Exact results for boundaries and domain walls in 2d supersymmetric theories

Honda, Daigo; Okuda, Takuya

doi:10.1007/jhep09(2015)140

Cited by 94 publications

(164 citation statements)

References 103 publications

(276 reference statements)

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“…These can be computed using localization, along the lines of [64,65] (4d) and [66][67][68][69] (2d and 3d). We will investigate these partition functions in a future publication.…”

Section: Partition Functionsmentioning

confidence: 99%

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Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 $$ \mathcal{N}=4 $$ gauge theory

Bullimore

Dimofte

Gaiotto

et al. 2016

J. High Energ. Phys.

109

229

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Abstract:We introduce several families of N = (2, 2) UV boundary conditions in 3d N = 4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs-and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality -an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.

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“…These can be computed using localization, along the lines of [64,65] (4d) and [66][67][68][69] (2d and 3d). We will investigate these partition functions in a future publication.…”

Section: Partition Functionsmentioning

confidence: 99%

“…To describe the gradient-flow manifolds more explicitly, we split the chiral ring as 67) where C[M C ] 0 contains ϕ and monopole operators with t R ·A = 0, and…”

Section: Effect Of Real Fi and Real Massesmentioning

confidence: 99%

Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 $$ \mathcal{N}=4 $$ gauge theory

Bullimore

Dimofte

Gaiotto

et al. 2016

J. High Energ. Phys.

109

229

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“…For D-branes, appendix C outlines how one can compute the hemisphere partition functions, starting with the result in [7,9], via the tachyon condensation. In this approach, one does find the factor e −c 1 (N )/2 , where the key point lies with charge assignment for the Hilbert space vacua [7,9,24] associated with the boundary degrees of freedom.…”

Section: Jhep02(2014)103mentioning

confidence: 99%

“…Refs. [7][8][9] extended the above to a hemisphere partition function. Interestingly, the supersymmetry that survives the squashing of S 2 is such that it is naturally A-twisted (anti-A-twisted) at the poles but at the same time B-twisted at the equator.…”

mentioning

confidence: 99%

Exact partition functions on $ \mathbb{R}{{\mathbb{P}}^2} $ and orientifolds

Kim

Lee

2014

J. High Energ. Phys.

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We consider gauged linear sigma models (GLSM) on RP 2 , obtained from a parity projection of S 2 . The theories admit squashing deformation, much like GLSM on S 2 , which allows us to interpret the partition function as the overlap amplitude between the vacuum state and crosscap states. From these, we extract the central charge of Orientifold planes, and observe that the Gamma class makes a prominent appearance as in the recent D-brane counterpart. We also repeat the computation for the mirror Landau-Ginzburg theory, which naturally brings out the θ-dependence as a relative sign between two holonomy sectors on RP 2 . We also show how our results are consistent with known topological properties of D-brane and Orientifold plane world-volumes, and discuss what part of the wrapped D-brane/Orientifold central charge should be attributed to the quantum volumes.

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“…[30,31,32,36,37,38,39,40,41,42,43]. More recently, localization was applied to compute partition functions for hemispheres [44,45,46,47]. One of the results of that work was an expression for central charges of D-branes involving a new multiplicative characteristic class Γ [48,49,50,51], which has been applied to systematically generate arbitrarily-high order loop corrections to higher-dimensional Calabi-Yau geometries [52].…”

Section: Introductionsmentioning

confidence: 99%

Some recent advances in gauged linear sigma models

Sharpe¹

2014

Proceedings of Third International Satellite Conference on Mathematical Methods in Physics — PoS(ICMP 2013)

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Gauged linear sigma models (GLSM's) are simple generalizations of the supersymmetric CP n model which have played a surprisingly important role in string compactifications over the last twenty years. The last six years have seen a resurgence of interest in GLSM's and some new technologies that have significantly advanced our understanding of these tools. In this talk, we will first review the basic properties of GLSM's, and then briefly discuss a few of the recent advances in their understanding.

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Exact results for boundaries and domain walls in 2d supersymmetric theories

Cited by 94 publications

References 103 publications

Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 $$ \mathcal{N}=4 $$ gauge theory

Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 $$ \mathcal{N}=4 $$ gauge theory

Exact partition functions on $ \mathbb{R}{{\mathbb{P}}^2} $ and orientifolds

Some recent advances in gauged linear sigma models

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