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D-Branes And Mirror Symmetry
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We study (2,2) supersymmetric field theories on two-dimensional worldsheet with boundaries. We determine D-branes (boundary conditions and boundary interactions) that preserve half of the bulk supercharges in non-linear sigma models, gauged linear sigma models, and Landau-Ginzburg models. We identify a mechanism for brane creation in LG theories and provide a new derivation of a link between soliton numbers of the massive theories and R-charges of vacua at the UV fixed point. Moreover we identify Lagrangian submanifolds that arise as the mirror of certain D-branes wrapped around holomorphic cycles of K\"ahler manifolds. In the case of Fano varieties this leads to the explanation of Helix structure of the collection of exceptional bundles and soliton numbers, through Picard-Lefshetz theory applied to the mirror LG theory. Furthermore using the LG realization of minimal models we find a purely geometric realization of Verlinde Algebra for SU(2) level k as intersection numbers of D-branes. This also leads to a direct computation of modular transformation matrix and provides a geometric interpretation for its role in diagonalizing the Fusion algebra.
Forward citations
Cited by 7 Pith papers
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Abelian Orbifolds for Brane Brick Models
A construction procedure that induces an abelian orbifold action on the fields and J/E-terms of a parent brane brick model for a toric CY4, yielding explicit orbifolded theories that preserve consistency conditions.
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$Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory
In 5d N=1 U(N) gauge theory, codimension-two defects produce Q-operators whose q-difference equations are the Baxter TQ equations of XXZ spin chains built on bi-infinite evaluation modules of quantum affine algebras.
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Hodge-theoretic Open/Closed Correspondence
The relative periods and mixed Hodge structures of an open toric Calabi-Yau 3-orbifold with a brane agree, up to a Tate twist, with the periods and mixed Hodge structures of a closed toric Calabi-Yau 4-orbifold.
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Algebra of the Infrared with Curve-Valued Potential
Lifted secondary-polytope data on elliptic curves yield L∞ algebras and chamber-dependent directed A∞ algebras, with a quasi-isomorphism universality theorem and expected Maurer–Cartan recovery of Fukaya–Seidel total ...
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GLSM monodromy on quantum period lattice of Calabi-Yau fourfold flops
For Calabi-Yau fourfold flops, the window-shift monodromy equals an EZ twist composed with tensoring by the canonical bundle, and in two example families this twist decomposes into spherical twists.
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Monodromy of Calabi-Yau threefold flops via grade restriction rule and their quantum Kahler moduli
Derives general formula for monodromy action on B-brane charge lattice via hemisphere partition functions in GLSMs and refines it for examples using quantum Kähler discriminant and torus link fundamental groups.
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Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds
Mass deformations of 2d (0,2) brane brick models are shown in four explicit examples to implement birational transformations of toric Calabi-Yau 4-folds, including non-reflexive toric diagrams.
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