New string singularities enable quantum teleportation of massive particles.
problem Quantum teleportation of massive particles at large distances.
method Introduction of new world-sheet string singularities (cusps) that are stable and allow for the emission of captured massive quantum particles.
result Existence of a new mechanism for quantum teleportation of massive particles.
Formulae for divergent integrals with singularities, useful in string theory.
problem Handling divergent integrals with singularities.
method Formulae for finite part of divergent integrals, using local residue map.
result Formulae for finite part of divergent integrals expressed in terms of local residue map.
New smooth models for string groups defined in ∞-categories.
problem Defining string group models in smooth spaces.
method Homotopy-theoretic definition using singular complex functor.
result New smooth models for the string group.
T-duality in singular spacetime models with H-flux.
problem T-duality in singular spacetime models with H-flux.
method Initiate study of twisted equivariant Courant algebroids and apply to string theory.
result Ramond-Ramond charges classified by twisted equivariant cohomology groups.
Homflypt skein theory and string topology linked via 2-groupoids.
problem Understanding relations in Homflypt skein theory.
method Defined a 2-groupoid from the fundamental 2-groupoid of singular links, relating it to string topology.
result Relations in Homflypt skein theory are induced from a 2-groupoid.
Global solution found for string heat flow on surfaces.
problem Existence of global weak solutions for bosonic string heat flow.
method Proved existence with smallness conditions on form and potential.
result Global weak solution found, smooth with finitely many singular points.
Survey of advances in Higgs bundles and string theory.
problem Understanding gauge fields and matter representations in string theory.
method Geometric engineering and intersection of branes.
result Current advances and open problems in Higgs bundles.
We study elliptic fibrations by analyzing suitable deformations of the fibrations and vanishing cycles. We introduce geometric string junctions and describe some of their properties. We show how the structure of the geometric string junctions is naturally related to the Lie algebra structures of the associated singular…
Defines new canonical lifts for field theories, analyzing Klein-Gordon, Polyakov string, and Einstein-Cartan gravity.
problem Analyzing natural Noether symmetries and conserved quantities in field theories.
method Defining canonical lifts to study field theories and applying Noether's theorem.
result New geometrical interpretation of Virasoro constraint in string theory.
Study 6D localized matter spectrum on singular Calabi-Yau 3-folds.
problem Determining 6D localized charged matter spectrum on singular spaces.
method Using string junctions and SL(2,Z) monodromy to compute massless string junctions. result Agreement with 6D anomaly cancellation in all cases considered.
We present an explicit formula for the topology and H-flux of the T-dual of a general type II compactification, significantly generalizing earlier results. Our results apply to T-dualities with respect to any circle action on spacetime. As before, T-duality exchanges type IIA and type IIB string theories. A new consequ…
Abstract M5 branes on ADE singularities yields BPS spectrum and partition functions.
problem Determine the BPS spectrum and partition functions for M5 branes on ADE singularities.
method Analyze 6d N=(1,0) SCFTs on geometric backgrounds, using contributions from BPS strings and particles. result Explicit expressions for BPS string and particle contributions to partition functions.
We study the propagation of bosonic strings in singular target space-times. For describing this, we assume this target space to be the quotient of a smooth manifold M by a singular foliation F on it. Using the technical tool of a gauge theory, we propose a smooth functional for this scenario, such that the p…
Study of G2 compactifications in M- / string theory.
problem Understanding physical theories from G2 compactifications. method Gauge theory analysis of 3-manifold singularities.
result Found T-brane phenomena in G2 compactifications. Using intersection theory in the context of Hilbert manifolds and geometric homology we show how to recover the main operations of string topology built by M. Chas and D. Sullivan. We also study and build an action of the homology of reduced Sullivan's chord diagrams on the singular homology of free loop spaces, extend…
Develops graphical calculus for monoidal categories with twisted pivotal structures.
problem Constructing modules for surfaces with Morse functions or foliations.
method Graphical calculus and string nets for monoidal categories with twisted pivotal structures.
result Twisted string net modules assemble in an oriented categorified 2-TQFT.
