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Chiral Ring Generating Functions & Branches of Moduli Space
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We consider the worldvolume theory of N D3-branes transverse to various non-compact Calabi-Yau spaces, and describe subtleties in the counting of chiral primary operators in such theories due to the presence of multiple branches of moduli space. Extra branches, beyond those directly related to the transverse geometry, result in additional terms in the generating functions for single- and multi-trace operators. Ideals in the N=1 chiral ring correspond to various branches and, in the large N limit, the operator counting reveals a product of Fock spaces, including the Fock space of bosons on the space transverse to the branes.
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Critical dimensions and small cycle dominance from all-orders asymptotics of $d$-matrix theory
The weighted partition numbers of d-matrix theory admit an all-orders asymptotic expansion that switches from divergent to convergent at d=13 (bosonic) or 7 (fermionic).
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