Large Volume Perspective on Branes at Singularities

In this paper we consider a somewhat unconventional approach for deriving worldvolume theories for D3 branes probing Calabi-Yau singularities. The strategy consists of extrapolating the calculation of F-terms to the large volume limit. This method circumvents the inherent limitations of more traditional approaches used for orbifold and toric singularities. We illustrate its usefulness by deriving quiver theories for D3 branes probing singularities where a Del Pezzo surface containing four, five or six exceptional curves collapses to zero size. In the latter two cases the superpotential depends explicitly on complex structure parameters. These are examples of probe theories for singularities which can currently not be computed by other means.

[1]  C. Herzog,et al.  Dibaryons from Exceptional Collections , 2003, hep-th/0306298.

[2]  C. Herzog,et al.  Dibaryon Spectroscopy , 2003, hep-th/0305048.

[3]  Yang-Hui He,et al.  Unhiggsing the del Pezzo , 2002, hep-th/0209228.

[4]  Yang-Hui He,et al.  Quiver theories, soliton spectra and Picard-Lefschetz transformations , 2002, hep-th/0206152.

[5]  S. Katz,et al.  D-branes, open string vertex operators, and Ext groups , 2002, hep-th/0208104.

[6]  M. Douglas,et al.  Seiberg Duality for Quiver Gauge Theories , 2002, hep-th/0207027.

[7]  M. Douglas,et al.  D-branes on Calabi–Yau Manifolds and Superpotentials , 2002, hep-th/0203173.

[8]  S. Katz,et al.  A Geometric unification of dualities , 2001, hep-th/0110028.

[9]  Yang-Hui He,et al.  Toric duality as Seiberg duality and brane diamonds , 2001, hep-th/0109063.

[10]  M. Plesser,et al.  Toric duality is Seiberg duality , 2001, hep-th/0109053.

[11]  A. Iqbal,et al.  Quiver theories from D6 branes via mirror symmetry , 2001, hep-th/0108137.

[12]  Yang-Hui He,et al.  Phase structure of D-brane gauge theories and toric duality , 2001, hep-th/0104259.

[13]  P. Mayr,et al.  Phases of supersymmetric D-branes on Kähler manifolds and the McKay correspondence , 2000, hep-th/0010223.

[14]  A. Tomasiello D-branes on Calabi-Yau manifolds and helices , 2000, hep-th/0010217.

[15]  S. Govindarajan,et al.  D-branes, exceptional sheaves and quivers on Calabi-Yau manifolds: From Mukai to McKay , 2000, hep-th/0010196.

[16]  M. Douglas,et al.  D-branes, categories and N=1 supersymmetry , 2000, hep-th/0011017.

[17]  C. Vafa,et al.  D-Branes And Mirror Symmetry , 2000, hep-th/0005247.

[18]  M. Douglas,et al.  Stability and BPS branes , 2000, hep-th/0002037.

[19]  M. Douglas,et al.  D-branes on the Quintic , 1999, hep-th/9906200.

[20]  Gregory G. Smith,et al.  Computing Global Extension Modules , 1998, J. Symb. Comput..

[21]  L. Ibáñez,et al.  Anomalous U(1)'s in Type I and Type IIB D = 4, N = 1 string vacua , 1998, hep-th/9808139.

[22]  D. Morrison,et al.  Non-spherical horizons, I , 1998, hep-th/9810201.

[23]  C. Vafa,et al.  On conformal field theories in four dimensions , 1998, hep-th/9803015.

[24]  D.Yu. Nogin,et al.  Three-block exceptional collections over Del Pezzo surfaces , 1997, alg-geom/9703027.

[25]  Gregory G. Smith Computing Global Extension Modules for Coherent Sheaves on a Projective Scheme , 1998 .

[26]  M. Douglas,et al.  D-branes, quivers, and ALE instantons , 1996, hep-th/9603167.

[27]  J. Polchinski,et al.  Dirichlet Branes and Ramond-Ramond charges. , 1995, Physical review letters.

[28]  A.Bondal,et al.  Semiorthogonal decomposition for algebraic varieties , 1995, alg-geom/9506012.

[29]  A. Bondal,et al.  Semiorthogonal decompositions for algebraic varieties. , 1995 .

[30]  H. Ooguri,et al.  Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes , 1993, hep-th/9309140.

[31]  E. Witten Chern-Simons gauge theory as a string theory , 1992, hep-th/9207094.