Phases Of N=2 Theories In 1+1 Dimensions With Boundary

By M. Herbst, K. Hori, David C. Page. 2008

207 citations recorded by the source corpus.

We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-Paton factor, which can be used to define a family of D-branes over a region of the Kahler moduli space that connects special points of different character. As an application, we find a precise, transparent relation between D-branes in various geometric phases as well as free orbifold and Landau-Ginzburg points. The result reproduces and unifies many of the earlier mathematical results on equivalences of D-brane categories, including the McKay correspondence and Orlov's construction.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5387a90d3c51d940aa77bd815cc6ca5b787d098a

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Citations in the corpus

G-flux in F-theory and algebraic cycles (2011, methodology): “D2-branes on holomorphic curves, could be described via matrix factorizations, in [95, 96].”
D-brane Deconstructions in IIB Orientifolds (2008, background): “In particular the cosmological constant can in princi- ple be discretely tuned to become extremely small, easily of the order of the measured cosmological constant or less [6, 7].”
Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary (2013, methodology): “Because of the Wick rotation which changed the reality of the fields, a part of the conditions in [11] need to be split into the real and imaginary parts.”
Witten index and wall crossing (2014, methodology): “By the standard argument (see for example [49] Section 2.”
Aspects of non-abelian gauge dynamics in two-dimensional Script N = (2,2) theories (2006, background): “It would be very interesting to construct equivalences of categories from the physics point of view, as is done for Abelian theories [ 43 ].”
The derived category of a GIT quotient (2012, methodology): “1 was the grade restriction rules for the category of boundary conditions for B-branes of Landau-Ginzburg models studied by Hori, Herbst, and Page in [14], as interpreted mathematically by Segal [24].”
Gauged Floer Theory Of Toric Moment Fibers (2010, background): “ich is why the arguments of the last section are only conjectural. We do not discuss homological mirror symmetry from the point of gauged sigma models; this direction is discussed in Herbst-Hori-Page [36]. Finally we mention a few other related works. Alston [4], Alston-Amorim [5], and Abreu-Macarin”
The Crepant Transformation Conjecture for Toric Complete Intersections (2014, background): “Hori– Romo [50] explained why the Mellin–Barnes analytic continuation of hemisphere partition functions should be compatible with brane transportation [49] in the B-brane category.”
Duality in two-dimensional (2,2) supersymmetric non-Abelian gauge theories (2011, background): “They can be promoted to the relations between N = 2 theories with boundaries [38].”
Combinatorial constructions of derived equivalences (2016, background): “ace which is a mathematical interpretation of the “complexiﬁed Ka¨hler moduli space” studied in N = 2 superconformal ﬁeld theory. In particular, we generalize and make precise the physical picture of [HHP1]. As in the rest of the paper, we will ﬁx a quasi-symmetric linear representation X of a split”