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Distributions in CFT. Part II. Minkowski space
CFTs in Euclidean signature satisfy well-accepted rules, such as the convergent Euclidean OPE. It is nowadays common to assume that CFT correlators...
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Eliminating the ‘Impossible’: Recent Progress on Local Measurement Theory for Quantum Field Theory
Arguments by Sorkin (Impossible measurements on quantum fields. In: Directions in general relativity: proceedings of the 1993 International...
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Slit-Strip Ising Boundary Conformal Field Theory 1: Discrete and Continuous Function Spaces
This is the first in a series of articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling...
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Covariant Homogeneous Nets of Standard Subspaces
Rindler wedges are fundamental localization regions in AQFT. They are determined by the one-parameter group of boost symmetries fixing the wedge. The...
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Tropological sigma models
With the use of mathematical techniques of tropical geometry, it was shown by Mikhalkin some twenty years ago that certain Gromov-Witten invariants...
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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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Energy bounds for vertex operator algebra extensions
Let V be a simple unitary vertex operator algebra and U be a (polynomially) energy-bounded unitary subalgebra containing the conformal vector of V ....
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Gluing. Part I. Integrals and symmetries
We review some aspects of the cutting and gluing law in local quantum field theory (QFT) and study it from a new point of view. In particular, we...
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A mathematical theory of gapless edges of 2d topological orders. Part I
This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the...
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Loop Groups and QNEC
We construct and study solitonic representations of the conformal net associated to some vacuum Positive Energy Representation (PER) of a loop group LG ...
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Axiomatic Conformal Theory in Dimensions >2 and AdS/CT Correspondence
We formulate axioms of conformal theory (CT) in dimensions >2 modifying Segal’s axioms for two-dimensional CFT. (In the definition of...
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’t Hooft Anomalies of Discrete Gauge Theories and Non-abelian Group Cohomology
We study discrete symmetries of Dijkgraaf–Witten theories and their gauging in the framework of (extended) functorial quantum field theory....
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A Cellular Topological Field Theory
We present a construction of cellular BF theory (in both abelian and non-abelian variants) on cobordisms equipped with cellular decompositions....
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Extended Quantum Field Theory, Index Theory, and the Parity Anomaly
We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to...
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A Physical Origin for Singular Support Conditions in Geometric Langlands Theory
We explain how the nilpotent singular support condition introduced into the geometric Langlands conjecture by Arinkin and Gaitsgory arises naturally...
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Perturbative Quantum Gauge Theories on Manifolds with Boundary
This paper introduces a general perturbative quantization scheme for gauge theories on manifolds with boundary, compatible with cutting and gluing,...
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Construction of the Unitary Free Fermion Segal CFT
In this article, we provide a detailed construction and analysis of the mathematical conformal field theory of the free fermion, defined in the sense...
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Conformal Nets II: Conformal Blocks
Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction...
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The C*-algebra of the electromagnetic field
We show that there is a unique C *-algebra for the transverse quantum electromagnetic field obeying the Maxwell equations with any classical...
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Combinatorial Quantum Field Theory and Gluing Formula for Determinants
We define the combinatorial Dirichlet-to-Neumann operator and establish a gluing formula for determinants of discrete Laplacians using a...