Grassman Manifolds and Global Properties of the Riccati Equation
Riccati differential equations are studied as vector fields on a Grassman manifold. Such manifolds serve as a compactification for the Riccati equations.
Martin, Clyde↗
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ISLES: Probing Extra Dimensions Using a Superconducting Accelerometer
In string theories, extra dimensions must be compactified. The possibility that gravity can have large radii of compactification leads to a violation of the inverse square law at submillimeter distances. The objective of ISLES is to perform a null test of Newton s law in space with a resolution of one part in 10(exp 5) or better at 100 microns. The experiment will be cooled to less than or equal to 2 K, which permits superconducting magnetic levitation of the test masses. To minimize Newtonian errors, ISLES employs a near null source, a circular disk of large diameter-to-thickness ratio. Two test masses, also disk-shaped, are suspended on the two sides of the source mass at a nominal distance of 100 microns. The signal is detected by a superconducting differential accelerometer. A ground test apparatus is under construction.
Paik, Ho Jung↗
Joint statistics of cosmological constant and SUSY breaking in flux vacua with nilpotent Goldstino
We obtain the joint distribution of the gravitino mass and the cosmological constant in KKLT and LVS models with anti-D3 brane uplifting described via the nilpotent goldstino formalism. Moduli stabilisation (of both complex structure and Kähler moduli) is incorporated so that we sample only over points corresponding to vacua. Our key inputs are the distributions of the flux superpotential, the string coupling and the hierarchies of warped throats. In the limit of zero cosmological constant, we find that both in KKLT and LVS the distributions are tilted favourably towards lower scales of supersymmetry breaking.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Large U(1) charges from flux breaking in 4D F-theory models
We study the massless charged spectrum of U(1) gauge fields in F-theory that arise from flux breaking of a nonabelian group. The U(1) charges that arise in this way can be very large. In particular, using vertical flux breaking, we construct an explicit 4D F-theory model with a U(1) decoupled from other gauge sectors, in which the massless/light fields have charges as large as 657. This result greatly exceeds prior results in the literature. We argue heuristically that this result may provide an upper bound on charges for light fields under decoupled U(1) factors in the F-theory landscape. We also show that the charges can be even larger when the U(1) is coupled to other gauge groups.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Landscaping the strong CP problem
One often hears that the strong CP problem is the one problem which cannot be solved by anthropic reasoning. We argue that this is not so. Due to nonperturbative dynamics, states with a different CP violating paramenter θ acquire different vacuum energies after the QCD phase transition. These add to the total variation of the cosmological constant in the putative landscape of Universes. An interesting possibility arises when the cosmological constant is mostly cancelled by the membrane nucleation mechanism. If the step size in the resulting discretuum of cosmological constants, ΔΛ, is in the interval (meV) 4 < ΔΛ < (100 MeV) 4 , the cancellation of vacuum energy can be assisted by the scanning of θ. For (meV) 4 < ΔΛ < (keV) 4 this may yield θ < 10 -10 , meeting the observational limits. This scenario opens up 24 orders of magnitude of acceptable parameter space for ΔΛ compared to membrane nucleation acting alone. In such a Universe one may not need a light axion to solve the strong CP problem.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Topological data analysis for the string landscape
Persistent homology computes the multiscale topology of a data set by using a sequence of discrete complexes. In this paper, we propose that persistent homology may be a useful tool for studying the structure of the landscape of string vacua. As a scaled-down version of the program, we use persistent homology to characterize distributions of Type IIB flux vacua on moduli space for three examples: the rigid Calabi-Yau, a hypersurface in weighted projective space, and the symmetric six-torus $T^6 = (T^2)^3$. These examples suggest that persistence pairing and multiparameter persistence contain useful information for characterization of the landscape in addition to the usual information contained in standard persistent homology. We also study how restricting to special vacua with phenomenologically interesting low-energy properties affects the topology of a distribution
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On brane gaugino condensates in 10d
We analyze the structure of gaugino interactions on D7-branes from a 10d perspective. This is essential if one wants to lift the standard 4d approach to type IIB moduli stabilization to 10d. In particular, a 10d picture has recently been used to raise concerns about the KKLT proposal for constructing de Sitter vacua, and to lend support to swampland conjectures against de Sitter. However, the analyses of brane gaugino condensation so far are plagued by UV divergences and do not include local 4-fermion terms. They also fail to reproduce the 4-fermion terms required by supergravity when compactified to four dimensions. Motivated by the structure of heterotic and Hořava-Witten theories, we suggest an extension of the brane action by a particular 4-fermion operator that resolves the above problems. Crucially, the UV divergence is cancelled and the expected structure of the 4d effective action is reproduced. We believe that attempts at a 10d description of KKLT have to be reconsidered in this new light.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Consistent truncations and dualities
Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in double field theory, which have been shown to be in one-to-one correspondence with Poisson-Lie T-duality. Here we demonstrate that this relation is only the tip of the iceberg. Currently, the most general known classes of T-dualities (excluding mirror symmetry) are based on dressing cosets. But as we discuss, they can be further extended to the even larger class of generalised cosets. We prove that the latter give rise to consistent truncations for which the ansatz can be constructed systematically. Hence, we pave the way for many new examples of T-dualities and consistent truncations. The arising structures result in covariant tensors with more than two derivatives and we argue how they might be key to understand generalised T-dualities and consistent truncations beyond the leading two derivative level.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
AdS scale separation and the distance conjecture
It has been argued that orientifold vacua with fluxes in type IIA string theory can achieve moduli stabilisation and arbitrary decoupling between the AdS and KK scales upon sending certain unconstrained RR-flux quanta to infinity. In this paper, we find a novel scalar field in the open-string sector that allows us to interpolate between such IIA vacua that differ in flux quanta and find that the limit of large fluxes is nicely consistent with the distance conjecture. This shows that the massive IIA vacua pass an important Swampland criterion and suggests that scale-separated AdS vacua might not be in the Swampland. Our analysis also naturally suggests a flux analogue of “Reid’s fantasy” where flux vacua that differ in quantised flux numbers can be connected through trajectories in open-string field space and not just via singular domain walls.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Towards natural and realistic E 7 GUTs in F-theory
We consider phenomenological aspects of a natural class of Standard Model-like supersymmetric F-theory vacua realized through flux breaking of rigid E 7 gauge factors. Three generations of Standard Model matter are realized in many of these vacua. We further find that many other Standard Model-like features are naturally compatible with these constructions. For example, dimension-4 and 5 terms associated with proton decay are ubiquitously suppressed. Many of these features are due to the group theoretical structure of E 7 and associated F-theory geometry. In particular, a set of approximate global symmetries descends from the E 7 group, leading to exponential suppression of undesired couplings.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Understanding KKLT from a 10d perspective
Some of the most well-celebrated constructions of metastable de Sitter vacua from string theory, such as the KKLT proposal, involve the interplay of gaugino condensation on a D7-brane stack and an uplift by a positive tension object. These constructions have recently been challenged using arguments that rely on the trace-reversed and integrated 10d Einstein equation. We give a critical assessment of such concerns. We first relate an integrated 10d Einstein equation to the extremization condition for a 10d-derived 4d effective potential. Then we argue how to obtain the latter from a 10d action which incorporates gaugino condensation in a (recently proposed) manifestly finite, perfect-square form. This effective potential is consistent with 4d supergravity and does not present obstacles for an uplifted minimum. Moreover, within standard approximations, we understand the uplift explicitly in one of the popular versions of the integrated 10d equation. Our conclusion is that de Sitter constructions of the KKLT type cannot be dismissed simply based on the integrated 10d equations considered so far.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
An F-theory realization of the chiral MSSM with Z 2 -parity
Using F-theory we construct 4D N=1 SUGRA theories with the Standard Model gauge group, three chiral generations, and matter parity in order to forbid all dimension four baryon and lepton number violating operators. The underlying geometries are derived by constructing smooth genus-one fibered Calabi-Yau fourfolds using toric tops that have a Jacobian fibration with rank one Mordell-Weil group and SU( 3 ) × SU( 2 ) singularities. The necessary gauge backgrounds on the smooth fourfolds are shown to be fully compatible with the quantization condition, including positive integer D3-tadpoles. This construction realizes for the first time a consistent UV completion of an MSSM-like model with matter parity in F-theory. Moreover our construction is general enough to also exhibit other relevant Z 2 charge extensions of the MSSM such as lepton and baryon parity. Such models however are rendered inconsistent by non-integer fluxes, which are necessary for producing the exact MSSM chiral spectrum. As a result, these inconsistencies turn out to be intimately related to field theory considerations regarding a UV-embedding of the Z 2 into a U( 1 ) and the resulting discrete anomalies.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Towards an “$\mathrm{AdS}_1$/$\mathrm{CFT}_0$” correspondence from the $\mathrm{D}$(-1)/$\mathrm{D}$7 system?
