Establishes higher T-duality for super M-branes.
problem Generalizing T-duality for super p-branes.
method Super L-infinity-algebraic T-duality for super WZW-terms.
result Spherical T-duality of super M5-branes.
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48 results for “super M-branes”
New approach identifies hidden degrees of freedom in M-theory.
problem Identifying hidden degrees of freedom at ADE-singularities in M-theory.
method Real equivariant cohomotopy on superspaces, using Elmendorf's theorem.
result Reveals ADE-singularities as part of super-cocycles on 11d super-spacetime.
Researchers solve M-theory's gauge enhancement problem using advanced homotopy theory.
problem Lift nonabelian gauge fields from D-branes to M-theory.
method Universal constructions in super homotopy theory, focusing on the cyclification adjunction and fiberwise stabilization.
result Gauge enhancement in M-theory is explained by lifting against the fiberwise stabilization of the unit of the cyclification adjunction.
Researchers create holographic super-embeddings for M5 and M2 branes.
problem No concrete examples of super-embeddings for M5 and M2 branes existed.
method Constructed explicit holographic super-embeddings of probe M5 and M2 branes into their super-AdS backgrounds.
result Explicit holographic super-embeddings of M5 and M2 branes were successfully constructed.
11D supergravity completes with quantized C-field flux.
problem Completing 11D supergravity with quantized C-field flux.
method Duality-symmetric formulation of on-shell 11d supergravity on superspace.
result 11d super-spacetimes are quantizable by duality-symmetric super-C-field flux.
Unified super-symmetry and higher fluxes using super-Lie-infinity algebras.
problem Unified extended super-symmetry and higher flux densities.
method Using super-Lie-infinity algebras and their extensions and cyclifications.
result Derivation of topological T-duality laws from super-Lie-infinity structure.
New framework solves string theory's RR-field tadpole cancellation problems.
problem Precise global nature of RR-field tadpole cancellation conditions in string theory.
method Formulated M-theory C-field on flat M-orientifolds using equivariant cohomotopy.
result Equivariant cohomotopy implies anomaly cancellation conditions for M-branes and D-branes.
Studying the M-branes leads us naturally to new structures that we call Membrane-, Membrane^c-, String^K(Z,3)- and Fivebrane^K(Z,4)-structures, which we show can also have twisted counterparts. We study some of their basic properties, highlight analogies with structures associated with lower levels of the Whitehead tow…
We investigate the local geometry on the moduli space of G_2 structures that arises in compactifications of M-theory on holonomy G_2 manifolds. In particular, we determine the homogeneity properties of couplings of the associated N=1, D=4 supergravity under the scaling of moduli space coordinates. We then find some bra…
We study the most general supersymmetric warped M-theory backgrounds with non-trivial G-flux of the type R^{1,2} x M_8 and AdS_3 x M_8. We give a set of necessary and sufficient conditions for preservation of supersymmetry which are phrased in terms of G-structures and their intrinsic torsion. These equations may be in…
We uncover and highlight relations between the M-branes in M-theory and various topological invariants: the Hopf invariant over , and , the Kervaire invariant, the -invariant, and the -invariant. This requires either a framing or a corner structure. The canonical framing pro…
Geometric and topological structures related to M-branes II: Twisted String and String^c structureshep-th
The actions, anomalies, and quantization conditions allow the M2-brane and the M5-brane to support, in a natural way, structures beyond Spin on their worldvolumes. The main examples are twisted String structures. This also extends to twisted String^c structures, which we introduce and relate to twisted String structure…
Higher gauge theory via differential nonabelian cohomology
problem Global infrared completion of higher gauge fields
method Maxwell-type higher gauge fields
result Electromagnetic flux quantization
We consider the topological and geometric structures associated with cohomological and homological objects in M-theory. For the latter, we have M2-branes and M5-branes, the analysis of which requires the underlying spacetime to admit a String structure and a Fivebrane structure, respectively. For the former, we study h…
Study super cluster algebras from super Plücker and Ptolemy relations.
problem Developing super cluster algebra structure in super Grassmannians.
method Analyzing super Plücker and Ptolemy relations, developing super cluster structure.
result New simple form of super Plücker relations for $\Gr_{r|1}(n|1)$.
Revises super unitary representations by relaxing Hilbert space definition.
problem Left-regular representations of super Lie groups are not super unitary.
method Weaken super Hilbert space definition and introduce a new metric.
result Left-regular representations of all super Lie groups are super unitary.
