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T-branes, monopoles and S-duality

Andres Collinucci, Simone Giacomelli, Roberto Valandro

Abstract

M2 branes probing T-brane backgrounds in M-theory with ADE surface singularities perceive deformations on their worldvolume superpotentials by monopole operators. The dynamics and moduli spaces of the resulting theories can be studied using a dual description involving conventional superpotential terms and (the dimensional reduction of) class S trinion theories. By using the S-dual description of N=2 SU(N) SQCD with 2N flavors in four dimensions, we are able to study T-branes corresponding to all minimal nilpotent orbits for the whole ADE series. Our proposed dualities are supported by the match in squashed sphere partition functions.

T-branes, monopoles and S-duality

Abstract

M2 branes probing T-brane backgrounds in M-theory with ADE surface singularities perceive deformations on their worldvolume superpotentials by monopole operators. The dynamics and moduli spaces of the resulting theories can be studied using a dual description involving conventional superpotential terms and (the dimensional reduction of) class S trinion theories. By using the S-dual description of N=2 SU(N) SQCD with 2N flavors in four dimensions, we are able to study T-branes corresponding to all minimal nilpotent orbits for the whole ADE series. Our proposed dualities are supported by the match in squashed sphere partition functions.

Paper Structure

This paper contains 38 sections, 172 equations, 24 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Goal and general strategy
  3. Reducing to the Abelian problem
  4. Monopole deformations along $U(1)$ nodes
  5. $U(2)$ nodes
  6. $U(2)$ vs $SU(2)\times U(1)$ dual theories
  7. The external $U(2)$ node of the $E_7$ quiver
  8. An internal $U(2)$ node of the $D_N$ quiver
  9. The $U(2)$ node of $D_4$
  10. Monopole deformation along the $U(2)$ node
  11. $U(3)$ nodes and $E_6$ Minahan-Nemeschansky theory
  12. Argyres Seiberg duality with gauged $U(1)$
  13. Lagrangian side:
  14. Non-Lagrangian side:
  15. Coupling S-dual theories into the $E$ quiver
  16. ...and 23 more sections

Figures (24)

  • Figure 2: Effective theory of a single quiver node after monopole deformation.
  • Figure 4: Theory $A_{\rm loc}$.
  • Figure 5: $E_7$ quiver.
  • Figure 6: Modified $E_7$ quiver (with $\phi'=\phi+\psi$ the only $U(1)$ scalar coupled to $v,\tilde{v}$).
  • Figure 7: $U(2)$ nodes in the $D_N$ quiver.
  • ...and 19 more figures