Advances in Theoretical and Mathematical Physics

Spectra of D-branes with Higgs vevs

Ron Donagi, Sheldon Katz, and Eric Sharpe


In this paper we continue previous work on counting open string states between D-branes by considereing open strings between D-branes with nonzero Higgs vevs, and in particular, nilpotent Higgs vevs, as arise, for example, when studying D-branes in orbifolds. Ordinarily Higgs vevs can be interpreted as moving the D-brane, but nilpotent Higgs vevs have zero eigenvalues, and so their interpretation is more interesting - for example, they often correspond to nonreduced schemes, which furnishes an important link in understanding old results relating classical D-brane moduli spaces in orbifolds to Hilbert schemes, resolutions of quotient spaces, and the McKay correspondence. We give a sheaf-theoretic description of D-branes with Higgs vevs, including nilpotent Higgs vevs, and check that description by noting that Ext groups between the sheaves modelling the D-branes, do in fact correctly count open string states. In particular, our analysis expands the types of sheaves which admit on-shell physical interpretations, which is an important step for making derived categories useful for physics.

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Adv. Theor. Math. Phys., Volume 8, Number 5 (2004), 813-859.

First available in Project Euclid: 2 June 2005

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Donagi, Ron; Katz, Sheldon; Sharpe, Eric. Spectra of D-branes with Higgs vevs. Adv. Theor. Math. Phys. 8 (2004), no. 5, 813--859.

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