Super twisted productsmath.DG
The paper defines and analyzes curvature tensors on super twisted product spaces.
problem Investigating curvature tensors on super twisted product spaces.
method Defined -curvature tensor, computed curvature tensors and Ricci tensors, and studied curvature flatness.
result Mixed Ricci-flat super twisted product semi-Riemannian manifolds can be expressed as super warped product manifolds.
Develops Riemannian geometry for noncommutative super surfaces.
problem No specific problem stated; focuses on mathematical development.
method Introduces metric and connections on noncommutative super surfaces, showing compatibility and zero torsion under certain conditions.
result Noncommutative super surfaces have a well-defined Riemannian geometry with properties analogous to classical Riemannian geometry.
Defines super stable maps and proves quotient superorbifolds for genus zero.
problem Defines stable supercurves and super stable maps of genus zero.
method Uses labeled trees and slice theorem for super Lie groups.
result Proves moduli space of stable supercurves and super stable maps are quotient superorbifolds.
Defines semi-symmetric metric connection on super warped products.
problem Computing curvature and Ricci tensors on super warped products.
method Introduced semi-symmetric metric connection and conditions for Einstein spaces.
result Conditions for super warped product spaces to be Einstein with semi-symmetric metric connection.
Super McShane identitymath.GT
Authors derive McShane identity for super tori.
problem Deriving McShane identity for super tori.
method Super Teichmüller theory and supergeometry.
result Asymptotic growth rate of length spectra established.
Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an analogue of Riemann surfaces in the world of super geometry. After a short intro…
New theorem disproves Angle Defect for super triangles.
problem Angle Defect Theorem for N=1 super hyperbolic geometry.
method Action of OSp(1|2) on real super Minkowski space and brute-force computation.
result Disproves Angle Defect Theorem and provides novel additive function.
Constructs the moduli space of super J-holomorphic curves.
problem Defines and constructs the moduli space of super J-holomorphic curves.
method Uses component fields of a super differential equation and a transversality argument.
result Constructs the moduli space of super J-holomorphic curves as a smooth subsupermanifold.
The underlying even manifold of a super Riemann surface is a Riemann surface with a spinor valued differential form called gravitino. Consequently infinitesimal deformations of super Riemann surfaces are certain infinitesimal deformations of the Riemann surface and the gravitino. Furthermore the action functional of no…
The paper studies special warped products with a specific connection on super Riemannian manifolds.
problem Investigating curvature and Ricci tensors on super warped product spaces with a semi-symmetric non-metric connection.
method Defined a semi-symmetric non-metric connection, computed curvature and Ricci tensors, and introduced and analyzed two types of super warped product spaces.
result Conditions for two super warped product spaces with a semi-symmetric non-metric connection to be Einstein spaces are provided.
Super tau-covers extend bihamiltonian hierarchies' symmetries.
problem Extending symmetries of bihamiltonian hierarchies.
method Constructing super tau-covers for bihamiltonian integrable hierarchies.
result Symmetries of bihamiltonian hierarchies extended to super tau-covers.
We derive the canonical forms of super Riemannian metrics and the local isometry groups of such metrics. For certain super metrics we also compute the simply connected covering groups of the local isometry groups and interpret these as local spin groups of the super metric. Using a generalization of a Theorem of Rogers…
A super Lie group is a group whose operations are mappings in the sense of Rogers. Thus the underlying supermanifold possesses an atlas whose transition functions are functions. Moreover the images of our charts are open subsets of a graded infinite-dimensional Banach space since our space of …
Defines a super analog of Plücker embedding for Grassmannian.
problem Generalizing Plücker embedding to super vector spaces with mixed parity.
method Combines super vector space and its parity-reversion to construct embedding.
result Proves the embedding is an isomorphism to a weighted projective space.
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.
The paper develops a theory of -superrings and their superschemes.
problem Developing a theory for -superrings and superschemes.
method Proving an equivalence between categories of fair affine -superschemes and fair -superrings.
result A key equivalence between fair affine -superschemes and fair -superrings.
Characterizes super-replication prices in a financial market model.
problem Characterizing prices in a financial market model.
method Characterizes prices as the supremum of mono-prior super-replication prices through extreme priors and martingale measures.
result Super-replication prices are the supremum of mono-prior super-replication prices.
