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Global symmetries and 't Hooft anomalies in brane tilings

Yosuke Imamura

TL;DR

The paper builds a detailed brane-tile realization of ${\cal N}=1$ quiver gauge theories, identifying global symmetries with brane data and showing that several key ’t Hooft anomalies arise from inflow and boundary variations of the brane action. By analyzing D5-NS5 systems, toric data, and zig-zag path topology, it derives explicit constructions for baryonic, mesonic, and R-symmetries and demonstrates anomaly matching for ${U(1)_M U(1)_B^2}$ and ${U(1)_R U(1)_B^2}$, with ${U(1)_B^3}$ vanishing. The conifold example illustrates the anomaly inflow mechanism in a concrete setting, and the general toric case confirms the same pattern via Maxwell and RR flux couplings. The work highlights both the power of brane-inflown analyses and the need for further development to capture full IR data and remaining anomalies.

Abstract

We investigate the relation between gauge theories and brane configurations described by brane tilings. We identify U(1)_B (baryonic), U(1)_M (mesonic), and U(1)_R global symmetries in gauge theories with gauge symmetries in the brane configurations. We also show that U(1)_MU(1)_B^2 and U(1)_RU(1)_B^2 't Hooft anomalies are reproduced as gauge transformations of the classical brane action.

Global symmetries and 't Hooft anomalies in brane tilings

TL;DR

The paper builds a detailed brane-tile realization of quiver gauge theories, identifying global symmetries with brane data and showing that several key ’t Hooft anomalies arise from inflow and boundary variations of the brane action. By analyzing D5-NS5 systems, toric data, and zig-zag path topology, it derives explicit constructions for baryonic, mesonic, and R-symmetries and demonstrates anomaly matching for and , with vanishing. The conifold example illustrates the anomaly inflow mechanism in a concrete setting, and the general toric case confirms the same pattern via Maxwell and RR flux couplings. The work highlights both the power of brane-inflown analyses and the need for further development to capture full IR data and remaining anomalies.

Abstract

We investigate the relation between gauge theories and brane configurations described by brane tilings. We identify U(1)_B (baryonic), U(1)_M (mesonic), and U(1)_R global symmetries in gauge theories with gauge symmetries in the brane configurations. We also show that U(1)_MU(1)_B^2 and U(1)_RU(1)_B^2 't Hooft anomalies are reproduced as gauge transformations of the classical brane action.

Paper Structure

This paper contains 17 sections, 177 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Brane tilings and D5-NS5 systems
  3. Global symmetries
  4. Strings and chiral operators
  5. Baryonic symmetries
  6. $\theta$ angles and $\mathop{\rm U}(1)_{\rm B}\mathop{\rm SU}(N_a)^2$ anomalies
  7. Mesonic symmetries
  8. R-symmetry
  9. 't Hooft anomalies
  10. $\mathop{\rm U}(1)_{\rm B}^3$
  11. $\mathop{\rm U}(1)_{\rm M}\mathop{\rm U}(1)_{\rm B}^2$
  12. $\mathop{\rm U}(1)_R\mathop{\rm U}(1)_B^2$
  13. The conifold theory
  14. General case
  15. Conclusions and Discussions
  16. ...and 2 more sections

Figures (6)

  • Figure 1: A toric diagram (a) and the corresponding web diagram (b).
  • Figure 2: The oriented segments (arrows) corresponding to the bi-fundamental fields
  • Figure 3: Each leg in the web diagram represents an NS5-brane. It is semi-infinite radial line $L_{\phi_\mu}$ in the non-compact 4689 space. In the internal space along 57, it is wrapped on the cycle ${\bm\mu}$.
  • Figure 4: (a) Structure of branes around an edge. This is correct only topologically. (b) The real shape of the brane configuration in the strong coupling limit.
  • Figure 5: Transition between one D-string and $N$ F-strings. The pairs of small numbers are string charges.
  • ...and 1 more figures