Identifies marginal deformations of heterotic G2 sigma models using cohomology.
problem Understanding marginal deformations of heterotic G2 sigma models.
method Relates marginal deformations to cohomology classes of a worldsheet BRST operator.
result Cohomologies of the BRST operator are isomorphic to those in supergravity.
Study connects derivations and holonomy symmetries in heterotic geometries.
problem Understanding the algebra of derivations and holonomy symmetries in heterotic geometries.
method Analyzing the superalgebra of derivations and exploring the relation to holonomy symmetries in sigma models.
result Proposed Lie bracket on the space of fundamental forms and derivation algebras for heterotic geometries.
New construction reveals SU(2)-flavor fields in heterotic M5-brane model.
problem Tackles the emergence of SU(2)-flavor fields in heterotic M5-brane models.
method Classifies super-exceptional field content and works out interactions.
result SU(2)xU(1)-valued scalar and vector fields emerge from probe M2- and M5-branes.
The symmetries of two-dimensional supersymmetric sigma models on target spaces with covariantly constant forms associated to special holonomy groups are analysed. It is shown that each pair of such forms gives rise to a new one, called a Nijenhuis form, and that there may be further reductions of the structure group. I…
Novel flow modifies Ricci flow with string theory correction.
problem Study of three-dimensional solitons in modified curvature flow.
method Introduce Heterotic-Ricci flow, analyze its three-dimensional solitons.
result Prove rigid Einstein solitons with constant dilaton.
M5-branes' flux quantization linked to non-abelian cohomology.
problem Flux quantization on M5-branes and its implications.
method Analogous to Dirac's charge/flux quantization, constraining M5's flux-quantization law to non-abelian cohomology theory.
result Skyrmion-like and anyonic solitons on M5-branes and open M5-branes.
We construct explicit compact supersymmetric solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimension five. We present a quadratic condition on the curvature which is necessary and sufficient the heterotic supersymmetry and the anomaly cancellation t…
We construct explicit compact solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic string equations in dimensions seven and eight. We present a quadratic condition on the curvature which is necessary and sufficient the heterotic supersymmetry and the anomaly cancellation to i…
Unified solution to M-theory problems using super-exceptional geometry.
problem M-theory's Lagrangian construction, gauge field origin, and supersymmetric enhancement.
method Combining homotopy theory, supergeometry, and super-homotopy theory.
result Unified description of M-theory Lagrangians and emergence of gauge fields.
Universal geometry organizes heterotic moduli spaces.
problem Understanding the structure of heterotic compactifications.
method Fibering compactification data over moduli space and analyzing universal curvatures.
result Deformations are components of universal curvatures, incorporating α′2 corrections. Explains compactification for heterotic superstrings on Calabi-Gray manifolds.
problem Compactification of heterotic superstrings with torsion.
method Generalized Calabi-Gray geometry.
result Expository overview of compactification methods.
New smooth solutions of the Strominger system with non vanishing flux, non-trivial instanton and non-constant dilaton based on the quaternionic Heisenberg group are constructed. We show that through appropriate contractions the solutions found in the G2-heterotic case converge to the heterotic solutions on 6-dimensi…
We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an instanton. For heterotic compactifications in dimension six this reduces the choice of …
The (abelian bosonic) heterotic string effective action, equations of motion and Bianchi identity at order alpha prime in ten dimensions, are shown to be equivalent to a higher dimensional action, its derived equations of motion and Bianchi identity. The two actions are the same up to the gauge fields: the latter are a…
The paper explores moduli space of heterotic system using two deformation paths.
problem Exploring the moduli space of the heterotic system.
method Considering two dual deformation paths starting from a Kähler solution, one along Bott-Chern cohomology class and the other along Aeppli cohomology class. Using the implicit function theorem to prove local existence of heterotic solutions.
result Established an initial step to construct local moduli coordinates around a Kähler solution.
Study of Heterotic solitons on 4-manifolds, focusing on their properties and deformations.
problem Investigating solutions of Heterotic supergravity equations on 4-manifolds.
method Analyzing Heterotic solitons defined by a metric, connection with skew torsion, and a closed one-form.
result Characterization of Heterotic solitons as suspensions of certain 3-manifolds, yielding new compactification backgrounds.
