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Supersymmetry Breaking with Fields, Strings and Branes (2511.04367v1)
Published 6 Nov 2025 in hep-th, gr-qc, hep-ph, math-ph, and math.MP
Abstract: The first part of this review tries to provide a self-contained view of supersymmetry breaking from the bottom-up perspective. We thus describe N=1 supersymmetry in four dimensions, the Standard Model and the MSSM, with emphasis on the soft terms'' that can link it to supergravity. The second part deals with the top-down perspective. It addresses, insofar as possible in a self-contained way, the basic setup provided by ten-dimensional strings and their links with supergravity, toroidal orbifolds, Scherk-Schwarz deformations and Calabi-Yau reductions, before focusing on a line of developments that is closely linked to our own research. Its key input is drawn from ten-dimensional non-tachyonic string models where supersymmetry is absent or non-linearly realized, and runawaytadpole potentials'' deform the ten-dimensional Minkowski vacua. We illustrate the perturbative stability of the resulting most symmetrical setups, which are the counterparts of circle reduction but involve internal intervals. We then turn to a discussion of fluxes in Calabi-Yau vacua and the KKLT setup, and conclude with some aspects of Cosmology, emphasizing some intriguing clues that the tadpole potentials can provide for the onset of inflation. The appendices collect some useful material on global and local N=1 supersymmetry, in components and in superspace, on string vacuum amplitudes, and on convenient tools used to examine the fluctuations of non-supersymmetric string vacua.
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Overview
This paper is a review about “supersymmetry breaking” in physics. Supersymmetry is a big idea that suggests every known particle (like electrons or quarks) has a partner particle. We haven’t seen these partner particles yet, so if supersymmetry exists, it must be hidden or “broken” in our universe. The authors explain how scientists try to understand and model this breaking using two viewpoints: one that starts from known physics and builds up (bottom‑up), and one that starts from string theory and higher dimensions and works down to our world (top‑down).
Key Objectives and Questions
The paper looks at friendly, step‑by‑step ways to answer questions like:
- How could supersymmetry work together with the Standard Model of particle physics?
- How can supersymmetry be broken in a controlled way so the math stays sensible?
- What can string theory (which uses tiny vibrating strings and extra dimensions) teach us about supersymmetry breaking?
- How do special shapes of extra dimensions, “fluxes,” and “branes” help create realistic universes?
- Can these ideas connect to the early universe and explain things like inflation (a very fast expansion right after the Big Bang)?
Methods and Approach
The authors organize the review into two main paths and explain the tools used along the way.
Bottom‑Up: From Known Physics to Supersymmetry
- Start with the Standard Model (the best current theory describing particles and forces, except gravity).
- Extend it to the MSSM (Minimal Supersymmetric Standard Model), which adds superpartner particles.
- Discuss “soft terms.” These are small, carefully chosen tweaks that break supersymmetry gently, so calculations don’t blow up. Think of “soft breaking” like loosening a bolt just enough that the machine still runs smoothly.
- Connect to “supergravity,” which is supersymmetry plus gravity. This helps link particle physics to the shape of spacetime.
Top‑Down: From String Theory to Our Universe
- Begin with supergravity in 10 and 11 dimensions and with string theory, where particles are tiny strings and can live on “branes” (membranes of various dimensions where strings can end).
- Compactification: roll up extra dimensions so they are too small to see. A torus (like a donut) is a simple example. More complex shapes called Calabi–Yau spaces are like intricate, curled-up six‑dimensional surfaces.
- Orbifolds and orientifolds: ways of folding and reflecting these shapes to create different physical effects, similar to making patterns by folding and cutting paper.
- Scherk–Schwarz mechanism: a clever “twist” you add when going around a compact dimension, like returning to the start of a loop but with a rule that flips a setting. This twist breaks supersymmetry in a controlled way.
- Fluxes: imagine magnetic or electric lines threading through holes of the extra dimensions. These fluxes help “lock in” the sizes and shapes of the extra dimensions.
