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$M$-strings and AdS$_3$ solutions to M-theory with small $\mathcal{N}=(0,4)$ supersymmetry

Yolanda Lozano, Carlos Nunez, Anayeli Ramirez, Stefano Speziali

TL;DR

The authors construct and analyze three interconnected holographic families: (i) AdS$_3$ solutions in M-theory with small $\mathcal{N}=(0,4)$ supersymmetry describing $M_A$-strings, (ii) a momentum-extended AdS$_3$ branch whose dual is a 1d SCQM, and (iii) AdS$_2$ solutions in (massive) IIA arising from double analytic continuation. They demonstrate that the central charge scales linearly with the total number of $M_A$-strings and provide both holographic and field-theoretic derivations, including a long-quiver analysis. The constructions unify uplifts from IIA to M-theory and establish a complete class of AdS$_3$ solutions with SU(2) structure, while the AdS$_2$ branches extend to massive IIA with four Poincaré supercharges. These results illuminate the microscopic degrees of freedom of M_A-strings, connect to M(atrix) theory descriptions, and suggest broader links to defect CFTs and OM theory.

Abstract

We construct a general class of (small) $\mathcal{N}=(0,4)$ superconformal solutions in M-theory of the form AdS$_3\times S^3/\mathbb{Z}_k\times \text{CY}_2$, foliated over an interval. These solutions describe M-strings in M5-brane intersections. The $M$-strings support $(0,4)$ quiver CFTs that are in correspondence with our backgrounds. We compute the central charge and show that it scales linearly with the total number of $M$-strings. We introduce momentum charge, thus allowing for a description in terms of M(atrix) theory. Upon reduction to Type IIA, we find a new class of solutions with four Poincaré supercharges of the form AdS$_2\times S^3\times \text{CY}_2\times \mathcal{I}$, that we extend to the massive IIA case. We generalise our constructions to provide a complete class of AdS$_3$ solutions to M-theory with (0,4) supersymmetry and SU(2) structure. We also construct new $AdS_2\times S^3\times \text{M}_4\times \mathcal{I}$ solutions to massive IIA, with M$_4$ a 4d Kähler manifold and four Poincaré supercharges.

$M$-strings and AdS$_3$ solutions to M-theory with small $\mathcal{N}=(0,4)$ supersymmetry

TL;DR

The authors construct and analyze three interconnected holographic families: (i) AdS solutions in M-theory with small supersymmetry describing -strings, (ii) a momentum-extended AdS branch whose dual is a 1d SCQM, and (iii) AdS solutions in (massive) IIA arising from double analytic continuation. They demonstrate that the central charge scales linearly with the total number of -strings and provide both holographic and field-theoretic derivations, including a long-quiver analysis. The constructions unify uplifts from IIA to M-theory and establish a complete class of AdS solutions with SU(2) structure, while the AdS branches extend to massive IIA with four Poincaré supercharges. These results illuminate the microscopic degrees of freedom of M_A-strings, connect to M(atrix) theory descriptions, and suggest broader links to defect CFTs and OM theory.

Abstract

We construct a general class of (small) superconformal solutions in M-theory of the form AdS, foliated over an interval. These solutions describe M-strings in M5-brane intersections. The -strings support quiver CFTs that are in correspondence with our backgrounds. We compute the central charge and show that it scales linearly with the total number of -strings. We introduce momentum charge, thus allowing for a description in terms of M(atrix) theory. Upon reduction to Type IIA, we find a new class of solutions with four Poincaré supercharges of the form AdS, that we extend to the massive IIA case. We generalise our constructions to provide a complete class of AdS solutions to M-theory with (0,4) supersymmetry and SU(2) structure. We also construct new solutions to massive IIA, with M a 4d Kähler manifold and four Poincaré supercharges.

Paper Structure

This paper contains 16 sections, 64 equations, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Review of the AdS$_3\times$ S$^2\times$ CY$_2$ solutions to massive Type IIA
  3. Brief description of the 2d dual CFTs
  4. Brief description of the 2d dual CFTs
  5. New AdS$_3\times$ S$^3/\mathbb{Z}_k\times$ CY$_2$ solutions in M-theory
  6. Brane set-up
  7. Central charge
  8. Field theory calculation
  9. Double analytic continuation
  10. Dual quantum mechanics
  11. New AdS$_2\times$S$^3\times$CY$_2$ solutions to massive Type IIA
  12. Brane set-up
  13. Conclusions
  14. Review of the general AdS$_3 \times$ S$^2 \times$ M$_4$ solutions in Lozano:2019emq
  15. New AdS$_3 \times$ S$^2 \times$ M$_4$ solutions in M-theory
  16. ...and 1 more sections

Figures (6)

  • Figure 1: Generic quiver field theory whose IR is holographic dual to the solutions reviewed in this section. The solid black line represents a (4,4) hypermultiplet, the grey line a (0,4) hypermultiplet and the dashed line a (0,2) Fermi multiplet. The degrees of freedom at each node are (4,4) vector multiplets.
  • Figure 2: Generic quiver field theories dual to the AdS$_3$ solutions with vanishing Romans' mass.
  • Figure 3: Left: Generic quiver field theory whose IR limit is holographic dual to the $AdS_3$ solutions with $I=S^1$. Right: Quiver field theory for $M=1$. In the right quiver, the (0,4) hypermultiplets combine with two (0,2) Fermi multiplets to produce (4,4) hypermultiplets. Supersymmetry is thus enhanced to (4,4).
  • Figure 4: Left: 2d (0,4) quiver CFT dual to the AdS$_3\times$ S$^3\times$CY$_2\times$ I solution. Right: 4d $\mathcal{N}=2$ quiver CFT with flavours.
  • Figure 5: Completed quiver field theories whose IR limits are holographic duals to the AdS$_3\times$ S$^3/\mathbb{Z}_k$ solutions in M-theory. $N_2^{(j)}$ refer to M2-brane charges and $N_6=k$ to the constant, KK-monopole charge. M5-branes provide for the $2N_2^{(i)}-N_2^{(i-1)}-N_2^{i+1)}$ flavour groups that render the quiver non-anomalous.
  • ...and 1 more figures