Abstract
A recent theorem of Foscolo-Haskins-Nordström [1] which constructs complete G2-holonomy orbifolds from circle bundles over Calabi-Yau cones can be utilised to construct and investigate a large class of generalisations of the M-theory flop transition. We see that in many cases a UV perturbative gauge theory appears to have an infrared dual described by a smooth G2-holonomy background in M-theory. Various physical checks of this proposal are carried out affirmatively.
Highlights
On the physics side such new insights often rely on dualities with other string theories and F-theory [35,36,37,38], in addition to dimensional reductions [39,40,41,42,43]
In this paper we will apply a recent and powerful new construction of non-compact G2-holonomy manifolds and orbifolds [1] to M -theory. These examples are motivated from M -theory/Type IIA duality because they arise as circle bundles over asymptotically conical Calabi-Yau threefolds
As we will show, a fixed G2-holonomy cone from this set can have a variety of topologically distinct desingularisations, a fact which has a natural physical interpretation: they correspond to distinct classical vacua of a perturbative ultra violet (UV) gauge theory; simultaneously we show that there is a corresponding infra red (IR) picture of these vacua in terms of a smooth G2-holonomy space which has the interpretation in Type IIA string theory as different flux configurations on a fixed Calabi-Yau threefold
Summary
We begin with a short review of the original M -theory flop and its reduction to type IIA string theory [8, 44, 45]. In the two flops of the form R4 × S3/ZN the M -theory circle is the Hopf fibre of the S3 and the IIA limit is R4 × P1, which we can view as the resolved conifold with N units of Ramond-Ramond flux on the two-sphere. This is referred to as the closed string side since there are no D-branes. We will consider the corresponding effective theories, ask about the lift to M -theory and the corresponding G2-holonomy metrics and investigate the M -theory flop in this setting and the corresponding UV dynamics which turns out to be governed by SU(N ) theories on Lens spaces S3/Zp
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