- KKLT setup: a famous recipe (named after Kachru, Kallosh, Linde, Trivedi) for stabilizing the extra dimensions and sometimes producing a small positive vacuum energy (similar to dark energy), along with broken supersymmetry.
- Tadpole potentials: energy shapes that act like a slope pushing fields to run away to large values. In simple terms, picture a ball on a hillside that won’t settle. The authors explore how such “runaway” tendencies can still be used to build stable models and might spark early‑universe inflation.
The paper also touches on nonlinear supersymmetry (the Volkov–Akulov model), where the symmetry is “hidden” and shows up in a special way, and on the technical tools used to check stability (making sure small vibrations don’t cause the model to fall apart).
Main Findings and Why They Matter
- Clear link between bottom‑up and top‑down: The review shows how gentle breaking of supersymmetry (“soft terms”) in particle physics connects to ideas from supergravity and string theory. This helps unify how we think about the small (particles) and the large (spacetime).
- Stable string setups without standard supersymmetry: The authors focus on 10‑dimensional string models that don’t have ordinary supersymmetry (or have it in a hidden, nonlinear way). Despite that, they find ways to keep these models stable, especially using compactifications on intervals (like shrinking a line segment rather than a circle) and checking “perturbative stability” (small shakes don’t make it collapse).
- Useful tools for building realistic universes: Techniques like Scherk–Schwarz twisting, Calabi–Yau compactifications, and fluxes help “fix” the extra dimensions and control energy. This is crucial for getting models that resemble our universe.
- KKLT and moduli stabilization: The review explains how KKLT stabilizes “moduli,” the fields that describe the size and shape of extra dimensions. Stabilizing moduli is necessary to prevent the universe’s properties from drifting unpredictably.
- Cosmology clues from tadpole potentials: The authors argue that “runaway” shapes of energy in non‑supersymmetric string setups might naturally kick off cosmic inflation. This offers a fresh way to link string theory ideas to early‑universe behavior.
These results matter because they offer a map of how different supersymmetry‑breaking ideas fit together and how they might lead to realistic physics that connects to observations.
Implications and Potential Impact
- Particle physics: If supersymmetry exists but is broken, the paper’s bottom‑up strategies show how it could still help solve problems like why the Higgs mass is stable and how new particles might be organized.
- Quantum gravity: The top‑down approach ties supersymmetry breaking to the shape of spacetime and string theory, pushing forward our understanding of how gravity and quantum mechanics can be combined.
- Cosmology: The possibility that stringy “tadpole” effects can start inflation provides a new bridge between high‑energy theory and the early universe. It could inspire models that better match cosmic observations.
- Future research: By collecting methods, examples, and tests of stability, the review gives researchers a toolkit for building and checking new models, making progress toward a unified, testable picture of our universe.
In short, the paper is a guide to how supersymmetry might be broken in nature, showing multiple paths—from everyday particle physics up to the grand ideas of strings and extra dimensions—and how these paths might meet to explain both the particles we see and the history of our cosmos.
Knowledge Gaps
Knowledge gaps, limitations, and open questions
The following items identify what remains missing, uncertain, or unexplored based on the scope described in the paper and the current state of the field it surveys:
- Quantitative mapping from top-down constructions to 4D soft SUSY-breaking terms: compute complete spectra (gaugino, scalar, A-terms), flavor/CP patterns, and RG running for explicit compactifications discussed, and confront with experimental bounds.
- Non-perturbative stability of the proposed non-supersymmetric vacua: identify and estimate decay channels (e.g., bubble of nothing, brane nucleation, tunneling to tachyonic phases), and compute lifetimes.
- Backreaction and higher-order corrections: solve the full 10D equations including localized sources, tadpole-induced potentials, warping, string loop () and corrections, and assess parametric control regimes.
- Explicit, chiral, and globally consistent Calabi–Yau models: construct concrete examples with fluxes/tadpoles yielding the SM/MSSM spectrum, ensure anomaly/K-theory cancellation, flux quantization, and moduli stabilization in non-(or nonlinearly-)supersymmetric settings.