Paper introduces a new invariant for virtual knotoids and proves it's a Vassiliev invariant of order one.
problem Tackles the problem of understanding invariants for virtual knotoids.
method Uses a 0-smoothing invariant constructed from local modifications at classical crossings.
result Demonstrates that the 0-smoothing invariant provides less information than the gluing invariant.
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.
New Morse theory for path homology with coefficients.
problem Defining operations on path homology with differential graded coefficients.
method Using tools from Morse theory and string topology.
result Morse-theoretic description of a product on path homology.
Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper we consider ribbon tubes and ribbon torus-link…
This paper gives a leisurely introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by a survey of recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture. It is aimed at graduate students i…
Let M be a closed oriented surface of genus g≥1, let Bn(M) be the braid group of M on n strings, and let SBn(M) be the corresponding singular braid monoid. Our purpose in this paper is to prove that the desingularization map η:SBn(M)→Z[Bn(M)], introduced in the definition of the Vassiliev in…
We consider how microlocal methods developed for tomographic problems can be used to detect singularities of the Lorentzian metric of the Universe using measurements of the Cosmic Microwave Background radiation. The physical model we study is mathematically rigorous but highly idealized.
We study the string topology of a closed oriented Riemannian manifold M. We describe a compact moduli space of diagrams, and show how the cellular chain complex of this space gives algebraic operations on the singular chains of the free loop space LM of M. These operations are well-defined on the homology of a quotient…
Develops a geometric framework for spaces of distributional sections and calculates curvature of conical metrics.
problem Defining spaces of distributional sections and their geometric operations.
method Geometric framework for generalized sections, incorporating tensor calculus.
result Calculates the curvature of conical metrics used to describe cosmic strings.
We develop a suitable generalization of Almgren's theory of varifolds in a lorentzian setting, focusing on area, first variation, rectifiability, compactness and closure issues. Motivated by the asymptotic behaviour of the scaled hyperbolic Ginzburg-Landau equations, and by the presence of singularities in lorentzian m…
Unified theory of orbifolds and cohomology.
problem Formulating a general theory of orbifolds unifying differential and equivariant cohomology.
method Abstract axiomatization in higher topos theory and concrete models for various orbifolds.
result Fully faithful embedding of orbifolds into a cohesive infinity-topos with proper equivariant cohomology.
D-branes on noncommutative spaces mimic string theory, offering new insights into mirror symmetry.
problem Exploring noncommutative mirror symmetry through D-branes on noncommutative Calabi-Yau spaces.
method Constructing noncommutative ringed spaces from local resolutions, realizing D-branes as morphisms, and defining kinetic energy.
result Dynamical D-branes on noncommutative spaces can be described by a Polyakov-like action, suggesting a bridge between string theory and noncommutative geometry.
Existence and uniqueness of gravitating vortices on Riemann surfaces with specific properties.
problem Existence and uniqueness of gravitating vortices on compact Riemann surfaces.
method Existence via solving a continuity path, proving existence of singular gravitating vortices, and establishing existence of singular Einstein-Bogomol'nyi equations.
result Existence and uniqueness of gravitating vortices on Riemann surfaces with suitable properties.
New hyperKähler orbifolds of Kummer type discovered.
problem Identifying new compact hyperKähler orbifolds.
method Construction of orbifolds and analysis of singularities.
result Only orbifolds with known holomorphic symplectic resolutions lead to known hyperKähler 8-manifolds.
Let B_n be the Artin braid group on n strings with standard generators sigma_1, ..., sigma_{n-1}, and let SB_n be the singular braid monoid with generators sigma_1^{+-1}, ..., sigma_{n-1}^{+-1}, tau_1, ..., tau_{n-1}. The desingularization map is the multiplicative homomorphism eta: SB_n --> Z[B_n] defined by eta(sigma…
In this paper we compute the singular homology of the space of immersions of the circle into the n-sphere. Equipped with Chas-Sullivan's loop product these homology groups are graded commutative algebras, we also compute these algebras. We enrich Morse spectral sequences for fibrations of free loop spaces together wi…
5D SCFTs can have confining vacua with strings and unbroken symmetries.
problem Investigating phases of 5D SCFTs by varying couplings.
method Using geometric realisation of M-theory on metrically conical Calabi-Yau threefolds.
result Many 5D SCFTs have couplings leading to massive, confining vacua with strings and unbroken symmetries.
