{"arxiv_id":"0912.4261","incoming":{"papers":10,"sentences":47,"groups":[{"kind":"extends","label":"Builds on it","papers":2,"sentences":5,"quotes":[{"arxiv_id":"1006.3313","title":"Supersymmetric Surface Operators, Four-Manifold Theory and Invariants in Various Dimensions","url":"/paper/1006.3313","section":"Introduction","sentence":"In this paper, we continue the program initiated in [ref] ; we consider arbitrarily-embedded surface operators in a topologically-twisted $=2$ pure $SU(2)$ gauge theory, and apply them to the study of four-manifolds and invariants in two, three and four dimensions.","intent_p":0.93,"contests_p":null},{"arxiv_id":"1810.07057","title":"Donaldson-Witten theory, surface operators and mock modular forms","url":"/paper/1810.07057","section":"Introduction","sentence":"In this paper we continue towards this paradigm by further investigating the ramified $u$-plane integral inspired by the works of Tan [ref] .","intent_p":0.88,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":7,"sentences":10,"quotes":[{"arxiv_id":"1810.07057","title":"Donaldson-Witten theory, surface operators and mock modular forms","url":"/paper/1810.07057","section":"The ramified $u$-plane integral as a total derivative","sentence":"Let us begin by discussing the domain of integration $/Γ^0(4)$ which is the union of six images of the fundamental domain of $SL(2,)$ [ref] This is depicted in Figure [ref].","intent_p":0.88,"contests_p":null},{"arxiv_id":"1302.7297","title":"Defects in Cohomological Gauge Theory and Donaldson-Thomas Invariants","url":"/paper/1302.7297","section":"Surface operators in four dimensional $=2$ Yang–Mills","sentence":"In the case of $SU(2)$ the problem has been set up by Kronheimer and Mrowka in [ref] and discussed from the field theory point of view in [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"1307.2578","title":"Surface Defects and Resolvents","url":"/paper/1307.2578","section":"Introduction","sentence":"BPS surface defects (a.k.a. surface operators) in $=2$ four-dimensional gauge theories are an interesting theoretical subject which ties together many subjects in mathematical physics [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1105.0357","title":"Instanton counting with a surface operator and the chain-saw quiver","url":"/paper/1105.0357","section":"Defining data of a surface operator","sentence":"In this section we review the basic properties of the surface operator following [ref] [See also [ref] for the surface operators in $𝒩=2$ theories.].","intent_p":0.96,"contests_p":null},{"arxiv_id":"1005.4469","title":"Affine SL(2) conformal blocks from 4d gauge theories","url":"/paper/1005.4469","section":"Surface operator","sentence":"The $=2$ version has been less studied, see e.g. [ref] .","intent_p":0.99,"contests_p":null}]}],"unlabelled_sentences":32},"outgoing":{"papers":3,"sentences":4,"groups":[{"kind":"comparison","label":"Compares with","papers":2,"sentences":2,"quotes":[{"arxiv_id":"alg-geom/9405002","title":"The blowup formula for Donaldson invariants","url":"/paper/alg-geom/9405002","section":"Introduction","sentence":"Note that the blowup factors ([ref]) and ([ref]) coincide with those for the generating function of the ordinary Donaldson invariants computed in [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"alg-geom/9612020","title":"Jacobi forms and the structure of Donaldson invariants for 4-manifolds with b_+=1","url":"/paper/alg-geom/9612020","section":"Introduction","sentence":"Note that the blowup factors ([ref]) and ([ref]) coincide with those for the generating function of the ordinary Donaldson invariants computed in [ref] .","intent_p":0.98,"contests_p":null}]}],"unlabelled_sentences":2},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/0912.4261"}}