Abstract
Abstract We present a string theoretical description, given in terms of branes and orientifolds wrapping vanishing cycles, of the dual pairs of gauge theories analyzed in [1]. Based on the resulting construction we argue that the duality that we observe in field theory is inherited from S-duality of type IIB string theory. We analyze in detail the complex cone over the zeroth del Pezzo surface and discuss an infinite family of orbifolds of flat space. For the del Pezzo case we describe the system in terms of large volume objects, and show that in this language the duality can be understood from the strongly coupled behavior of the O7+ plane, which we analyze using simple F-theory considerations. For all cases we also give a different argument based on the existence of appropriate torsional components of the 3-form flux lattice. Along the way we clarify some aspects of the description of orientifolds in the derived category of coherent sheaves, and in particular we discuss the important role played by exotic orientifolds — ordinary orientifolds composed with auto-equivalences of the category — when describing orientifolds of ordinary quiver gauge theories.
Highlights
In [1], we have argued that the USp theory is dual to the SO theory when N = N − 3 for odd N, where in our conventions Nhas to be even for USp(N + 4) to be defined. (In section 2, we argue that the SO theory is self-dual for even N .)
Based on the resulting construction we argue that the duality that we observe in field theory is inherited from S-duality of type IIB string theory
The action of SL(2, Z) on the discrete torsion triplet reproduces the duality found in field theory; in particular, the dual theories are related by S-duality (τ → −1/τ ), and at most one can be weakly coupled for a given value of the string coupling, leading to a strong/weak duality which descends from ten-dimensional S-duality
Summary
We generalize the argument [2] that O3 planes fall into SL(2, Z) multiplets classified by their discrete torsion to the case of fractional O7 planes at an orbifold singularity. For odd N and for the USp theory, there is no Z6 discrete symmetry, but only a Z3 discrete symmetry as in (1.1), (1.3), with corresponding minimal baryons BN and ANrespectively As before, this is explained in the gravity dual by the topological condition (2.3), which requires a D3 brane to wrap the torsion three-cycle an even number of times in the presence of discrete torsion. The geometric arguments presented apply to other isolated orbifold singularities besides C3/Z3, suggesting that in each case there should be three different gauge theories corresponding to the different choices of discrete torsion. We expect new gauge theory dualities relating the SO and USp theories The appearance of these dualities is a highly nontrivial check on the discrete torsion classification presented above, and is the subject of the section
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