Coupling a QFT to a TQFT and duality

By A. Kapustin, N. Seiberg. 2014

431 citations recorded by the source corpus.

A bstractWe consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On $ \mathbb{R} $d the new theory differs from the original one by the spectrum of operators. Sometimes the local operators are the same but there are different line operators, surface operators, etc. The effects of the added topological degrees of freedom are more dramatic when we compactify $ \mathbb{R} $d, and they are crucial in the context of electric-magnetic duality. We explore several examples including DijkgraafWitten theories and their generalizations both in the continuum and on the lattice. When we couple them to ordinary quantum field theories the topological degrees of freedom allow us to express certain characteristic classes of gauge fields as integrals of local densities, thus simplifying the analysis of their physical consequences.

Subfields: Algebra and Number Theory, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c2d114679bb24bab819ed15317657b9a7312dfd0

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Citations in the corpus

Chern-Simons-matter dualities with SO and USp gauge groups (2016, background): “h are the coeﬃ- cients of terms like w 2w 1 of the gauge bundle [23]. These can be thought of as CS terms of various discrete gauge ﬁelds or as discrete theta parameters analogous to those studied in [44,45,37]. We will not discuss them here. In the N= 2 supersymmetric version of the Chern-Simons-ma”
Gapped boundary phases of topological insulators via weak coupling (2016, methodology): “From the TQFT point of view, this can be described as gauging a Z2 global oneform symmetry that acts on the two sectors [61, 62].”
Higher Gauging and Non-invertible Condensation Defects (2022, methodology): “Following [104,1], we introduce a Stueckelberg field Φ to write the action for this boundary condition: 2i 2π ∫”
Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond (2022, background): “One such generalization, suggested by experience from string theory and SUSY QFT,11 was spelled out in [24, 21]:12 replace the 1-form current j(1) by a (p+1)-form current J(p) satisfying d ∗ J(p+1) = 0 .”
Comments on global symmetries, anomalies, and duality in (2 + 1)d (2017, background): “As in [51,52], these can be represented by a two-form field B with a (3+1)d coupling B ∧ B.”
JT gravity and the ensembles of random matrix theory (2019, background): “The same anomalies are relevant in many different problems; examples without time-reversal symmetry include the Kitaev chain of Majorana fermions [69], the Ising model [70], and intersection theory on the moduli space of Riemann surfaces with boundary [71, 72].”
On 2-group global symmetries and their anomalies (2018, background): “where ∪2 is a bilinear cup product from Cp(X,A)×Cq(X,A′) to Cp+q−2(X,A′′) (its definition can be found in [65] or [35]).”
Exploring 2-group global symmetries (2018, background): “0 More generally, the on-shell currents are given by c-number terms in the background elds, and hence their correlation functions can have non-trivial contact terms, see below. 31 As was explained in [25,26,1], the Z jq Cjgauge theory described by the BF theory in (1.49) has a discrete Z (1) jq Cj 1”
Generalized global symmetries (2014, background): “12 This symmetry acts on the gauge fields by shifting them by a flat Z(G)-valued gauge field [11].”
Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions (2022, background): “Following similar steps in [89, 90], the worldvolume Lagrangian (6.”
Comments on one-form global symmetries and their gauging in 3d and 4d (2018, methodology): “a lot of freedom in adding boundary degrees of freedom. Our main tool for analyzing the system is its ZN one-form global symmetry. Related to this symmetry is an integer label pwith p˘p+ 2Nand pNeven [4,1]. Furthermore, we have an identication in labeling the theories [4,1,2] (;p) ˘(+ 2ˇk;p+ k(N 1))”
Theta, time reversal and temperature (2017, methodology): “This discussion uses some results that appeared in [18,19].”
Anomalies in the space of coupling constants and their dynamical applications II (2019, methodology): “In the presence of this background gauge field, the SUpNq bundle is twisted into a PSUpNq bundle with fixed second Stiefel-Whitney class w2paq “ B [25,1].”
State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter (2016, neutral): “ 1) + A( 2 + 1; 0 1 ) A ( 2; 1 + 0 1 ): (2.38) Using (2.9), we nd !( 0 2; 1; 1 ) = 1 [ 0 1 + [ 1 0 1 ; (2.39) where [ 1 is the Steenrod higher product [24] (see also Appendix B.1. of [25] for a brief summary). In particular, we see that ! = R !does not depend on 2 in this case. Another manifesta”