Monopole Operators and Mirror Symmetry in Three Dimensions

By V. Borokhov, A. Kapustin, Xinkai Wu. 2002

255 citations recorded by the source corpus.

We study vortex-creating, or monopole, operators in 3d CFTs which are the infrared limit of N = 2 and N = 4 supersymmetric QEDs in three dimensions. Using large-Nf expansion, we construct monopole operators which are primaries of short representations of the superconformal algebra. Mirror symmetry in three dimensions makes a number of predictions about such operators, and our results confirm these predictions. Furthermore, we argue that some of our large-Nf results are exact. This implies, in particular, that certain monopole operators in N = 4 d = 3 SQED with Nf = 1 are free fields. This amounts to a proof of 3d mirror symmetry in a special case.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/fe3e192d0af6859d6ff35a74a1a81f59d962a205

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Citations in the corpus

A Duality Web in 2+1 Dimensions and Condensed Matter Physics (2016, unknown): “12), an interesting background field A can be constructed by removing a point P from our 2+1d manifold and specifying “monopole boundary conditions” [61,62] on an S(2) surrounding P, ∫ S2 dA = 2π.”
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.”
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].”
Charges of monopole operators in Chern-Simons Yang-Mills theory (2009, methodology): “A proposal for the U(1) R-charge of the monopole operator in gauge theories with N = 3 supersymmetry was made in [29, 30] based on the results of [20] and group theoretic arguments.”
N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals (2008, background): “nal U(1) gauge group. This is a ﬂux on the S2 surrounding the point where the operator is inserted. These operators are called ’t Hooft operators or monopole operators and were discussed in detail in [24,25]. Let us begin by discussing this in the U(1)×U(1) case. A conﬁguration with nunits of ﬂux in”
Chiral flavors and M2-branes at toric CY4 singularities (2009, methodology): “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”
Three-dimensional N=6 SCFT's and their membrane dynamics (2008, background): “,∞ (see also [43] for the spectrum of the associated Dirac equation).”
Towards the F-theorem: $ \mathcal{N} = 2 $ field theories on the three-sphere (2011, unknown): “[28,29] based on the work of [31].”
3d dualities from 4d dualities (2013, background): “he construction of a ’t Hooft loop in four dimensions, 16 by removing the point xand requiring that we sum over gauge ﬁeld conﬁgurations that have one unit of magnetic ﬂux on the S2 around the point x[55,56,57]. This high-energy operator ﬂows to exp(ia(x)) in the low-energy eﬀective action. In the s”
Comments on 3d Seiberg-like dualities (2011, background): “The first kind is known as mirror symmetry [3, 4]: its hallmark is that it exchanges the role of fundamental fields and monopole operators [5, 6].”
3-Manifolds and 3d Indices (2011, unknown): “, [49].”
Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality (2005, methodology): “ 3d dual pairs have indeed been discovered [3, 4, 5, 6, 7]. Duality of this kind is known as 3d mirror symmetry. The operator in the gauge theory creating the ANO vortex has been constructed in Refs. [8, 9]. It is a topological disorder operator in the sense that the gauge ﬁeld looks like the ﬁeld o”
The Coulomb Branch of 3d N = 4 Theories (2015, background): “The construction is local, in the sense that it can be performed separately for each U(1) gauge group in a general theory, where the SQED results apply.”
Nonperturbative tests of three-dimensional dualities (2010, methodology): “To prove the basic abelian mirror symmetry one needs to use less direct methods [10].”
S-duality of boundary conditions in N=4 super Yang-Mills theory (2008, methodology): “) The monopole operator of charge a is defined in the same way, and is still a chiral operator, but as shown in [6], it now carries a non-zero R-charge”