Rigidity proven for a specific type of solitons with harmonic curvature.
problem Proving rigidity of a specific class of solitons.
method Proof of rigidity for compact three-dimensional Heterotic solitons with vanishing torsion and harmonic curvature.
result Compact three-dimensional Heterotic solitons with vanishing torsion and harmonic curvature are rigid.
Heterotic backgrounds described using generalised geometry, preserving minimal supersymmetry.
problem Characterizing heterotic backgrounds preserving minimal supersymmetry in four dimensions.
method Using generalised geometry, characterizing backgrounds by an SU(3)imesSpin(6+n) structure and an involutive subbundle of the generalised tangent bundle. result The analysis of infinitesimal deformations reproduces known cohomologies of massless moduli.
Researchers compute the heterotic moduli-space metric up to α′2.
problem Computing the heterotic moduli-space metric up to a specific order.
method Using α′2 for backgrounds with a smooth α′o0 limit, focusing on the Kaehler potential and metric corrections. result Metric corrections from the deformation of the Hull connection are identified.
We study a supersymmetry-preserving solution-generating method in heterotic supergravity. In particular, we use this method to construct one-parameter non-Kahler deformations of Calabi-Yau manifolds with a U(1) isometry, in which the complex structure remains invariant. We explain how to obtain corresponding solutions …
We construct new explicit compact supersymmetric valid solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic equations of motion in dimension six. We present balanced Hermitian structures on compact nilmanifolds in dimension six satisfying the heterotic supersymmetry equations…
The paper defines a moduli space for heterotic G2 systems.
problem Deformations of heterotic string compactifications on G2 manifolds.
method Defines a covariant exterior derivative and shows it is equivalent to a heterotic G2 system.
result Determines the infinitesimal moduli space of heterotic G2 systems.
Study finite deformations from heterotic superpotential, leading to new complex effective action.
problem Finite deformations of the Hull--Strominger system.
method Expanding the heterotic superpotential around a supersymmetric vacuum, identifying complex coordinates, and using Maurer--Cartan equation.
result Generalizes complex effective action of Kodaira--Spencer and holomorphic Chern--Simons theory, with a supersymmetric locus described by an L3 algebra. Researchers find limits on curvature of certain 3D solitons.
problem Limits on curvature of 3D Heterotic solitons with parallel torsion.
method Rigidity result for compact 3D Heterotic solitons with parallel non-trivial torsion.
result Universal bound of -24 for scalar curvature of Heterotic solitons with parallel skew-symmetric torsion.
Constructing solutions to the heterotic G2 system on specific types of manifolds.
problem Finding solutions to the heterotic G2 system on certain types of manifolds. method Investigating a 1-parameter family of G2-connections on tangent bundles. result Obtaining several approximate and one new class of exact solutions on degenerate 3-(α,δ)-Sasaki manifolds. Study examines corrections to heterotic geometry on SU(3) manifolds.
problem Analyzing α′2 corrections to heterotic supersymmetry algebra. method Derives integrability condition and pure gauge correction from graviton equation of motion.
result Curvature of tangent bundle connection acquires a (0,2) component, disrupting semi-classical intuition.
New isometric solutions found for heterotic G2-system.
problem Solving the heterotic G2-system with non-abelian gauge groups.
method An ansatz to vary G2-structure and gauge data while keeping metric fixed.
result Distinct isometric solutions on the same manifold with different gauge groups.
We give a complete algorithm and source code for constructing what we refer to as heterotic risk models (for equities), which combine: i) granularity of an industry classification; ii) diagonality of the principal component factor covariance matrix for any sub-cluster of stocks; and iii) dramatic reduction of the facto…
We outline the solution of the Killing spinor equations of the heterotic supergravity. In addition, we describe the classification of all half supersymmetric solutions.
The heterotic G2 system is solved on Calabi-Yau 3-orbifolds.
problem Solving the heterotic G2 system on Calabi-Yau 3-orbifolds.
method Adjusting circle bundles and powers of α' to obtain cocalibrated G2 structures.
result Non-trivial solutions to the heterotic G2 system are found.
Reviews uses of nonlinear sigma models in various systems.
problem Understanding nonlinear sigma models in different physical contexts.
method General discussion and focus on geometrical interpretations.
result Connection between sigma models and various geometries.
Study dualities between G2-manifolds and string theories.
problem Determine dualities between M-theory and heterotic string theories on G2-manifolds.
method Analyze K3-fibered G2-manifolds and their dual heterotic and F-theory realizations.
result Identify dual heterotic and F-theory realizations for a large class of G2-manifolds.
