End of the World Brane Dynamics in Holographic 4d $\mathcal{N}=4$ SU(N) with 3d $\mathcal{N}=2$ Boundary Conditions

TL;DR

This paper investigates 4d $ ext{N}=4$ super Yang-Mills with boundary conditions derived from brane configurations, revealing novel boundary phenomena, anomalies, and gravity duals, advancing understanding of boundary conditions in holography and quantum gravity.

Contribution

It introduces new boundary conditions for 4d $ ext{N}=4$ SYM via brane setups, uncovering associated anomalies, boundary couplings, and explicit gravity duals, enriching the classification of boundary phenomena in holography.

Findings

Discovery of a 5d $ extbf{Z}_2$ global gauge anomaly canceled by a 6d inflow.

Identification of localized 3d $ ext{N}=2$ Chern-Simons couplings at the boundary.

Construction of explicit gravity duals with End of the World boundaries.

Abstract

We consider 4d $\mathcal{N}=4$ $SU(N)$ super Yang-Mills on half-space with boundary conditions defined by configurations of Gaiotto-Witten NS5- and D5-branes modded out by a rotated orientifold 5-plane breaking an extra half of the supersymmetries. We focus on configurations in which this O5'-brane is split by an NS5-brane into two oppositely charged halves, leading to a breaking of supersymmetry down to 3d $\mathcal{N}=2$ at the local level. The 5-brane configurations turn into non-trivial $(p,q)$ webs and lead to non-trivial brane and gauge theory phenomena, including a 5d $\mathbf{Z}_2$ global gauge anomaly cancelled by a novel 6d global anomaly inflow, and the appearance of localized 3d $\mathcal{N}=2$ Chern-Simons couplings and the 3d parity anomaly at the boundary of the 4d theory. The systems have explicit gravity duals, given by orientifolds of the AdS$_4\times\mathbf{S}^2\times\mathbf{S}^2$ fibrations over a Riemann surface dual to the Gaiotto-Witten setups. They describe solutions with an asymptotic AdS$_5\times\mathbf{S}^5$ terminating at AdS$_4$ End of the World boundary configurations, whose rich dynamics reproduces the above physical properties. They also provide the SymTFT of the 4d $\mathcal{N}=4$ on half-space with a new class of boundary conditions. We explore the interplay of bulk and boundary topological couplings and draw general lessons for the classification of cobordism defects of bulk quantum gravity theories in the swampland program.