We argue that a type IIB Euclidean supergravity solution of the form $\mathbb{R}$ x S 1 x $\mathbb{T}$ 8 with imaginary self-dual F 1 flux through $\mathbb{R}$ x S 1 belongs to the chain of AdS d x S d x $\mathbb{T}$ 10-2d vacua with (imaginary) self-dual Fd flux, where d ≤ 5. Such vacua come from the near-horizon of D(d - 2)/D(8 - d) branes and are supersymmetric for odd values of d. For d = 1 we speculate that the hallmark of conformal symmetry for the matrix model dual is a vanishing free energy. The matrix dual was recently constructed by [1] by adding matrix interactions coming from strings stretching between the D(-1) and D7 branes to the IKKT matrix model. We find that the corresponding supergravity solution indeed has vanishing on-shell action. Specific F 5 fluxes need to be switched on as a consequence of (a T-dual version of) the Hanany-Witten effect.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Neutralizing topological obstructions to bubbles of nothing
Theories with compact extra dimensions can exhibit a vacuum instability known as a bubble of nothing. These decay modes can be obstructed if the internal manifold is stabilized by fluxes, or if it carries Wilson lines for background gauge fields, or if the instanton is incompatible with the spin structure. In each of these cases the decay can proceed by adding dynamical charged membranes or gauge fields. We give a general, bottom-up procedure for constructing approximate bubble of nothing solutions in models with internal spheres stabilized by flux and study the influence of the brane tension on the tunneling exponent, finding two branches of solutions that merge at a minimal superextremal value of the tension. In the case of Wilson operators and incompatible fermions, the relevant bubble is shown to be the Euclidean Reissner-Nordstrom black hole, and the ordinary decay exponent is modified by 1/g 2 effects. We examine the Dirac operator on this background and comment on the relevance for models of supergravity with gauged R-symmetry.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Searching the landscape of flux vacua with genetic algorithms
In this paper, we employ genetic algorithms to explore the landscape of type IIB flux vacua. We show that genetic algorithms can efficiently scan the landscape for viable solutions satisfying various criteria. More specifically, we consider a symmetric T 6 as well as the conifold region of a Calabi-Yau hypersurface. We argue that in both cases genetic algorithms are powerful tools for finding flux vacua with interesting phenomenological properties. We also compare genetic algorithms to algorithms based on different breeding mechanisms as well as random walk approaches.
79 ASTRONOMY AND ASTROPHYSICS↗
Heterotic backgrounds via generalised geometry: moment maps and moduli
We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an SU(3) × Spin(6 + n) structure within O(6, 6 + n) x $\mathbb{R}$ + generalised geometry. Supersymmetry of the background is encoded in the existence of an involutive subbundle of the generalised tangent bundle and the vanishing of a moment map for the action of diffeomorphisms and gauge symmetries. We give both the superpotential and the Kähler potential for a generic background, showing that the latter defines a natural Hitchin functional for heterotic geometries. Intriguingly, this formulation suggests new connections to geometric invariant theory and an extended notion of stability. Finally we show that the analysis of infinitesimal deformations of these geometric structures naturally reproduces the known cohomologies that count the massless moduli of supersymmetric heterotic backgrounds.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Gauge symmetry breaking with fluxes and natural Standard Model structure from exceptional GUTs in F-theory
We give a general description of gauge symmetry breaking using vertical and remainder fluxes in 4D F-theory models. The fluxes can break a geometric gauge group to a smaller group and induce chiral matter, even when the larger group admits no chiral matter representations. We focus specifically on applications to realizations of the Standard Model gauge group and chiral matter spectrum through breaking of rigid exceptional gauge groups E 7 , E 6 , which are ubiquitous in the 4D F-theory landscape. Supplemented by an intermediate SU(5) group, these large classes of models give natural constructions of Standard Model-like theories with small numbers of generations of matter in F-theory.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Do we live in the swampland?
A low-energy effective theory is said to be in the swampland if it does not have any consistent UV completion inside a theory of quantum gravity. The natural question is if the standard model of particle physics, possibly with some minimal extensions, are in the swampland — we are in trouble if the answer to this question is yes. We discuss this question in view of the recent swampland conjectures. We prove a no-go theorem concerning the modification of the Higgs sector. Moreover, we find that QCD axion is incompatible with the recent swampland conjectures, unless some sophisticated possibilities are considered. We discuss the implications of this result for spontaneous breaking of CP symmetry. We comment on dynamical supersymmetry breaking as well as the issue of multi-valuedness of the potential. We also propose a refinement of the de Sitter swampland conjecture.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