Scheme resolves super-brane topology via equivariant structures.
problem Topological issues in super-brane dynamics.
method Geometric scheme for Green-Schwarz cocycles, equivariant structures.
result Equivariant structures resolve super-brane topology.
Defines super projective modules and explores their properties.
problem Exploring the geometric-algebraic link in super geometry.
method Defined and explored super projective modules over supersmooth functions.
result Module of vector fields over a supersphere is a super projective module.
This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e. not "super-) differential geometry. The discussion is based on symmetry considerations and aims to clarify the "borderline" between classical and super differential geometry with respect to the…
Matrix formulas for super Teichmüller spaces generalize previous work and yield super λ-lengths.
problem Calculating super λ-lengths on bordered surfaces with marked points.
method Using holonomy matrices of elements in the supergroup OSp(1|2) to compute super λ-lengths in decorated super Teichmüller spaces.
result Matrix formulas for arcs on bordered surfaces yield super λ-lengths in Penner-Zeitlin's decorated super Teichmüller space.
3d Super Hyperbolic Geometrymath.GT
Extends Wigner's representation to study super hyperbolic geometry.
problem Understanding geometry in super hyperbolic three-space.
method Extended Wigner's representation of the Lorentz group to OSp_C(1|2) and applied to Minkowski (3,1|4)-dimensional super space.
result Proof of divergence of the volume of a typical ideal tetrahedron in super hyperbolic three-space.
Extends differential geometry concepts to manifolds with super tangent bundles.
problem No specific problem stated; extending differential geometry to super tangent bundles.
method Introduces super tangent bundle and extends differential geometry concepts.
result Basic notions of differential geometry extended to manifolds with super tangent bundles.
Paper constructs super integrable systems on color Lie algebra.
problem Super integrable systems on color Lie algebra.
method Using non-isospectral problems with matrices from color Lie algebra , constructing (1+1)- and (2+1)-dimensional systems.
result Super integrable systems and their Hamiltonian structures constructed on color Lie algebra .
Note on instabilities in super-time-stepping methods for Heston model.
problem Instabilities in super-time-stepping methods applied to Heston model.
method Exploration of explicit super-time-stepping schemes (RK-Chebyshev, RK-Legendre) for Heston model.
result Relevance of stability remarks beyond super-time-stepping schemes.
Super-convergence allows neural nets to train faster with large learning rates.
problem Training neural networks too slowly.
method Training with large learning rates and one learning rate cycle.
result Neural networks can be trained an order of magnitude faster.
The super or Z_2-graded Schouten-Nijenhuis bracket is introduced. Using it, new generalized super-Poisson structures are found which are given in terms of certain graded-skew-symmetric contravariant tensors Λof even order. The corresponding super `Jacobi identities' are expressed by stating that these tensors have zero…
The Hidden M-Grouphep-th
The hidden M-algebra is integrated into a super-Lie group, allowing for compactification of extra dimensions.
problem Integrating the hidden M-algebra into a super-Lie group to model super-exceptional spacetimes.
method Left-invariant extension of the decomposed M-theory 3-form, providing a computer-checked re-derivation and streamlined conception of super-Lie groups.
result Lattice subgroups of the hidden M-group allow toroidal compactification of hidden dimensions, akin to topological T-duality.
Super-A-polynomialmath.AG
We review a construction of a new class of algebraic curves, called super-A-polynomials, and their quantum generalizations. The super-A-polynomial is a two-parameter deformation of the A-polynomial known from knot theory or Chern-Simons theory with SL(2,C) gauge group. The two parameters of the super-A-polynomial encod…
Extends super-replication theorem with dynamic strategies and transaction costs.
problem Dynamic super-replication under proportional transaction costs.
method Generalizes admissible strategies and defines a well-defined super-replication price process.
result Well-defined super-replication price process in dynamic setting.
Study on super-Toda system on Riemann surfaces, analyzing solutions with four types of bubbling.
problem Analyzing solutions to the super-Toda system on Riemann surfaces.
method Blow-up analysis, energy gap results for spinor parts of solutions.
result Showed energy identities for spinor parts of a blow-up sequence of solutions.
The paper studies martingales and super-martingales under a convex set of measures.
problem Understanding martingales and super-martingales in a convex set of equivalent measures.
method Introduced local regular super-martingales and proved necessary and sufficient conditions for their regularity.
result Generalized Doob's decomposition theorem for super-martingales under a convex set of measures.