Abstract
The web of dual gauge theories engineered from a class of toric Calabi-Yau threefolds is explored. In previous work, we have argued for a triality structure by compiling evidence for the fact that every such manifold XN,M (for given (N, M)) engineers three a priori different, weakly coupled quiver gauge theories in five dimensions. The strong coupling regime of the latter is in general described by Little String Theories. Furthermore, we also conjectured that the manifold XN,M is dual to XN ′,M ′ if NM = N′M′ and gcd(N, M) = gcd(N′, M′). Combining this result with the triality structure, we currently argue for a large number of dual quiver gauge theories, whose instanton partition functions can be computed explicitly as specific expansions of the topological partition function {mathcal{Z}}_{N,M} of XN,M. We illustrate this web of dual theories by studying explicit examples in detail. We also undertake first steps in further analysing the extended moduli space of XN,M with the goal of finding other dual gauge theories.
Highlights
A class of theories [6,7,8,9] that has recently attracted attention concerns the theories that are engineered from F-theory compactifications [10,11,12,13,14,15,16] on a two-parameter family of toric, non-compact Calabi-Yau threefolds XN,M
We conjectured that the manifold XN,M is dual to XN,M if N M = N M and gcd(N, M ) = gcd(N, M )
Combining this result with the triality structure, we currently argue for a large number of dual quiver gauge theories, whose instanton partition functions can be computed explicitly as specific expansions of the topological partition function ZN,M of XN,M
Summary
Recent studies [8, 30, 32] of the extended Kahler moduli space of the toric Calabi-Yau threefolds XN,M have suggested the existence of a large number of new dualities of the type. If line segments associated with the coupling constants undergo flop transitions, the duality requires to pass through a region in which the instanton counting parameter becomes of order 1, i.e. a regime in which the gauge coupling constants blow up. In this case, the duality cannot be understood from the perspective of the weakly coupled gauge theories alone: in the corresponding Kahler cone, even before hitting the actual wall that signals the flop transition, the theory enters into a strong coupling phase, in which the description in terms of a (quiver) gauge theory breaks down and needs to be replaced (in general) by an LST.
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