lower bound for the lightest tower in a given infinite-distance limit in d dimensions: λ ≥ $1/\sqrt{d-2}$. In support of this proposal, we show that (1) it is exactly preserved under dimensional reduction, (2) it is saturated in many examples of string/M-theory compactifications, including maximal supergravity in d = 4 – 10 dimensions, and (3) it is saturated in many examples of minimal supergravity in d = 4 – 10 dimensions, assuming appropriate versions of the Weak Gravity Conjecture. We argue that towers with λ < $1/\sqrt{d-2}$ discussed previously in the literature are always accompanied by even lighter towers with λ ≥ $1/\sqrt{d-2}$, thereby satisfying our proposed bound. We discuss connections with and implications for the Emergent String Conjecture, the Scalar Weak Gravity Conjecture, the Repulsive Force Conjecture, large-field inflation, and scalar field potentials in quantum gravity. In particular, we argue that if our proposed bound applies beyond massless moduli spaces to scalar fields with potentials, then accelerated cosmological expansion cannot occur in asymptotic regimes of scalar field space in quantum gravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Degenerate domain walls in supersymmetric theories

In supersymmetric Yang–Mills theories tension-degenerate domain walls are typical. Adding matter fields in fundamental representation, we arrive at supersymmetric quantum chromodynamics (SQCD) supporting similar walls. We demonstrate that the degenerate domain walls can belong to one of two classes: i) locally distinguishable, i.e. those which differ from each other locally (which could be detected in local measurements); and ii) those which have identical local structure and are differentiated only topologically, through a judicially chosen compactification of R 4 . Depending on the number of flavors F and the pattern of Higgsing, both classes can coexist among SQCD k walls interpolating between the vacua n and n + k . We prove that the overall multiplicity of the domain walls obtained after accounting for both classes is ν N , k walls = N ! / [ ( N − k ) ! k ! ] , as was discovered previously in limiting cases. (Here, N is the number of colors.) Thus, ν N , k walls is a peculiar index. For the locally distinguishable degenerate domain walls, we observe two-wall junctions, a phenomenon specific for supersymmetry with central extensions. This phenomenon does not exist for topological replicas.

Chen, Shi↗
DOE OSTI2020

Baryogenesis from a modulus dominated universe

String/ M-theory compactifications predict the existence of a modulus field with a mass of 100-10000 TeV. Its decay at MeV-temperatures generates large amounts of entropy and washes out any previously produced baryon asymmetry. We describe how the baryon asymmetry can be (re)generated by the modulus decay. Lastly, the mechanism relates the smallness of the asymmetry to the hierarchy between the Planck- and the Fermi-scale.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Early-time measure in eternal inflation

In a situation like eternal inflation, where our data is replicated at infinitely-many other space-time events, it is necessary to make a prior assumption about our location to extract predictions. The principle of mediocrity entails that we live at asymptotic late times, when the occupational probabilities of vacua has settled to a near-equilibrium distribution. In this paper we further develop the idea that we instead exist during the approach to equilibrium, much earlier than the exponentially-long mixing time. In this case we are most likely to reside in vacua that are easily accessed dynamically. Using first-passage statistics, we prove that vacua that maximize their space-time volume at early times have: 1. maximal ever-hitting probability; 2. minimal mean first-passage time; and 3. minimal decay rate. These requirements are succinctly captured by an early-time measure. The idea that we live at early times is a predictive guiding principle, with many phenomenological implications. First, our vacuum should lie deep in a funneled region, akin to folding energy landscapes of proteins. Second, optimal landscape regions are characterized by relatively short-lived vacua, with lifetime of order the de Sitter Page time. For our vacuum, this lifetime is ~ 10 130 years, which is consistent with the Standard Model estimate due to Higgs metastability. Third, the measure favors vacua with small, positive vacuum energy. This can address the cosmological constant problem, provided there are sufficiently many vacua in the entire ensemble of funnels. As a concrete example, we study the Bousso-Polchinski lattice of flux vacua, and find that the early-time measure favors lattices with the fewest number of flux dimensions. This favors compactifications with a large hierarchy between the lightest modulus and all other Kähler and complex structure moduli.

79 ASTRONOMY AND ASTROPHYSICS↗