- Scherk–Schwarz and interval compactifications: derive the full 4D effective theories (mass gaps, moduli, boundary conditions, junction conditions), and check perturbative stability beyond leading order (two-loop, string non-perturbative effects).
- Finite- supersymmetry breaking: compute loop-induced threshold corrections and effective potentials at finite coupling; determine how control is maintained and which observables are reliably predicted.
- Tadpole potentials and their control: provide general mechanisms (branes, orientifolds, fluxes) that cancel or tame runaway behavior; catalogue when these mechanisms work and quantify residual runaways.
- Inflation from tadpole potentials: derive detailed single/multi-field dynamics, reheating, and precise predictions for , , non-Gaussianity, isocurvature, and compare with Planck/Simons Observatory/CMB-S4 forecasts; identify distinctive signatures.
- De Sitter constructions and no-go theorems: rigorously assess compatibility of the setups (KKLT and tadpole-driven scenarios) with Gibbons–Maldacena–Nuñez and related constraints; specify which ingredients evade them without uncontrolled backreaction.
- Swampland consistency: test the constructions against the de Sitter/Distance/Weak Gravity conjectures; quantify tensions or provide counterexamples with transparent control of corrections.
- Volkov–Akulov and constrained superfields: clarify the precise string-theoretic origin of non-linear SUSY sectors used in 4D EFTs and their couplings to supergravity; check UV consistency and completeness.
- D-brane stability and anomaly/K-theory conditions in non-SUSY backgrounds: classify allowed brane configurations in the presence of fluxes/tadpoles and compute their spectra, potential tachyons, and anomaly inflow.
- Moduli hierarchies and the cosmological moduli problem: compute moduli masses, couplings to the visible sector, and decay histories; identify mechanisms to avoid late-time entropy injection or fifth-force constraints.
- MSSM-specific issues: generate and control the and terms, align flavor structures, and suppress CP phases in the top-down models presented; connect to EWSB and Higgs mass predictions.
- KKLT vs Large Volume Scenarios in the reviewed context: perform a side-by-side, controlled comparison (sources of uplift, scales, control of corrections, phenomenology) within the same geometric/flux data.
- Global consistency of interval endpoints: analyze localized curvature/deficit angles, boundary actions, and matching/junction conditions; determine their impact on spectra and stability.
- Worldsheet and amplitude consistency in non-supersymmetric strings: demonstrate modular invariance and one-loop (and higher) finiteness for the vacua used; compute vacuum amplitudes and check for hidden instabilities.
- Numerical 10D solutions: develop and share tools to obtain fully backreacted solutions with fluxes, warping, intervals, and tadpoles; validate EFT reductions against these solutions.
- Landscape statistics: estimate the number and distribution of controlled non-supersymmetric vacua (with stabilized moduli and acceptable cosmology) and identify dominant obstructions.
- Phenomenological bridges: derive collider, flavor, EDM, and dark matter predictions (including non-WIMP possibilities) from the specific compactifications; propose experimental tests that can falsify classes of models.
- Early-Universe extensions: address baryogenesis mechanisms, reheating temperatures, and relic production (e.g., gravitino-like issues in non-SUSY contexts); ensure consistency with BBN and CMB constraints.
Practical Applications
Below are practical, real-world applications that follow from the paper’s findings, methods, and innovations, grouped into immediate and longer-term opportunities. Each item notes relevant sectors, potential tools/products/workflows, and key assumptions or dependencies.
Immediate Applications
- Academia (Particle Physics): MSSM soft-term pipelines for phenomenology
- Use cases: Generate and scan supersymmetric spectra consistent with supergravity “soft terms” to paper collider observables (mass hierarchies, flavor/CP constraints, dark matter relic density).
- Tools/workflows: Integrate supergravity-informed Kähler potentials and superpotentials into existing toolchains (e.g., SARAH/SPheno/SoftSUSY, micrOMEGAs) to automate parameter inference and global fits.
