Abstract
We study non-perturbative effects in supersymmetric U(N) gauge theories in eight dimensions realized by means of D(–1)/D7-brane systems with non-trivial world-volume fluxes turned on. Using an explicit string construction in terms of vertex operators, we derive the action for the open strings ending on the D(–1)-branes and exhibit its BRST structure. The space of vacua for these open strings is shown to be in correspondence with the moduli space of generalized ADHM gauge connections which trigger the non-perturbative corrections in the eight-dimensional theory. These corrections are computed via localization and turn out to depend on the curved background used to localize the integrals on the instanton moduli space, and vanish in flat space. Finally, we show that for specific choices of the background the instanton partition functions reduce to weighted sums of the solid partitions of the integers.
Highlights
This analysis can be generalized to other brane systems
The space of vacua for these open strings is shown to be in correspondence with the moduli space of generalized ADHM gauge connections which trigger the nonperturbative corrections in the eight-dimensional theory
When orientifold planes are inserted, these exotic instanton configurations [8,9,10,11,12,13,14,15] can generate non-perturbative effects in the effective action which are prohibited in perturbation theory, like for instance certain Majorana mass terms or Yukawa couplings, which may be relevant for phenomenological applications
Summary
The directions with I = 1, 2, 3, 4 are longitudinal to branes, while the direction with I = 5 is transverse In this complex notation, the background (2.12) implies that in the 7/7 sector, the complex string coordinates ZI (z), ZI (z) and their fermionic partners ΨI (z), ΨI (z) with I = 1, 2, 3, 4 are twisted with a twist parameter θI given by. The bosonic and fermionic coordinates Z5(z), Z5(z) and Ψ5(z), Ψ5(z) are instead untwisted They have the standard mode expansion of untwisted fields, but with Dirichlet/Dirichlet boundary conditions since they are transverse to both type of branes. If we define the GSO projector as 1 + (−1)F. using (2.27) and (2.31), we see that it selects the vacuum in the NS sector and the component with positive chirality in the R sector, realizing in this way a supersymmetric physical spectrum containing just two states, the bosonic vacuum |Ω NS and the fermionic vacuum |Ω, + R. These states of the 7 /7 sector transform in the anti-fundamental of U(N ) and in the fundamental of U(M )
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