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Chern Simons duality with a fundamental boson and fermion

Sachin Jain, Shiraz Minwalla, Shuichi Yokoyama

TL;DR

The paper derives exact, large-$N$ results for three-dimensional Chern-Simons theories coupled to a fundamental boson and fermion, obtaining exact pole masses via gap equations and the full thermal free energy through a holonomy-averaged matrix model. It proposes a level-rank type duality that exchanges bosons and fermions and connects Giveon–Kutasov duality at the ${ m N}=2$ point to bosonization in decoupling limits, with precise parameter mappings. The authors show the gap equations and the finite-temperature free energy are duality-invariant under these mappings and analyze three scaling limits (fermionic, bosonic, critical) where duality interchanges the limits or yields self-duality. These results provide strong evidence that the bosonization duality persists beyond leading order and hint at a richer web of dualities in non-supersymmetric CS-matter theories, with potential holographic and finite-$N$ implications.

Abstract

We compute the thermal free energy for all renormalizable Chern Simon theories coupled to a single fundamental bosonic and fermionic field in the 't Hooft large N limit. We use our results to conjecture a strong weak coupling duality invariance for this class of theories. Our conjectured duality reduces to Giveon Kutasov duality when restricted to {\cal N}=2 supersymmetric theories and to an earlier conjectured bosonization duality in an appropriate decoupling limit. Consequently the bosonization duality may be regarded as a deformation of Giveon Kutasov duality, suggesting that it is true even at large but finite N.

Chern Simons duality with a fundamental boson and fermion

TL;DR

The paper derives exact, large- results for three-dimensional Chern-Simons theories coupled to a fundamental boson and fermion, obtaining exact pole masses via gap equations and the full thermal free energy through a holonomy-averaged matrix model. It proposes a level-rank type duality that exchanges bosons and fermions and connects Giveon–Kutasov duality at the point to bosonization in decoupling limits, with precise parameter mappings. The authors show the gap equations and the finite-temperature free energy are duality-invariant under these mappings and analyze three scaling limits (fermionic, bosonic, critical) where duality interchanges the limits or yields self-duality. These results provide strong evidence that the bosonization duality persists beyond leading order and hint at a richer web of dualities in non-supersymmetric CS-matter theories, with potential holographic and finite- implications.

Abstract

We compute the thermal free energy for all renormalizable Chern Simon theories coupled to a single fundamental bosonic and fermionic field in the 't Hooft large N limit. We use our results to conjecture a strong weak coupling duality invariance for this class of theories. Our conjectured duality reduces to Giveon Kutasov duality when restricted to {\cal N}=2 supersymmetric theories and to an earlier conjectured bosonization duality in an appropriate decoupling limit. Consequently the bosonization duality may be regarded as a deformation of Giveon Kutasov duality, suggesting that it is true even at large but finite N.

Paper Structure

This paper contains 21 sections, 109 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Exact Results for the thermal free energy
  3. Results for pole masses and thermal free energy
  4. Invariance of the gap equations under duality
  5. Invariance of the free energy under duality
  6. Scaling limits
  7. Fermionic scaling limit
  8. Bosonic scaling limit
  9. The critical scaling limit
  10. Action of duality on scaling limit
  11. Critical boson vs regular fermion
  12. Self duality of the critical scaling limit
  13. Discussion
  14. Details of the computation
  15. Exact effective action
  16. ...and 6 more sections

Figures (2)

  • Figure 1: In Fig \ref{['nu-zero-1']},\ref{['nu-half']},\ref{['nu-one']} we indicate where each of the two conditions in \ref{['condition1']} is obeyed for three separate values of $\nu_B$, namely $|\nu_B|=0, {1\over2}, 1$ respectively. The $y$ axis in each plot is $\hat{m}_{B}^{\text{cri}}$ while the $x$ axis is $\lambda_B$. In each of these plots $|c_B|>|\nu_B|$ if we lie either above the highest curve on the graph or below the lowest curve on the graph. On the other hand $\epsilon>0$ above the middle (blue) curve, but $\epsilon < 0$ below the blue curve. Both conditions in \ref{['condition1']} are only met above the highest curve on each plot.
  • Figure 2: We replot the highest curve in each of the graphs \ref{['nu-zero-1']},\ref{['nu-half']},\ref{['nu-one']} for comparison. The highest curve on this plot is for $|\nu_F|=1$, the middle curve is at $|\nu_F|={1\over2}$ while the lowest curve is at $|\nu_F|=0$.