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Embedding three-dimensional bosonization dualities into string theory

Kristan Jensen, Andreas Karch

TL;DR

This work provides a concrete string-theory embedding of 3d bosonization dualities by using flavored holography in a cigar/AdS-soliton background. In the large-$N$ and fixed-$k$ regime, the bulk hosts a $U(k)_N$ CS theory with $N_f$ scalars while the boundary supports an $SU(N)_{-k+N_f/2}$ CS-matter sector with $N_f$ fermions, realizing the dual pair $SU(N)_{-k+N_f/2}$ with $N_f$ fermions ⇄ $U(k)_N$ with $N_f$ scalars. The construction also naturally extends to orientifolds to obtain $SO$/$USp$ variants and clarifies the baryon–monopole operator mapping, supporting the consistency of the dualities at finite $N$. These results offer a UV-complete, geometric framework for 3d bosonization, enabling new generalizations, phase analyses, and potential applications in defects, quivers, and beyond.

Abstract

We give simple string theory embeddings of several recently introduced dualities between 2+1-dimensional Chern-Simons matter theories using probe brane holography. Our construction is reliable in the limit of a large number of colors $N$ with fixed Chern-Simons level $k$.

Embedding three-dimensional bosonization dualities into string theory

TL;DR

This work provides a concrete string-theory embedding of 3d bosonization dualities by using flavored holography in a cigar/AdS-soliton background. In the large- and fixed- regime, the bulk hosts a CS theory with scalars while the boundary supports an CS-matter sector with fermions, realizing the dual pair with fermions ⇄ with scalars. The construction also naturally extends to orientifolds to obtain / variants and clarifies the baryon–monopole operator mapping, supporting the consistency of the dualities at finite . These results offer a UV-complete, geometric framework for 3d bosonization, enabling new generalizations, phase analyses, and potential applications in defects, quivers, and beyond.

Abstract

We give simple string theory embeddings of several recently introduced dualities between 2+1-dimensional Chern-Simons matter theories using probe brane holography. Our construction is reliable in the limit of a large number of colors with fixed Chern-Simons level .

Paper Structure

This paper contains 10 sections, 11 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Level/rank duality
  3. Adding Flavors
  4. Bulk Theory
  5. Boundary Theory
  6. Applications and Discussion
  7. Orientifolds
  8. Baryons and Monopoles
  9. Future Applications
  10. Numerical analysis of a D5 probe brane on the cigar geometry

Figures (2)

  • Figure 1: Holographic bulk dual of ${\cal N}=4$ SYM compactified on a circle with anti-periodic boundary conditions for fermions and a linear theta angle. Not displayed are the internal $\mathbb{S}^5$ and the 3d Minkowski part of the spacetime. The $N_f$ flavor D5 and anti-D5 branes extending from the boundary to the Hall D7 branes at the tip of the cigar are introduced in Section \ref{['S:flavors']}. The dashed line corresponds to an alternate D5/anti-D5 embedding that is also discussed in Section \ref{['S:flavors']}.
  • Figure 2: The $SU(2)_R$ triplet condensate and free energy as a function of triplet mass in the topological (black) and gapless (red) phases respectively. The gapless phase dominates the topological one whenever it exists. We work in units where the parameter $r_0$ appearing in \ref{['cigar']} is unity.