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Chiral 2d Theories from N=4 SYM with Varying Coupling

Craig Lawrie, Sakura Schafer-Nameki, Timo Weigand

TL;DR

This work constructs and analyzes 2d chiral theories arising from 4d $N=4$ SYM with a varying coupling $\tau$, achieved by a duality-twisted dimensional reduction on complex curves. The authors provide a comprehensive framework linking D3-brane realizations in F-theory to M5- and M2-brane duals, deriving twisted actions, BPS equations, and spectra across 6d, 4d, and 2d settings, and computing anomaly polynomials with inflow arguments. Central to the analysis is the duality twist that couples the curve’s geometry to the $U(1)_D$ bonus symmetry via the line bundle $\mathcal{L}_D$, yielding generalized Hitchin equations and cohomology-counted zero-modes. The study reveals a consistent web of dual descriptions and confirms anomaly cancellation across dimensions, including non-perturbative Higgsing phenomena in F-theory, with implications for 2d SCFTs and their holographic realizations.

Abstract

We study 2d chiral theories arising from 4d N=4 Super-Yang Mills (SYM) with varying coupling tau. The 2d theory is obtained by dimensional reduction of N=4 SYM on a complex curve with a partial topological twist that accounts for the non-constant tau. The resulting 2d theories can preserve (0,n) with n = 2, 4, 6, 8 chiral supersymmetry, and have a natural realization in terms of strings from wrapped D3-branes in F-theory. We determine the twisted dimensional reduction, as well as the spectrum and anomaly polynomials of the resulting strings in various dimensions. We complement this by considering the dual M-theory configurations, which can either be realized in terms of M5-branes wrapped on complex surfaces, or M2-branes on curves that result in 1d supersymmetric quantum mechanics.

Chiral 2d Theories from N=4 SYM with Varying Coupling

TL;DR

This work constructs and analyzes 2d chiral theories arising from 4d SYM with a varying coupling , achieved by a duality-twisted dimensional reduction on complex curves. The authors provide a comprehensive framework linking D3-brane realizations in F-theory to M5- and M2-brane duals, deriving twisted actions, BPS equations, and spectra across 6d, 4d, and 2d settings, and computing anomaly polynomials with inflow arguments. Central to the analysis is the duality twist that couples the curve’s geometry to the bonus symmetry via the line bundle , yielding generalized Hitchin equations and cohomology-counted zero-modes. The study reveals a consistent web of dual descriptions and confirms anomaly cancellation across dimensions, including non-perturbative Higgsing phenomena in F-theory, with implications for 2d SCFTs and their holographic realizations.

Abstract

We study 2d chiral theories arising from 4d N=4 Super-Yang Mills (SYM) with varying coupling tau. The 2d theory is obtained by dimensional reduction of N=4 SYM on a complex curve with a partial topological twist that accounts for the non-constant tau. The resulting 2d theories can preserve (0,n) with n = 2, 4, 6, 8 chiral supersymmetry, and have a natural realization in terms of strings from wrapped D3-branes in F-theory. We determine the twisted dimensional reduction, as well as the spectrum and anomaly polynomials of the resulting strings in various dimensions. We complement this by considering the dual M-theory configurations, which can either be realized in terms of M5-branes wrapped on complex surfaces, or M2-branes on curves that result in 1d supersymmetric quantum mechanics.

Paper Structure

This paper contains 48 sections, 256 equations, 2 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Duality Twists of $N=4$ SYM and Brane Realizations
  3. Duality Twisted $N=4$ SYM
  4. Brane Realizations
  5. M5-branes on Elliptic Surfaces
  6. M2-branes on Curves and Super-QM
  7. Strings from Duality-Twisted $N=4$ SYM
  8. Strings in 6d $N=(1,0)$ Theories
  9. Duality Twist for 2d $N=(0,4)$
  10. Action and BPS Equations
  11. Spectrum
  12. Strings in 4d $N=1$
  13. Duality Twist
  14. Action and BPS Equations
  15. Spectrum
  16. ...and 33 more sections

Figures (2)

  • Figure 1: Overview of setup and duality maps between D3-branes and their M-theory dual description in terms of M2- and M5-branes wrapping the curve $C$ or the elliptic surface with base $C$, respectively.
  • Figure 2: $SL(2,\mathbb Z)$ monodromies on the D3-brane in a degenerate $SO(8)$ model. The perturbative restoration of the $U(1)$ gauge symmetry as $\delta \rightarrow0$ corresponds to absence of any monodromies along $C$.