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Topological Quantum Field Theory and Algebraic Structures*
These notes are from lectures given at the Quantum field theory and noncommutative geometry workshop at Tohoku University in Sendai, Japan from...
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Transgression Field Theory at the Interface of Topological Insulators
Topological phases of matter can be classified by using Clifford algebras through Bott periodicity. We consider effective topological field theories...
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Mellin–Barnes Representation of the Topological String
We invoke integrals of Mellin–Barnes type to analytically continue the Gopakumar–Vafa resummation of the topological string free energy in the string...
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Airy Equation for the Topological String Partition Function in a Scaling Limit
We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies...
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Higher Abelian Dijkgraaf–Witten Theory
Dijkgraaf–Witten theories are quantum field theories based on (form degree 1) gauge fields valued in finite groups. We describe their generalization...
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A Note on Permutation Twist Defects in Topological Bilayer Phases
We present a mathematical derivation of some of the most important physical quantities arising in topological bilayer systems with permutation twist...
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Quantum Curves for Hitchin Fibrations and the Eynard–Orantin Theory
We generalize the topological recursion of Eynard–Orantin (JHEP 0612:053,
2006 ; Commun Number Theory Phys 1:347–452,2007 ) to the family of spectral... -
Torus Knots and the Topological Vertex
We propose a class of toric Lagrangian A-branes on the resolved conifold that is suitable to describe torus knots on S 3 . The key role is played by...
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Coisotropic Submanifolds and Dual Pairs
The Poisson sigma model is a widely studied two-dimensional topological field theory. This note shows that boundary conditions for the Poisson sigma...
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Topological Field Theories and Harrison Homology
Tools and arguments developed by Kevin Costello are adapted to families of “Outer Spaces” or spaces of graphs. This allows us to prove a version of...
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Boundary Coupling of Lie Algebroid Poisson Sigma Models and Representations up to Homotopy
A general form for the boundary coupling of a Lie algebroid Poisson sigma model is proposed. The approach involves using the Batalin–Vilkovisky...
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Bubble Divergences from Cellular Cohomology
We consider a class of lattice topological field theories, among which are the weak-coupling limit of 2d Yang–Mills theory, the Ponzano–Regge model...
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Finite-Dimensional AKSZ–BV Theories
We describe a canonical reduction of AKSZ–BV theories to the cohomology of the source manifold. We get a finite-dimensional BV theory that describes...
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Global Stringy Orbifold Cohomology, K-Theory and de Rham Theory
There are two approaches to constructing stringy multiplications for global quotients. The first one is given by first pulling back and then pushing...
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Courant–Dorfman Algebras and their Cohomology
We introduce a new type of algebra, the Courant–Dorfman algebra. These are to Courant algebroids what Lie–Rinehart algebras are to Lie algebroids, or...
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A Survey on Mathematical Feynman Path Integrals: Construction, Asymptotics, Applications
Theory and main applications of infinite dimensional oscillatory integrals are discussed, with special attention to the mathematical realization of...
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Two-Dimensional Topological Strings Revisited
The topological string of the type A with a two-dimensional target space is studied, an explicit formula for the string partition function is found...
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Wilson Loops and Topological Phases in Closed String Theory
Using covariant phase space formulations for the natural topological invariants associated with the world-surface in closed string theory, we find...