D-branes, categories and N=1 supersymmetry

By Michael R Douglas. 2000

413 citations recorded by the source corpus.

We show that boundary conditions in topological open string theory on Calabi–Yau (CY) manifolds are objects in the derived category of coherent sheaves, as foreseen in the homological mirror symmetry proposal of Kontsevich. Together with conformal field theory considerations, this leads to a precise criterion determining the supersymmetry preserving branes at any point in CY moduli space, completing the proposal of II-stability.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ea0456f0c684555d6d34fae94a0615c89516b75d

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Citations in the corpus

Remarks on A-branes, mirror symmetry, and the Fukaya category (2001, methodology): “en pairs of B-branes, and the compositions of morphisms are computed by the correlators of the B-model. This correspondence has been intensively discussed in the 1 physics literature (see for example [10, 11, 12, 13] and references therein), and will be taken as a starting point here. An N= 2 SCFTha”
D-Branes on Calabi-Yau Manifolds (2004, methodology): “dentity map Cone(id : E• →E•) is quasi-isomorphic to zero for any complex E•. From section 5.5 it follows that E•[1] represents the anti-brane to E•. The gauge symmetry is therefore stated as follows [83] The B-model is subject toagaugesymmetry generated by simultaneously shifting all the B-brane co”
Quantum quivers and Hall / hole halos (2002, methodology): “ ground state counting should give identical results, so there must be a symmetry between these diﬀerent representations. To get a satisfactory uniﬁed description of such situations, the framework of [13] is needed. A problem left unanswered in this paper is whether the precise match between the gro”
D-brane Deconstructions in IIB Orientifolds (2008, background): “dependon thecomplex structuremoduli. TheDﬂatness constraints are nonholomorphicand depend on the K¨ahlermoduli. Mathematically, these correspond to stability conditions, most generally to Π-stability [130, 59, 131]. They are also related to stability conditions of BPS black hole bound states [132, 8”
D-branes and K-theory in 2D topological field theory (2006, positive): “The use of projective representations was proposed in [49], and further explored in [54].”
Sheaves of t-structures and valuative criteria for stable complexes (2003, background): “Let D ⊂ D1; D ⊂ D2 be the completions inside S1 and S2. Since ¯ E has no torsion in D, we have that Li∗D ¯ E ∈ CD⊂ D1 .”
D-branes, open string vertex operators, and Ext groups (2002, background): “…groups Sheldon Katz1,2 and Eric Sharpe1 1 Department of Mathematics 1409 W. Green St., MC-382 University of Illinois Urbana, IL 61801 2 Department of Physics University of Illinois at Urbana-Champaign Urbana, IL 61801 katz@math.uiuc.edu, ersharpe@uiuc.edu In this note we explicitly work out the…”
Witten index and wall crossing (2014, methodology): “After the pioneering works on D-brane stability and the rôle of FI parameter [20, 21], the relationship was first discussed in detail by F.”
Exact solutions for supersymmetric stationary black hole composites (2003, neutral): “We also give an example of moduli-dependent black hole entropy.”
Gluing Stability Conditions (2009, methodology): “A G ] 1 3 M ay 2 01 0 Introduction Stability conditions on triangulated categories were introduced by Bridgeland in [4] as a mathematical formalization of Douglas’ work on Π-stability in [7, 8].”
Seiberg Duality for Quiver Gauge Theories (2002, background): “ed, and one can further extend the class of geometrically engineered theories by allowing more general combinations of cycles. In the stringy regime, the very deﬁnition of cycle has to be generalized [19, 3]. Eventually this line of development merges with the general discussion of N = 1 string/M th”