## Advances in Theoretical and Mathematical Physics

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

### Spectra of D-branes with Higgs vevs

Ron Donagi, Sheldon Katz, and Eric Sharpe

#### Abstract

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.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 2 June 2005

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1117751921

**Mathematical Reviews number (MathSciNet)**

MR2160772

**Zentralblatt MATH identifier**

1092.81056

#### Citation

Donagi, Ron; Katz, Sheldon; Sharpe, Eric. Spectra of D-branes with Higgs vevs. Adv. Theor. Math. Phys. 8 (2004), no. 5, 813--859. https://projecteuclid.org/euclid.atmp/1117751921