{"arxiv_id":"hep-th/9412236","incoming":{"papers":91,"sentences":275,"groups":[{"kind":"extends","label":"Builds on it","papers":7,"sentences":7,"quotes":[{"arxiv_id":"0810.0012","title":"Summing the Instantons in Half-Twisted Linear Sigma Models","url":"/paper/0810.0012","section":"A Summary of the Results","sentence":"This (0,2) extension of the quantum restriction formula of [ref] is derived in section [ref].","intent_p":1.0,"contests_p":null},{"arxiv_id":"2502.08002","title":"Beyond Algebraic Superstring Compactification","url":"/paper/2502.08002","section":"A Showcasing Deformation Family","sentence":"Expanding on earlier work [ref] , I focus on a particular infinite sequence of constructions corresponding to Calabi–Yau hypersurfaces in Hirzebruch scrolls, the rich mathematical history of the latter [ref] affording their study from multiple different points of view, including their realization within GLSM models [ref] — which is where we start.","intent_p":0.95,"contests_p":null},{"arxiv_id":"2308.12334","title":"Quantum cohomology from mixed Higgs-Coulomb branches","url":"/paper/2308.12334","section":"Conclusions","sentence":"In this paper, we have generalized the Coulomb-branch based computations of quantum cohomology described in [ref] to cases with mixed Higgs-Coulomb branches, discussing in detail the case of GLSMs for hypersurfaces in projective spaces, $ℙ^n[d]$.","intent_p":0.99,"contests_p":null},{"arxiv_id":"1010.4667","title":"The Revival of (0,2) Linear Sigma Models","url":"/paper/1010.4667","section":"Coulomb Branch","sentence":"These results are all natural generalisations of the $(2,2)$ A-twisted model discussed in [ref] .","intent_p":0.89,"contests_p":null},{"arxiv_id":"1504.06308","title":"The equivariant A-twist and gauged linear sigma models on the two-sphere","url":"/paper/1504.06308","section":"Quantum cohomology and recursion relations in $$","sentence":"We verify the quantum restriction formula of [ref] , and derive its $$-deformed version in a similar fashion.","intent_p":0.87,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":17,"sentences":27,"quotes":[{"arxiv_id":"2308.12334","title":"Quantum cohomology from mixed Higgs-Coulomb branches","url":"/paper/2308.12334","section":"IR correlation functions","sentence":"By using the GLSM fields and localization, the correlation functions $⟨O[η]^k⟩$ can also be calculated in the IR by the methods of [ref] for the Higgs contribution and those of [ref] for the Coulomb contribution.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1806.05850","title":"Testing the (0,2) mirror map","url":"/paper/1806.05850","section":"A/2 correlators","sentence":"In order to solve the A/2-twisted $M$ model we employ the strategy developed in [ref] for (2,2) theories and later extended to a class of (0,2) linear models in [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"1003.1303","title":"A (0,2) Mirror Map","url":"/paper/1003.1303","section":"GLSM moduli space of reflexively plain models","sentence":"To construct these, we first note that the action on the $α_m$ is the same as in the (2,2) case, and there is a well-known way to pick invariant coordinates [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"1103.1322","title":"Old issues and linear sigma models","url":"/paper/1103.1322","section":"Puzzle resolution via the mirror map","sentence":"This is easily done for the “toric” $_a$ and “polynomial” $_m$ via the monomial-divisor mirror map [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1801.04100","title":"Aspects of (2,2) and (0,2) hybrid models","url":"/paper/1801.04100","section":"Instanton corrections?","sentence":"Following [ref] , we construct a linear model ($V^+$ model in the terminology of [ref] ) with target space $(-2)⊕^⊕3→^1$ by introducing the (0,2) chiral matter superfields [equation] together with a neutral chiral field $Σ$, with lowest component $σ$.","intent_p":0.83,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":6,"sentences":10,"quotes":[{"arxiv_id":"0810.0012","title":"Summing the Instantons in Half-Twisted Linear Sigma Models","url":"/paper/0810.0012","section":"Localization and Quantum Restriction","sentence":"On the (2,2) locus $M_(0) = K = -∑_i,a Q_i^a σ_a$, and our result reduces to that obtained in [ref] and given in eqn.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1504.06308","title":"The equivariant A-twist and gauged linear sigma models on the two-sphere","url":"/paper/1504.06308","section":"Geometric and orbifold phases in the $=0$ and $m^F=0$ limit","sentence":"This matches precisely the results of [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1712.02551","title":"2D BPS Rings from Sphere Partition Functions","url":"/paper/1712.02551","section":"Relations and the ring","sentence":"This result was previously obtained in [ref] using the topologically A-twisted version of the GLSM which doesn't require the supersymmetric localization and the counterterm analysis that we did.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1608.03607","title":"Recent developments in 2d $\\mathcal{N} = (2,2)$ supersymmetric gauge theories","url":"/paper/1608.03607","section":"Geometric applications","sentence":"The localization formulae for $A$-twisted correlation functions for Calabi-Yau GLSMs also reproduce classic results obtained by employing mirror symmetry [ref] or by direct counting of holomorphic curves [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"1509.08630","title":"2d Partition Function in Omega-background and Vortex/Instanton Correspondence","url":"/paper/1509.08630","section":"$U(1)$ Gauge theories with $N$ Chiral multiplets","sentence":"This agrees with the known result [ref] .","intent_p":0.94,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2308.12334","title":"Quantum cohomology from mixed Higgs-Coulomb branches","url":"/paper/2308.12334","section":"Introduction","sentence":"This was confirmed for Calabi-Yau hypersurface examples in [ref] by summing the gauge instanton sums.