- Assumptions/dependencies: Validity of 4D EFT, choice of mediation mechanism, R-parity assumptions, flavor structure and CP phases, current experimental bounds.
- Academia (String Theory): Perturbative stability analysis of non-supersymmetric vacua
- Use cases: Systematically assess non-tachyonic string models with non-linear SUSY and runaway “tadpole” potentials; identify perturbatively stable interval compactifications (Scherk–Schwarz-like setups).
- Tools/workflows: One-loop vacuum amplitude calculators; spectrum generators for interval/toroidal compactifications; anomaly cancellation checks; symbolic algebra for superspace/components.
- Assumptions/dependencies: Modular invariance and anomaly freedom of specific constructions; control of higher-loop corrections; consistent boundary conditions and localized sources.
- Academia (Cosmology): Inflation onset modeling from tadpole-driven potentials
- Use cases: Implement “climbing” behavior and related potentials in cosmological solvers to fit CMB features and test early-universe scenarios; explore reheating phenomenology.
- Tools/workflows: CLASS/CAMB for background and perturbations; Monte Carlo/Bayesian fits (MontePython/Cobaya); integration with EFT-of-inflation frameworks.
- Assumptions/dependencies: Reliable 4D reduction of 10D dynamics; neglect of backreaction beyond controlled regimes; priors on moduli stabilization and supersymmetry breaking scale.
- Academia/Software Engineering: Compactification builders for twisted boundary conditions
- Use cases: Rapid prototyping of Scherk–Schwarz deformations and interval compactifications to generate KK spectra for model exploration; automatable consistency checks.
- Tools/workflows: Modular code libraries (Python/Julia/Mathematica) that compose boundary conditions, fluxes, and orbifold data to produce mass spectra and couplings; CI pipelines for consistency tests.
- Assumptions/dependencies: Correct implementation of global constraints (tadpole cancellation, flux quantization); numerical stability of solvers; reproducibility across toolchains.
- Education (Graduate Training): Cohesive curriculum bridging bottom-up and top-down
- Use cases: Course modules and reading groups that traverse SUSY, MSSM soft terms, supergravity, string compactifications, fluxes, KKLT, and non-linear SUSY (Volkov–Akulov).
- Tools/workflows: Lecture notes, problem sets using superspace/component calculations; lab-style projects with open-source packages for spectra and cosmology.
- Assumptions/dependencies: Availability of computational resources; alignment with departmental curricula.
- Policy/Research Strategy: Near-term guidance for SUSY searches
- Use cases: Briefs for experimental programs (colliders, EDM/rare decays, direct/indirect DM searches) outlining testable soft-breaking patterns, viable parameter regions, and risk-managed benchmarks.
- Tools/workflows: Living documents linking theory priors to detector sensitivities; cross-team dashboards for global fits and exclusion updates.
- Assumptions/dependencies: Current and planned experimental capabilities; community consensus on benchmark definitions.
- Cross-Disciplinary (Photonics/Condensed Matter): Design patterns using twisted boundary conditions
- Use cases: Conceptual transposition of Scherk–Schwarz twists to engineer band gaps or mode structures in photonic crystals and metamaterials (phase-twisted boundary conditions).
- Tools/workflows: Electromagnetic simulation packages (COMSOL, Meep) with phase-twisted boundary setups; parametric sweeps for band structure control.
- Assumptions/dependencies: Valid mapping from field-theory boundary conditions to wave physics; manufacturability of boundary/twist implementations.
Long-Term Applications
- Particle Physics (Experiment): Discovery-era parameter inference and model discrimination
- Use cases: If SUSY or related signatures are found, use the paper’s bottom-up/top-down bridge to extract mediation mechanisms, link soft terms to UV completions (supergravity/string), and constrain moduli sectors.
- Tools/workflows: Joint fits across collider, flavor, EDM, and cosmology; EFT-to-UV inference pipelines; model comparison via Bayesian evidence.
