scholarly journals “Lagrangian disks” in M-theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Sebastían Franco ◽  
Sergei Gukov ◽  
Sangmin Lee ◽  
Rak-Kyeong Seong ◽  
James Sparks
Keyword(s):  
String Theory ◽  
Large Class ◽  
Lagrangian Submanifolds ◽  
The Other ◽  
Holomorphic Curves ◽  
Special Lagrangian ◽  
Special Lagrangian Submanifolds ◽  
Brane Models ◽  
The One ◽  
M Theory

Abstract While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in G2 holonomy spaces and to Spin(7) metrics on 8-manifolds with T2 fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories T[M4] on the other.

scholarly journals Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

scholarly journals SKEW CATEGORY ALGEBRAS ASSOCIATED WITH PARTIALLY DEFINED DYNAMICAL SYSTEMS

2012 ◽  
Vol 23 (04) ◽  
pp. 1250040 ◽  
Author(s):  
PATRIK LUNDSTRÖM ◽  
JOHAN ÖINERT
Keyword(s):  
Dynamical Systems ◽  
Topological Space ◽  
Large Class ◽  
Additive Group ◽  
Nonzero Ideal ◽  
Intersection Property ◽  
The Other ◽  
The One ◽  
Category Algebras ◽  
The Ideal

We introduce partially defined dynamical systems defined on a topological space. To each such system we associate a functor s from a category G to Topop and show that it defines what we call a skew category algebra A ⋊σ G. We study the connection between topological freeness of s and, on the one hand, ideal properties of A ⋊σ G and, on the other hand, maximal commutativity of A in A ⋊σ G. In particular, we show that if G is a groupoid and for each e ∈ ob (G) the group of all morphisms e → e is countable and the topological space s(e) is Tychonoff and Baire. Then the following assertions are equivalent: (i) s is topologically free; (ii) A has the ideal intersection property, i.e. if I is a nonzero ideal of A ⋊σ G, then I ∩ A ≠ {0}; (iii) the ring A is a maximal abelian complex subalgebra of A ⋊σ G. Thereby, we generalize a result by Svensson, Silvestrov and de Jeu from the additive group of integers to a large class of groupoids.

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