Decouples moduli groups in heterotic string theory cohomology.
problem Decomposing moduli groups in heterotic string theory cohomology.
method Computing cohomology groups at the standard embedding and showing their direct sum decomposition.
result Decomposes moduli groups into a direct sum of cohomologies at the standard embedding.
We construct a class of stable SU(5) bundles on an elliptically fibered Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass fibration, which admits a free involution. The bundles are invariant under the involution, solve the topological constraint imposed by the heterotic anomaly equation and …
Study heterotic G2-system on 2-step nilmanifolds with torus bundles.
problem Investigate G2-structures on 7D nilmanifolds with torus bundles.
method Prove coclosure of G2-structures, discuss existence of solutions for all isomorphism classes.
result Existence of solutions for various 7D nilpotent Lie algebras with constant dilaton.
We classify the simply-connected supersymmetric parallelisable backgrounds of heterotic supergravity. They are all given by parallelised Lie groups admitting a bi-invariant lorentzian metric. We find examples preserving 4, 8, 10, 12, 14 and 16 of the 16 supersymmetries.
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. …
Generalizes momentum sections to higher-dimensional gauged sigma models.
problem Understanding momentum sections in Hamiltonian mechanics and sigma models.
method Introduces a generalization of momentum sections on pre-multisymplectic manifolds.
result Shows a connection between constrained Hamiltonian systems and gauged sigma models.
We discuss the mathematical properties of six--dimensional non--Kähler manifolds which occur in the context of N=1 supersymmetric heterotic and type IIA string compactifications with non--vanishing background H--field. The intrinsic torsion of the associated SU(3) structures falls into five different classes. …
Generalizes Hamiltonian structures to Dirac structures for new mechanics models.
problem Extending Hamiltonian structures to non-symplectic manifolds.
method Introduces Hamiltonian Lie algebroids and momentum sections over Dirac structures.
result Constructs new sigma models based on these structures.
In arXiv:1008.1018 it is shown that a given stable vector bundle V on a Calabi-Yau threefold X which satisfies c2(X)=c2(V) can be deformed to a solution of the Strominger system and the equations of motion of heterotic string theory. In this note we extend this result to the polystable case and construct explic…
Study connects supermanifold Laplacian to harmonic superfunctions via sigma model.
problem Understanding harmonic superfunctions on supermanifolds.
method Calculus of variations applied to a supersymmetric sigma model.
result Relates Laplacian to harmonic superfunctions on supermanifolds.
New solutions found for G2 system on squashed manifolds.
problem Finding solutions to the heterotic G2 system on squashed manifolds.
method Constructing families of solutions using squashed metrics on 7-sphere or Aloff-Wallach space.
result Obtained AdS3 solutions for most squashing parameters, excluding a specific case.
New theory connects string theory to swampland distance conjecture.
problem Connecting string theory to swampland distance conjecture.
method Deformations of the heterotic superpotential, treating separately for large fluxes or large distances, integrating out fields to obtain a new field theory.
result New holomorphic theory defined, connects to swampland distance conjecture.
Sigma models linked to Gross-Neveu models via quiver varieties.
problem Understanding the relationship between sigma models and Gross-Neveu models.
method Exploring the mathematical correspondence between sigma models and Gross-Neveu models, including their geometric and trigonometric/elliptic deformations.
result Sigma models are mathematically equivalent to Gross-Neveu models under certain conditions.
We classify non-nilpotent complex structures on 6-nilmanifolds and their associated invariant balanced metrics. As an application we find a large family of solutions of the heterotic supersymmetry equations with non-zero flux, non-flat instanton and constant dilaton satisfying the anomaly cancellation condition with re…
This is an introductory review of topological field theories (TFTs) called AKSZ sigma models. The AKSZ construction is a mathematical formulation for the construction and analyses of a large class of TFTs, inspired by the Batalin-Vilkovisky formalism of gauge theories. We begin by considering a simple two-dimensional t…
The Poisson--Weil sigma model, worked out by us recently, stems from gauging a Hamiltonian Lie group symmetry of the target space of the Poisson sigma model. Upon gauge fixing of the BV master action, it yields interesting topological field theories such as the 2--dimensional Donaldson-Witten topological gauge theory a…