The Web of D-branes at Singularities in Compact Calabi-Yau Manifolds

TL;DR

The paper demonstrates that in type IIB CY compactifications, otherwise disparate D3/D7-brane configurations at dP0 singularities are continuously connected through supersymmetric, zero-energy transitions driven by bulk D7-branes splitting into flavour branes or recombining with fractional branes. It develops a general kinematic framework (charge conservation and holomorphic divisor representatives) and flatness conditions (F- and D-flatness) to describe transitions of two building-block types, I and II, and then realizes them in a concrete compact model, tracing a path from the trinification quiver SU(3)^3 to a Standard Model–like quiver via successive moves. These results reveal a global web of quiver gauge theories parameterized by open-string moduli associated with bulk D7-branes, showing that local disconnects are bridged in the full compact setting. The work suggests rich open-string dynamics, potential links to inflationary scenarios, and avenues for extending to other singularities and F-theory uplifts, with implications for phenomenology and cosmology.

Abstract

We present novel continuous supersymmetric transitions which take place among different chiral configurations of D3/D7 branes at singularities in the context of type IIB Calabi-Yau compactifications. We find that distinct local models which admit a consistent global embedding can actually be connected to each other along flat directions by means of transitions of bulk-to-flavour branes. This has interesting interpretations in terms of brane recombination/splitting and brane/anti-brane creation/annihilation. These transitions give rise to a large web of quiver gauge theories parametrised by splitting/recombination modes of bulk branes which are not present in the non-compact case. We illustrate our results in concrete global embeddings of chiral models at a dP_0 singularity.

Figures (7)

• Figure 1: The dP$_0$ quiver encoding the $SU(n_0)\times SU(n_1)\times SU(n_2)$ gauge theory with flavour branes. Potential D7-D7 states are not shown.
• Figure 2: Transition from the $SU(3)^3$ quiver to the $SU(3)^2\times SU(2)$: One bulk D7-brane (solid green line) splits into a flavour brane intersecting the fractional branes (red and blue lines) and into an anti-fractional brane. This last one annihilates one fractional brane from the red set (yellow circle).
• Figure 3: Transition from the $SU(3)^3$ quiver to the $SU(4)\times SU(3)^2$ quiver: Two bulk D7-branes (solid green line) splits into a flavour brane of type 0 and type 2 respectively, intersecting the fractional branes (red and blue lines) and into a fractional brane.
• Figure 4: Transition from the $SU(3)^3$ quiver to the $SU(3)^2\times SU(2)$: One D7-brane (solid green line) on top of the O-plane (dotted line) splits into a flavour brane intersecting the fractional branes (red and blue lines) and an anti-fractional brane which annihilates with a fractional brane from the red set (yellow circle).
• Figure 5: Transition from the $SU(3)^3$ quiver to the $SU(4)\times SU(3)^2$ quiver: A rank-two bulk D7-brane (solid green line) splits into a fractional brane and two flavour branes (of type $0$ and $2$ respectively) intersecting the fractional branes (red and blue lines).