Baryons, monopoles and dualities in Chern-Simons-matter theories

Abstract

There is significant evidence for a duality between (non-supersymmetric) U(N ) Chern-Simons theories at level k coupled to fermions, and U(k) Chern-Simons theories at level N coupled to scalars. Most of the evidence comes from the large N 't Hooft limit, where many details of the duality (such as whether the gauge group is U(N ) or SU(N ), the precise level of the U(1) factor, and order one shifts in the level) are not important. The main evidence for the validity of the duality at finite N comes from adding masses and flowing to pure Chern-Simons theories related by level-rank duality, and from flowing to the non-supersymmetric duality from supersymmetric dualities, whose finite N validity is wellestablished. In this note we clarify the implications of these flows for the precise form of the duality; in particular we argue that in its simplest form the duality maps SU(N ) theories to U(k) theories, though there is also another version relating U(N ) to U(k). This precise form strongly affects the mapping under the duality of baryon and monopole operators, and we show, following arguments by Radičević, that their mapping is consistent with our claims. We also discuss the implications of our results for the additional duality between these Chern-Simons matter theories and (the UV completion of) high-spin gravity theories on AdS 4 . The latter theories should contain heavy particles carrying electric and/or magnetic charges under their U(1) gauge symmetry.

A master bosonization duality

“…In subsection 3.2 we deduce the faithful subgroup of the manifest SU(N f )×U(N s )×U(1) global symmetry that acts on both sides of the duality, finding that this faithful global symmetry matches. Our discussion closely imitates that of [7,32].…”

“…One then thinks of the Chern-Simons-matter theories in (1.2) and (1.3) as describing a second order transition separating these two phases. Crucially, the IR TFTs describing the massive phases of one side of the duality match those of the other [7]. For example, deforming SU(N ) −k+ N f 2 theory coupled to N f fermions by a negative mass leads to a SU(N ) −k TFT in the IR, while deforming U(k) N theory coupled to scalars by a positive mass-squared leads to an IR U(k) N TFT.…”

“…The best evidence comes from direct computations at large N, k with N/k finite. The exact global symmetries and their 't Hooft anomalies match [32], as do the quantum numbers of baryon and monopole operators [7]. At large N , these dualities appear to be inherited from a three-dimensional version of Seiberg duality [33,34], and there is some expectation that the non-supersymmetric bosonization dualities are always the offspring of a parent supersymmetric duality (see e.g.…”

“…There has been an accumulation of evidence this decade for dualities between nonsupersymmetric Chern-Simons theories coupled to fundamental matter [4][5][6][7][8]. These conjectured dualities may be thought of as taking the level/rank dualities, adding suitable matter content on both sides, and tuning to a conformal field theory (CFT).…”

“…These conjectured dualities may be thought of as taking the level/rank dualities, adding suitable matter content on both sides, and tuning to a conformal field theory (CFT). The basic sequences of interest in this work were precisely formulated by Aharony and read [7]: …”