An Introduction To The Web-Based Formalism

@article{Gaiotto2015AnIT,
  title={An Introduction To The Web-Based Formalism},
  author={Davide Gaiotto and Gregory W. Moore and Edward Witten},
  journal={arXiv: High Energy Physics - Theory},
  year={2015}
}
This paper summarizes our rather lengthy paper, "Algebra of the Infrared: String Field Theoretic Structures in Massive ${\cal N}=(2,2)$ Field Theory In Two Dimensions," and is meant to be an informal, yet detailed, introduction and summary of that larger work. 
Algebra of the Infrared: String Field Theoretic Structures in Massive ${\cal N}=(2,2)$ Field Theory In Two Dimensions
We introduce a "web-based formalism" for describing the category of half-supersymmetric boundary conditions in $1+1$ dimensional massive field theories with ${\cal N}=(2,2)$ supersymmetry andExpand
Topological charges in 2D N = ( 2 , 2 ) theories and massive BPS states
We study how charges of global symmetries that are manifest in the ultra-violet definition of a theory are realized as topological charges in its infra-red effective theory for two-dimensionalExpand
Secondary Products in Supersymmetric Field Theory
The product of local operators in a topological quantum field theory in dimension greater than one is commutative, as is more generally the product of extended operators of codimension greater thanExpand
Comments On The Two-Dimensional Landau-Ginzburg Approach To Link Homology
We describe rules for computing a homology theory of knots and links in $\mathbb{R}^3$. It is derived from the theory of framed BPS states bound to domain walls separating two-dimensionalExpand
Ju l 2 01 5 Topological charges in 2 d N = ( 2 , 2 ) theories and massive BPS states
We study how charges of global symmetries that are manifest in the ultra-violet definition of a theory are realized as topological charges in its infra-red effective theory for two-dimensionalExpand
Infrared computations of defect Schur indices
A bstractWe conjecture a formula for the Schur index of four-dimensional N=2$$ \mathcal{N}=2 $$ theories in the presence of boundary conditions and/or line defects, in terms of the low-energyExpand
Feynman diagrams and $Ω$-deformed M-theory
We derive the simplest commutation relations of operator algebras associated to M2 branes and an M5 brane in theΩ-deformed M-theory, which is a natural set-up for Twisted holography. Feynman diagramExpand
Singular BPS boundary conditions in N = (2, 2) supersymmetric gauge theories
We derive general BPS boundary conditions in two-dimensional N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow theExpand
Categorical Wall-Crossing in Landau-Ginzburg Models
We describe how categorical BPS data including chain complexes of solitons, CPT pairings, and interior amplitudes jump across a wall of marginal stability in two-dimensional $\mathcal{N}=(2,2)$Expand
Expanding the Bethe/Gauge dictionary
A bstractWe expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N$$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz.Expand
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References

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Algebra of the Infrared: String Field Theoretic Structures in Massive ${\cal N}=(2,2)$ Field Theory In Two Dimensions
We introduce a "web-based formalism" for describing the category of half-supersymmetric boundary conditions in $1+1$ dimensional massive field theories with ${\cal N}=(2,2)$ supersymmetry andExpand
A New supersymmetric index
Abstract We show that Tr(−1) F F e βH is an index for N = 2 supersymmetric theories in two dimensions, in the sense that it is independent of almost all deformations of the theory. This index isExpand
Khovanov homology and gauge theory
In these notes, I will sketch a new approach to Khovanov homology of knots and links based on counting the solutions of certain elliptic partial differential equations in four and five dimensions.Expand
Two Lectures On The Jones Polynomial And Khovanov Homology
In the rst of these two lectures, I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpretExpand
Fivebranes and Knots
We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is aExpand
Supersymmetry and Morse theory
It is shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian. Some of the implications of modern ideas in mathematics forExpand
Fukaya-Seidel category and gauge theory
A new construction of the Fukaya{Seidel category associated with a symplectic Lefschetz bration is outlined. Applying this construction in an innite dimensional case, a Fukaya{Seidel-type category isExpand
Knot Invariants from Four-Dimensional Gauge Theory
It has been argued based on electric-magnetic duality and other ingredients that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theoryExpand
Domain wall junctions are 1/4 - BPS states
We study N=1 SUSY theories in four dimensions with multiple discrete vacua, which admit solitonic solutions describing segments of domain walls meeting at one-dimensional junctions. We show thatExpand
Bogomol'nyi Equation for Intersecting Domain Walls
We argue that the Wess-Zumino model with quartic superpotential admits static solutions in which three domain walls intersect at a junction. We derive an energy bound for such junctions and show thatExpand
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