相关论文: High-Dimensional Topological Field Theory, Positiv…
We propose a new notion of positivity for topological field theories (TFTs), based on S. Eilenberg's concept of completeness for semirings. We show that a complete ground semiring, a system of fields on manifolds and a system of action…
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
Extending the work of the first author, we introduce a notion of semisimple topological field theory in arbitrary even dimension and show that such field theories necessarily lead to stable diffeomorphism invariants. The main result of this…
The object of this paper is to define a subcategory of the category of 3-cobordisms to which invariants of rational homology 3-spheres should generalize. We specify the notion of Topological Quantum Field Theory (in the sense of Atiyah) to…
Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p=<,> with values in (formal linear combinations of) closed…
We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system. These TQFTs associate an invariant to each ciliated surface, which is a Laurent…
We determine the $d+1$ dimensional topological field theory, which encodes the higher-form symmetries and their 't Hooft anomalies for $d$-dimensional QFTs obtained by compactifying M-theory on a non-compact space $X$. The resulting theory,…
Symmetry topological field theory (SymTFT), or topological holography, posits a correspondence between symmetries in a $d$-dimensional theory and topological order in a $(d+1)$-dimensional theory. In this work, we extend this framework to…
We follow the point of view that superstring theory, as the theory of quantum gravity in the number of spacetime dimensions bigger than 4, serves as mathematics for both, 4 dimensional QG and exotic smoothness on open 4-manifolds.…
When two smooth manifold bundles over the same base are fiberwise tangentially homeomorphic, the difference is measured by a homology class in the total space of the bundle. We call this the relative smooth structure class. Rationally and…
In this paper, we present a construction toward a new type of TQFTs at the crossroads of low-dimensional topology, algebraic geometry, physics, and homotopy theory. It assigns TMF-modules to closed 3-manifolds and maps of TMF-modules to…
Quantum field theories with identical local dynamics can admit different choices of global structure, leading to different partition functions and spectra of extended operators. Such choices can be reformulated in terms of a topological…
We study the path integral quantization of the topological 3BF theory, whose gauge symmetry is described by a 3-group. This theory is relevant for the quantization of general relativity coupled to Standard Model of elementary particles. We…
We construct a state-sum type invariant of smooth closed oriented $4$-manifolds out of a $G$-crossed braided spherical fusion category ($G$-BSFC) for $G$ a finite group. The construction can be extended to obtain a $(3+1)$-dimensional…
Topological quantum matter exhibits a range of exotic phenomena when enriched by subdimensional symmetries. This includes new features beyond those that appear in the conventional setting of global symmetry enrichment. A recently discovered…
Symmetry topological field theory (SymTFT) is a convenient tool for studying finite generalized symmetries of a given quantum field theory (QFT). In particular, SymTFTs encode all the symmetry structures and properties, including anomalies.…
The decomposition of an arbitrary axiomatic topological quantum field theory or TQFT into indecomposable theories is given. In particular, unitary TQFT's in arbitrary dimensions are shown to decompose into a sum of theories in which the…
We consider a toy model of a 3-dimensional topological quantum gravity. In this model, a contribution of a given 3-manifold is given by the partition function of an abelian Topological Quantum Field Theory (TQFT), with a topological…
We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of…
In this article we prove that any unitary, axiomatic topological quantum field theory in four-dimensions can not detect changes in the smooth structure of M, a simply connected, closed (compact without boundary), oriented smooth manifold.…