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Klein Topological Field Theories from Group Representations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers.
Sergey A. Loktev, Sergey M. Natanzon
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Topological defects in nonlocal field theories
Journal of High Energy Physics, 2022 In this paper we study for the first time topological defects in the context of nonlocal field theories in which Lagrangians contain infinite-order differential operators. In particular, we analyze domain walls.
Luca Buoninfante +2 more
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Generalized symmetries of topological field theories
Journal of High Energy Physics, 2023 We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed is forgotten ...
Ben Gripaios +2 more
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Integrality, duality and finiteness in combinatoric topological strings
Journal of High Energy Physics, 2022 A remarkable result at the intersection of number theory and group theory states that the order of a finite group G (denoted |G|) is divisible by the dimension d R of any irreducible complex representation of G.
Robert de Mello Koch +3 more
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On partition functions of refined Chern-Simons theories on S 3
Journal of High Energy Physics, 2021 We present a new expression for the partition function of the refined Chern-Simons theory on S 3 with an arbitrary gauge group, which is explicitly equal to 1 when the coupling constant is zero.
M.Y. Avetisyan, R.L. Mkrtchyan
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Connectomes and properties of quantum entanglement
Journal of High Energy Physics, 2023 Topological quantum field theories (TQFT) encode properties of quantum states in the topological features of abstract manifolds. One can use the topological avatars of quantum states to develop intuition about different concepts and phenomena of quantum ...
Dmitry Melnikov
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Knots, links, and long-range magic
Journal of High Energy Physics, 2021 We study the extent to which knot and link states (that is, states in 3d Chern-Simons theory prepared by path integration on knot and link complements) can or cannot be described by stabilizer states. States which are not classical mixtures of stabilizer
Jackson R. Fliss
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Revisiting the Melvin-Morton-Rozansky expansion, or there and back again
Journal of High Energy Physics, 2020 Alexander polynomial arises in the leading term of a semi-classical Melvin-Morton-Rozansky expansion of colored knot polynomials. In this work, following the opposite direction, we propose how to reconstruct colored HOMFLY-PT polynomials ...
Sibasish Banerjee +2 more
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Complementary projection defects and decomposition
Journal of High Energy Physics, 2021 As put forward in [1] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one.
Fabian Klos, Daniel Roggenkamp
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3 definitions of BF theory on homology 3-spheres
Journal of High Energy Physics, 2023 3-dimensional BF theory with gauge group G (= Chern-Simons theory with non-compact gauge group TG) is a deceptively simple yet subtle topological gauge theory.
Matthias Blau +2 more
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