- Assumptions/dependencies: Actual discovery of SUSY-like signals; robust control of higher-order corrections; sufficient data to break degeneracies.
- Dark Matter (Astroparticle Physics): Targeted searches informed by MSSM/UV constraints
- Use cases: Design direct/indirect detection strategies for candidates (e.g., neutralinos) consistent with supergravity and string-inspired constraints; cross-validate with cosmological relic density.
- Tools/workflows: End-to-end pipelines coupling spectrum generators and DM codes; experimental sensitivity optimization.
- Assumptions/dependencies: Existence of viable WIMP-like candidates; accurate thermal histories; control of non-thermal production channels.
- Cosmology (Early Universe): String-driven inflation and reheating with signature predictions
- Use cases: Build models where tadpole potentials or constrained superfields drive inflation; forecast distinguishing observables (e.g., , , features, non-Gaussianity) for CMB-S4/LiteBIRD/Simons Observatory.
- Tools/workflows: Hybrid analytic-numeric pipelines linking compactification data to inflationary potentials; Fisher forecasts; model selection across string-inspired families.
- Assumptions/dependencies: Reliable moduli stabilization (KKLT or alternatives), non-perturbative effects under control, compatibility with swampland criteria, forthcoming precision data.
- Quantum Gravity/String Theory (Foundations): Viable non-supersymmetric vacua and brane-world scenarios
- Use cases: Develop consistent non-SUSY string vacua that could furnish UV completions of the Standard Model; explore phenomenology of interval/brane setups for modified gravity tests.
- Tools/workflows: Extended amplitude computations; anomaly inflow and localized source analyses; interface with short-range gravity experiments.
- Assumptions/dependencies: Resolution of tadpole/runaway issues beyond perturbation theory; experimental access to relevant scales.
- Software/Products (Research Infrastructure): EFT-to-UV model builders and landscape explorers
- Use cases: Mature platforms that ingest effective data (spectra, couplings, cosmology), propose compatible UV completions (supergravity/string), and navigate flux/moduli landscapes with ML-assisted search.
- Tools/workflows: Scalable HPC services; surrogate modeling and active learning for high-dimensional spaces; provenance tracking for reproducibility.
- Assumptions/dependencies: Standardized interfaces between HEP tools; sustained community maintenance; compute resources.
- Industry/Data Science: High-dimensional landscape search methodologies
- Use cases: Translate flux-vacua scanning and constraint satisfaction workflows to materials discovery, pharmacology, or finance (search over constrained, rugged spaces).
- Tools/workflows: Constraint solvers, Bayesian optimization, reinforcement learning for exploration/exploitation trade-offs; domain-specific simulators.
- Assumptions/dependencies: Careful abstraction from physics to domain constraints; availability of accurate simulators and data.
- Policy/Strategic Planning: Theory-informed roadmaps for experimental investments
- Use cases: Use compact, theory-anchored scenario maps (SUSY, moduli stabilization, inflation signatures) to prioritize collider upgrades, precision flavor/EDM programs, and cosmology missions.
- Tools/workflows: Scenario-based cost–benefit and risk analyses; cross-agency coordination frameworks; dynamic updates as evidence accrues.
- Assumptions/dependencies: Transparent uncertainty quantification from theory; sustained funding and international collaboration.
- Daily Life (Indirect, Long Horizon): Technological spillovers from breakthroughs in fundamental physics
- Use cases: If new particles/forces are discovered and understood (e.g., dark sector couplings), long-run impacts may include novel sensing, imaging, or secure communication technologies.
- Tools/workflows: Technology maturation pipelines leveraging advanced detectors, cryogenics, superconducting devices; knowledge transfer programs.
- Assumptions/dependencies: Actual discovery and harnessing of new physical effects; translation from lab to industry.
