Baryonic symmetries and M5 branes in the AdS_4/CFT_3 correspondence

TL;DR

This work probes abelian baryonic U(1) symmetries in the $AdS_4/\mathrm{CFT}_3$ context for M2 branes on Calabi–Yau four-fold cones, using AdS$_4$ boundary-condition analysis to realize global vs gauged realizations and to identify M5-branes wrapped on toric divisors as dual baryonic operators. Focusing on isolated toric singularities without vanishing six-cycles, the authors solve the field-theory moduli spaces for the $\mathcal{C}(Q^{111})$ theory, match M5-brane baryonic states to gauge-invariant operators, and demonstrate spontaneous baryonic symmetry breaking with a gravity dual that exhibits the corresponding Goldstone mode. They extend the framework to geometries with six-cycles, derive a general warped-volume formula for M5-brane condensates, and discuss how six-cycle instantons can generate non-perturbative superpotentials (as illustrated in $\mathcal{C}(Q^{222})$), highlighting the role of $L^2$ harmonic two-forms in capturing these effects. The results provide explicit checks of holographic duality in a less supersymmetric setting and establish tools to study baryonic sectors and non-perturbative dynamics in warped Calabi–Yau backgrounds, with potential implications for broader AdS$_4$/CFT$_3$ constructions.

Abstract

We study U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau four-fold singularities. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying non-zero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing six-cycles, and study in detail the cone over Q^{111}. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gauge-invariant baryonic-type operators in this theory and wrapped M5 brane states. Moreover, the physics of vacua in which these symmetries are spontaneously broken precisely matches a dual gravity analysis involving resolutions of the singularity, where we are able to match condensates of the baryonic operators, Goldstone bosons and global strings. We also argue more generally that theories where the resolutions have six-cycles are expected to receive non-perturbative corrections from M5 brane instantons. We give a general formula relating the instanton action to normalizable harmonic two-forms, and compute it explicitly for the Q^{222} example. The holographic interpretation of such instantons is currently unclear.

Figures (6)

• Figure 1: The toric diagram for $\mathcal{C}(Q^{111})$.
• Figure 2: The quiver diagram for a conjectured dual of $\mathcal{C}(Q^{111})$.
• Figure 3: The GKZ fan for $Q^{111}$ is $\mathbb{R}^2$, divided into three cones.
• Figure 4: The toric diagram for $\mathcal{C}(Q^{222})$.
• Figure 5: The GKZ fan for $Q^{222}$ is $(\mathbb{R}_{\geq 0})^3$. The axes $\zeta_a$, $a=1,2,3$, may be identified with the Kähler classes of each factor in $\mathbb{CP}^1\times\mathbb{CP}^1\times\mathbb{CP}^1$, or equivalently the FI parameters in the GLSM.