Topological Disorder Operators in Three-Dimensional Conformal Field Theory
By V. Borokhov, A. Kapustin, Xinkai Wu. 2002
302 citations recorded by the source corpus.
Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogues of twist and winding-state operators in free 2d CFTs. We call them monopole operators for reasons explained in the text. The importance of monopole operators is that in the Higgs phase, they create Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in three-dimensional QED using large N-f expansion. In particular, we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N-f. We also show that monopole operators transform non-trivially under the flavor symmetry group, with the precise representation depending on the value of the Chern-Simons coupling.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/d9d712230812f3386ace2728b8258c632639ea09
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Nuclear and High Energy Physics
Citations in the corpus
- Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality (2005, background): “[ 8 , 9]. It is a topological disorder operator in the sense that the gauge field looks like the field of Dirac monopole near the insertion point.”
- Gapped boundary phases of topological insulators via weak coupling (2016, methodology): “As in [45], which we follow in the analysis below, the asymptotic conformal invariance near p enables one to determine the quantum numbers of monopole operators in radial quantization.”
- Deconfined quantum critical points: symmetries and dualities (2017, background): “This can be seen by analyzing the fermion zero modes [65] associated with the monopole operator M0a: each Dirac fermion ψ i contributes a complex fermion zero mode fi in the monopole background, and gauge invariance requires two of the four zero modes to be filled in the ground state, so a gauge-inv”
- Comments on twisted indices in 3d supersymmetric gauge theories (2016, methodology): “mix with the gauge symmetry U(1)a, either classically through Chern-Simons interactions, or at one-loop in the presence of matter fields [53, 54, 55, 56].”
- SL(2;Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry (2003, background): “Finally, in this section, we discuss this SL(2,Z) action on three-dimensional conformal field theories in the light of the AdS/CFT correspondence.”
- The "parity" anomaly on an unorientable manifold (2016, methodology): “We determine the quantum numbers of a charge 1 monopole operator in a standard way via radial quantization on S2 [36].”
- Fivebranes and Knots (2011, background): “’t Hooft operators – which in this context are often called monopole operators – do exist in Chern-Simons theories with matter fields [104, 105].”
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals (2008, background): “On the other hand, lifting the configuration (via T-duality) to M-theory will allow us to relate these theories (at low energies) to M2-branes probing a C4/Zk singularity, and thereby to justify the duality conjecture we made in the previous section.”
- Chiral flavors and M2-branes at toric CY4 singularities (2009, background): “1 Monopole operators and flavors A fundamental rôle in the study of the quantum moduli space of the flavored theories is played by monopole operators [34, 35, 36, 37, 38, 39, 40, 41]: in the Euclidean theory, their insertion creates quantized flux in a U(1) subgroup of the gauge group through a sphe”
- Charges of monopole operators in Chern-Simons Yang-Mills theory (2009, background): “Such a calculation has been performed in a different context in [19,20].”