Glossary
- Branes: Extended objects in string theory on which strings can end; they carry charges and shape the vacuum structure. "Branes and Vacua of (Non--)Supersymmetric Strings"
- Calabi–Yau: Special Ricci-flat Kähler manifolds used to compactify extra dimensions, often preserving supersymmetry. "Calabi--Yau reductions"
- Circle reduction: Compactifying a spatial dimension on a circle to obtain a lower-dimensional effective theory. "the counterparts of circle reduction but involve internal intervals."
- Critical strings: String theories formulated in their critical spacetime dimension (e.g., D=10 for superstrings) ensuring conformal consistency. "Critical Strings and their Circle Compactifications"
- Fluxes: Background field strengths threaded through cycles of a compact space, commonly used to stabilize moduli. "fluxes in Calabi-Yau vacua and the KKLT setup,"
- g_s: The string coupling constant controlling the strength of string interactions. "Supersymmetry Breaking with a Finite \texorpdfstring{} \ "
- KKLT setup: A moduli-stabilization framework (Kachru–Kallosh–Linde–Trivedi) using fluxes and nonperturbative effects, often in type IIB string theory. "the KKLT setup"
- Minkowski vacua: Vacuum solutions with flat spacetime and zero cosmological constant. "ten--dimensional Minkowski vacua"
- Moduli stabilization: Mechanisms that fix the otherwise continuous parameters (moduli) of compactifications. "Moduli stabilization, fluxes and the KKLT Setup"
- MSSM: The Minimal Supersymmetric Standard Model, a supersymmetric extension of the Standard Model. "the Standard Model and the MSSM,"
- Non-linearly realized supersymmetry: Supersymmetry realized via non-linear transformations (e.g., Volkov–Akulov), rather than linearly on fields. "where supersymmetry is absent or non--linearly realized,"
- Non-tachyonic string models: String constructions without tachyonic (imaginary-mass) instabilities that signal vacuum instability. "ten--dimensional non--tachyonic string models"
- Orbifolds (toroidal orbifolds): Singular quotient spaces (often of tori) used in compactifications to reduce symmetry or engineer spectra. "toroidal orbifolds"
- Orientifolds: Constructions obtained by quotienting by worldsheet parity and introducing orientifold planes, modifying spectra and interactions. "Six-Dimensional Orientifolds"
- Perturbative stability: Stability against small fluctuations analyzed within perturbation theory. "We illustrate the perturbative stability of the resulting most symmetrical setups,"
- Scherk–Schwarz: A mechanism for supersymmetry breaking via twisted boundary conditions along compact directions. "Scherk--Schwarz deformations"
- Soft terms: Supersymmetry-breaking terms that avoid reintroducing quadratic divergences in quantum corrections. "with emphasis on the ``soft terms'' that can link it to supergravity."
- Standard Model: The quantum field theory describing known particle physics interactions (SU(3)×SU(2)×U(1)). "the Standard Model and the MSSM,"
- String vacuum amplitudes: Worldsheet partition functions or correlators that encode properties of string vacua, including energies and spectra. "on string vacuum amplitudes,"
- Supergravity: The gauge theory of local supersymmetry that incorporates gravity. "their links with supergravity, toroidal orbifolds, Scherk--Schwarz deformations and Calabi--Yau reductions,"
- Superspace: An extension of spacetime with anticommuting coordinates used to formulate supersymmetric theories. "in components and in superspace,"
- Supersymmetry breaking: The phenomenon where supersymmetry is not preserved, lifting degeneracies between superpartners. "a self--contained view of supersymmetry breaking from the bottom--up perspective."
- Tadpole potentials: Potential terms induced by uncancelled tadpole diagrams, often driving runaway behavior. "runaway ``tadpole potentials'' deform the ten--dimensional Minkowski vacua."
- Toroidal compactifications: Compactifications on tori (products of circles) to reduce spacetime dimensionality. "Higher--Dimensional Toroidal Compactifications"
- Volkov–Akulov Model: A model realizing supersymmetry non-linearly via a goldstino mode. "Volkov-Akulov Model and Nonlinear Supersymmetry"
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