Related papers: Remarks on 2-dimensional HQFT's
We consider gauge theories in a String Field Theory-inspired formalism. The constructed algebraic operations lead in particular to homotopy algebras of the related BV theories. We discuss invariant description of the gauge fixing procedure…
We explore a novel interpretation of Symmetry Topological Field Theories (SymTFTs) as theories of gravity, proposing a holographic duality where the bulk SymTFT (with the gauging of a suitable Lagrangian algebra) is dual to the universal…
Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete…
We highlight that integer Heisenberg groups at level 2 underlie topological quantum phenomena: their group algebras coincide with the algebras of quantum observables of abelian anyons in fractional quantum Hall (FQH) systems on closed…
The problem of intertwined Hamiltonians in two dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane,Minkowski plane, Poincar{\' e} half plane ($AdS_2$), de Sitter Plane ($dS_2$), sphere, and torus. It…
In this paper we describe a homotopy torsion theory in the category of small symmetric monoidal categories. Thanks to the use of natural isomorphisms as basis for the nullhomotopy structure, this homotopy torsion theory enjoys some…
We consider various homotopy algebras related to Yang-Mills theory and two-dimensional conformal field theory (CFT). Our main objects of study are Yang-Mills $L_{\infty}$ and $C_{\infty}$ algebras and their relation to the certain algebraic…
We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu-Schwarz and Ramond sectors of the orbifold theory as well as…
We discuss the recent developments in the generalized continuous Heisenberg ferromagnet model formulated as a nonrelativistic field theory defined on the target space of the coadjoint orbits. Hermitian symmetric spaces are special because…
The lattice definition of a two-dimensional topological field theory (TFT) is given generically, and the exact solution is obtained explicitly. In particular, the set of all lattice topological field theories is shown to be in one-to-one…
We construct a PROP which encodes 2D-TQFTs with a grading. This defines a graded Frobenius algebra as algebras over this PROP. We also give a description of graded Frobenius algebras in terms of maps and relations. This structure naturally…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
We explore 6-dimensional compactifications of F-theory exhibiting (2,0) superconformal theories coupled to gravity that include discretely charged superconformal matter. Beginning with F-theory geometries with Abelian gauge fields and…
We present a one-dimensional mean field theory for topological 2D gravity. We discuss possible generalizations to other topological field theories, in particular those related to semisimple Frobenius manifolds.
The homotopy theory of representations of nets of algebras over a (small) category with values in a closed symmetric monoidal model category is developed. We illustrate how each morphism of nets of algebras determines a change-of-net…
Classifying Frobenius algebras is a key question that has been addressed in various contexts. The structure of finite-dimensional Frobenius algebras depends on the base field and the dimension of the algebra, leading to different…
By doubling the target space of a canonical Courant algebroid and subsequently projecting down to a specific subbundle, we identify the data of double field theory (DFT) and hence define its algebroid structure. We specify the properties of…
The notion of a Frobenius manifold appears in relation to various topics in algebraic and analytic geometry, such and quantum cohomology, deformation of meromorphic connections, unfolding of singularities and others. In the local setting…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
Based on a study of recently proposed solution of 2 dim. black hole we argue that the space-time singularities of general relativity may be described by topological field theories (TFTs). We also argue that in general TFT is a field theory…