M-Fivebranes Wrapped on Supersymmetric Cycles II
Jerome P. Gauntlett, Nakwoo Kim
TL;DR
Gauntlett and Kim construct D=11 supergravity solutions dual to twisted M5-brane field theories arising from wrapping M5-branes on supersymmetric cycles, using a D=7 maximal gauged supergravity framework that is uplifted to D=11. They analyze three wrapped-cycle configurations: a complex Lagrangian four-cycle in a D=8 hyper-Kähler manifold yielding a D=2 theory with $$(2,1)$$ supersymmetry, a product of two holomorphic two-cycles in CY$_2\times$CY$_2$ yielding a D=2 theory with $$(2,2)$$ supersymmetry, and a product of a SLAG three-cycle with a holomorphic two-cycle giving a quantum mechanics with two supercharges; for each case they derive BPS equations and identify IR fixed points of the flows, notably $AdS_3$-type geometries for the two-dimensional theories and $AdS_2$-type geometries for the quantum-mechanical case. The IR fixed points come with central charges that scale as $c\sim N^3$ and depend on the volumes of the wrapped cycles, illustrating new AdS/CFT dual pairs from wrapped M5-branes. The work extends the landscape of holographic duals for twisted brane theories and provides a framework for comparisons with corresponding field theories, including possible checks of central charges and detailed geometric data.
Abstract
We construct D=11 supergravity solutions dual to the twisted field theories arising when M-theory fivebranes wrap supersymmetric cycles. The cases considered are M-fivebranes wrapped on (i) a complex Lagrangian four-cycle in a D=8 hyper-Kaehler manifold corresponding to a D=2 field theory with (2,1) supersymmetry (ii) a product of two holomorphic two-cycles in a product of two Calabi-Yau two-folds corresponding to a D=2 field theory with (2,2) supersymmetry and (iii) a product of a holomorphic two-cycle and a SLAG three-cycle in a product of a Calabi-Yau two-fold and a Calabi-Yau three-fold corresponding to a quantum mechanics with two supercharges. In each case we construct BPS equations and find IR superconformal fixed points corresponding to new examples of AdS/CFT duality arising from the twisted field theories.