From Loop Space Mechanics to Nonabelian Strings
arXiv:hep-th/0509163
Abstract
Lifting supersymmetric quantum mechanics to loop space yields the superstring. A particle charged under a fiber bundle thereby turns into a string charged under a 2-bundle, or gerbe. This stringification is nothing but categorification. We look at supersymmetric quantum mechanics on loop space and demonstrate how deformations here give rise to superstring background fields and boundary states, and, when generalized, to local nonabelian connections on loop space. In order to get a global description of these connections we introduce and study categorified global holonomy in the form of 2-bundles with 2-holonomy. We show how these relate to nonabelian gerbes and go beyond by obtaining global nonabelian surface holonomy, thus providing a class of action functionals for nonabelian strings. The examination of the differential formulation, which is adapted to the study of nonabelian p-form gauge theories, gives rise to generalized nonabelian Deligne hypercohomology. The (possible) relation of this to strings in Kalb-Ramond backgrounds, to M2/M5-brane systems, to spinning strings and to the derived category description of D-branes is discussed. In particular, there is a 2-group related to the String-group which should be the right structure 2-group for the global description of spinning strings.
PhD thesis
References in corpus (72)
- M Theory As A Matrix Model: A Conjecture
- The Holographic Weyl anomaly
- Introduction to sh Lie algebras for physicists
- Born-Infeld particles and Dirichlet p-branes
- Comments on String Dynamics in Six Dimensions
- Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
- D-branes from M-branes
- Quantum Gravity: a Progress Report
- Some Comments On String Dynamics
- String Theory and Classical Absorption by Threebranes
- A brief review of "little string theories"
- Higher-Dimensional Algebra V: 2-Groups
- Toric Duality as Seiberg Duality and Brane Diamonds
- Strong/Weak Coupling Duality from the Dual String
- Deconstructing (2,0) and Little String Theories
- A Review on Tachyon Condensation in Open String Field Theories
- Conformal anomaly of (2,0) tensor multiplet in six dimensions and AdS/CFT correspondence
- WZW branes and gerbes
- A New Approach to Integrable Theories in any Dimension
- Seiberg Duality for Quiver Gauge Theories
- Bundle gerbes for Chern-Simons and Wess-Zumino-Witten theories
- Higher Gauge Theory: 2-Connections on 2-Bundles
- The sh Lie structure of Poisson brackets in field theory
- Higher Yang-Mills Theory
- Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries
- Current-Current Deformations of Conformal Field Theories, and WZW Models
- The Geometry of Bundle Gerbes
- Stability conditions on triangulated categories
- Introduction to the language of stacks and gerbes
- Open membranes in a constant C-field background and noncommutative boundary strings
- Algebroid Yang-Mills Theories
- Gerbes, M5-Brane Anomalies and E_8 Gauge Theory
- The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space
- Higgs fields, bundle gerbes and string structures
- Holonomy and parallel transport for Abelian gerbes
- D-brane categories
- Duality Symmetries and Noncommutative Geometry of String Spacetime
- Review of Open Superstring Field Theory
- BPS Spectrum of 5 Dimensional Field Theories, (p,q) Webs and Curve Counting
- Open Supermembranes Coupled to M-Theory Five-Branes
- Product Integral Formalism and Non-Abelian Stokes Theorem
- Non-Abelian Wilson Surfaces
- T-Duality in Arbitrary String Backgrounds
- 2-categorical Poincare Representations and State Sum Applications
- The Nambu-Goto Theory of Closed Bosonic Strings Moving in 1+3-Dimensional Minkowski Space: The Quantum Algebra of Observables
- Algebraic quantization of the closed bosonic string
- Canonical Equivalence between Super D-string and Type IIB Superstring
- An Effective Superstring Spectral Action
- Stability data and t-structures on a triangulated category
- Corrections to D-brane Action and Generalized Boundary State
- Aspects of M-5 brane world volume dynamics
- Local symmetries of the non-Abelian two-form
- Discrete Differential Geometry on causal graphs
- Open Wilson Lines as States of Closed String
- String Junctions and Bound States of Intersecting Branes
- DDF and Pohlmeyer invariants of (super)string
- Nonabelian 2-forms and loop space connections from SCFT deformations
- On deformations of 2d SCFTs
- Non-Abelian Gerbes from Strings on a Branched Space-Time
- A Comment on the chi_y Genus and Supersymmetric Quantum Mechanics
- Noncommutative Geometry, Strings and Duality
- Intersecting M2- and M5-branes
- Covariant Hamiltonian evolution in supersymmetric quantum systems
- Non-Linear Field Equation from Boundary State Formalism
- Constructing exotic D-branes with infinite matrices in type IIA string theory
- Parallel transport on non-Abelian flux tubes
- Physical Spectra in String Theories --- BRST Operators and Similarity Transformations
- Pohlmeyer invariants are expressible in terms of DDF invariants
- Superconformal Deformations and Space-Time Symmetries
- Superfield T-duality rules in ten dimensions with one isometry
- Combinatorial Stacks and the Four-Colour Theorem
- Super-Pohlmeyer invariants and boundary states for non-abelian gauge fields