New deformations for G2-orbifolds using spectral covers.
problem Deforming G2-orbifolds with coassociative fibrations. method Using spectral/cameral covers associated to Higgs bundles.
result Generalizes known deformations of Calabi-Yau threefolds.
The aim of this paper is to define a chain level refinement of the Batalin-Vilkovisky (BV) algebra structure on the homology of the free loop space of a closed, oriented C∞-manifold. For this purpose, we define a (nonsymmetric) cyclic dg operad which consists of "de Rham chains" of free loops with marked points…
Study non-perturbative quantum geometry of string theories using finite difference equations and resurgence analysis.
problem Non-perturbative quantum geometry of open and closed topological string on the resolved conifold.
method Finite difference equations, resurgence analysis, exact WKB techniques.
result Identify 5d BPS states and relate spectral problems to quantum integrable systems.
Derives path integrals for perturbative strings on various backgrounds.
problem Calculating path integrals for strings on curved backgrounds.
method Derives path integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path integrals of all order perturbative strings on various backgrounds.
We use the twistorial construction of D-instantons in Calabi-Yau compactifications of type II string theory to compute an explicit expression for the metric on the hypermultiplet moduli space affected by these non-perturbative corrections. In this way we obtain an exact quaternion-Kahler metric which is a non-trivial d…
Topological string theory derived from string geometry for non-perturbative effects.
problem Deriving non-perturbative effects in string theory.
method Formulating topological string geometry theory and deriving the partition function from fluctuations around a classical solution.
result Perturbative partition function of topological string theory derived.
Identifies all perturbative vacua in bosonic string theory.
problem Identifying all perturbative vacua in bosonic string theory.
method Completely identified perturbative vacua through string fluctuations.
result Derivation of path-integrals up to any order from fluctuations.
Lecture notes on non-Kähler complex threefolds, focusing on conifold transitions.
problem Understanding non-Kähler complex threefolds and conifold transitions.
method Review of basics, description of topological features, survey of recent developments.
result Survey of recent developments on the geometrization of conifold transitions.
Lecture notes on conifold transitions between Calabi-Yau manifolds.
problem Understanding conifold transitions in complex threefolds.
method Differential geometric approach, focusing on explicit calculations and examples.
result Necessary condition for smoothings of nodal Calabi-Yau threefolds proved.
String geometry theory connects strings to space-time and finds string vacua.
problem Identify and find the global minimum of the string vacuum.
method Identify perturbative vacua, derive path-integrals, and solve the global minimum using analytical and numerical methods.
result The global minimum of the effective potential is the string vacuum.
We introduce special Lagrangian submanifolds in C^m and in (almost) Calabi-Yau manifolds, and survey recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture. The paper is aimed at graduate students in Geometry, String Theorists, and others wishing to learn the sub…
Derives path-integrals for superstrings on curved backgrounds using string geometry theory.
problem Calculating path-integrals for superstrings on curved backgrounds.
method Derives path-integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path-integrals for perturbative superstrings on all string backgrounds.
This paper classifies virtual string links up to cobordism using group theory.
problem Classifying virtual string links up to cobordism.
method Using group theory, specifically the group Zn(n−1). result Virtual string links up to cobordism are classified by elements of Zn(n−1). Chiral string integrands simplify to ambitwistor string integrands in the tensionless limit.
problem Understanding the relationship between chiral and ambitwistor string integrands.
method Analyzing the tensionless limit of chiral superstring integrands.
result Chiral superstring integrands reduce to ambitwistor string integrands in the tensionless limit.
A virtual string can be defined as an equivalence class of planar diagrams under certain kinds of diagrammatic moves. Virtual strings are related to virtual knots in that a simple operation on a virtual knot diagram produces a diagram for a virtual string. In this paper we consider three operations on a virtual string …