# On algebraic singularities, finite graphs and D-brane gauge theories : a string theoretic perspective -- with a digression on string field theory

@inproceedings{He2002OnAS, title={On algebraic singularities, finite graphs and D-brane gauge theories : a string theoretic perspective -- with a digression on string field theory}, author={Yang-Hui He}, year={2002} }

In this writing we shall address certain beautiful inter-relations between the construction of 4-dimensional supersymmetric gauge theories and resolution of algebraic singularities, from the perspective of String Theory. We review in some detail the requisite background in both the mathematics, such as orbifolds, symplectic quotients and quiver representations, as well as the physics, such as gauged linear sigma models, geometrical engineering, Hanany-Witten setups and D-brane probes.
We…

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## 13 Citations

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## References

SHOWING 1-10 OF 343 REFERENCES

### Mirror symmetry in three-dimensional gauge theories, SL(2,Z) and D-brane moduli spaces

- Mathematics
- 1997

### D3-branes on partial resolutions of abelian quotient singularities of Calabi–Yau threefolds

- Mathematics
- 2000

### Dn Quivers From Branes

- Mathematics
- 1998

D-branes can end on orbifold planes if the action of the orbifold group includes (−1)L . We consider configurations of D-branes ending on such orbifolds and study the low-energy theory on their…

### Aspects of Type IIB Theory on ALE Spaces

- Mathematics
- 1996

D–brane technology and strong/weak coupling duality supplement traditional orbifold techniques by making certain background geometries more accessible. In this spirit, we consider some of the…

### D-n quivers from branes

- Mathematics
- 1998

D-branes can end on orbifold planes if the action of the orbifold group includes (-1) (FL). We consider configurations of D-branes ending on such orbifolds and study the low-energy theory on their…

### Marginal and relevant deformations of /N=4 field theories and non-commutative moduli spaces of vacua

- Mathematics
- 2000

### Aspects of type IIB theory on asymptotically locally Euclidean spaces

- Mathematics
- 1997

D-brane technology and strong/weak coupling duality supplement traditional orbifold techniques by making certain background geometries more accessible. In this spirit, we consider some of the…