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1705.00649","title":"Squashed toric sigma models and mock modular forms","url":"/paper/1705.00649","section":"Introduction and summary","sentence":"This sum-rule in turn implies that the initial toric manifold (and therefore its squashed deformation) is non-compact [ref] .","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":35,"sentences":56,"quotes":[{"arxiv_id":"1608.02956","title":"Gromov-Witten invariants and localization","url":"/paper/1608.02956","section":"Introduction","sentence":"We have drawn heavily upon [ref] , [ref] , [ref] , [ref] in preparing this review.","intent_p":0.91,"contests_p":null},{"arxiv_id":"2308.12334","title":"Quantum cohomology from mixed Higgs-Coulomb branches","url":"/paper/2308.12334","section":"Introduction","sentence":"While this is the natural choice of coordinates from the GLSM perspective, in general these are related in a non-trivial fashion to the natural coordinates of the nonlinear model: see the discussion around equation (4.20) in [ref] , for example. ] $r$ has nontrivial RG flow, and will flow between different phases of the GLSM.","intent_p":0.8,"contests_p":null},{"arxiv_id":"2501.11684","title":"Ricci-Flat Mirror Hypersurfaces in Spaces of General Type","url":"/paper/2501.11684","section":"Extending Gauged Linear Sigma Models","sentence":"For over three decades now, the standard vehicle to this end is Witten's gauged linear sigma model (GLSM) [ref] , where the space of ground-states is defined as the subset of the field space where a well-specified potential is minimized, at the intersection [equation] Here, $W(X)$ is the superpotnential function of chiral $(2,2)$-superfields[This brief discussion is limited to the simplest, $(2,2)$-supersymmetric case; $(0,2)$-generalizations are described in the literature [ref] , while the ultimate, minimally $(0,1)$-supersymmetric extensions remain largely unexplored.], $X_i$, with lowest component fields $x_i$.","intent_p":0.81,"contests_p":null},{"arxiv_id":"0810.0012","title":"Summing the Instantons in Half-Twisted Linear Sigma Models","url":"/paper/0810.0012","section":"The Linear Model on the (2,2) Locus","sentence":"The material in this section is largely a review of the results obtained in [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2605.24724","title":"Beyond Algebraic Solutions to Stringy Spacetime","url":"/paper/2605.24724","section":"Introduction, Rationale and Synopsis","sentence":"In the remainder of this introduction, we review the structure of our millieu, the quantum field theory (QFT) framework of (super)string theory, and from the worldsheet vantage point: Here, we focus on worldsheet $(2,2)$-supersymmetric models with scalar superfields and abelian gauge symmetry, and especially the (abelian) gauged linear sigma models (GLSM) [ref] .","intent_p":0.94,"contests_p":null}]}],"unlabelled_sentences":173},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"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":{"arxiv_id":"hep-th/9412236","kind":"model","paper_version":2,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T18:03:14+00:00","loaded_at":"2026-10-28T01:03:03.359277+00:00","evidence":"substantial","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":4,"entries":[{"p":0.91,"quote":null,"citing":[{"self":false,"year":2023,"title":"Quantum cohomology from mixed Higgs-Coulomb branches","arxiv_id":"2308.12334"}],"verified":true,"paraphrase":"Applied this paper's methods to the Coulomb branch, using the one-loop-exact twisted effective superpotential."},{"p":0.98,"quote":null,"citing":[{"self":false,"year":2018,"title":"Testing the (0,2) mirror map","arxiv_id":"1806.05850"}],"verified":true,"paraphrase":"Employed the strategy developed in this paper for (2,2) theories to solve the A/2-twisted M model."},{"p":0.8,"quote":null,"citing":[{"self":false,"year":2016,"title":"Hemisphere Partition Function and Analytic Continuation to the Conifold Point","arxiv_id":"1602.01382"}],"verified":true,"paraphrase":"Changed to the algebraic coordinate of this paper's GLSM."}],"papers_all":17,"self_papers":1,"self_entries":[{"p":0.89,"quote":null,"citing":[{"self":true,"year":2012,"title":"Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties","arxiv_id":"1205.3192"}],"verified":true,"paraphrase":"Used techniques developed in this paper for abelian GLSMs to analyze the phase structure of the quantum-corrected Kähler moduli spaces of linear determinantal varieties in projective space."}]},{"kind":"comparison","label":"Compares with it","papers":1,"entries":[{"p":0.98,"quote":null,"citing":[{"self":false,"year":2008,"title":"Summing the Instantons in Half-Twisted Linear Sigma Models","arxiv_id":"0810.0012"}],"verified":true,"paraphrase":"Said that on the (2,2) locus its own result reduces to that obtained in this paper and given in eqn."}],"papers_all":6,"self_papers":0,"self_entries":[]}],"counts":{"by_kind":{"extends":7,"comparison":6,"method_or_tool":17,"supports_this_paper":2},"dropped":{"relied_on":0,"unknown_ids":0,"account_lines":0,"contest_vetoed":0,"below_threshold":0,"contest_drawback":0,"contest_without_basis":0,"contest_not_one_sentence":0,"contest_on_group_citation":0},"papers_read":16,"self_papers":9,"citing_papers":92,"sentences_read":20,"citing_sentences":264,"unambiguous_read":20,"typed_independent":24,"independent_papers":83,"by_kind_independent":{"extends":7,"comparison":6,"method_or_tool":14,"supports_this_paper":2}},"input_sha256":"60a7ace070951fad10398fea85e61d74f18267cb23f075e48b9c003643eaeacb","method":"For a paper with five or more citing arXiv papers, Pith selected up to 40 citing sentences its citation classifier typed, read those whose citation markers point at this paper alone, and wrote one paraphrase for each later paper in each group, each resting on one sentence. A later paper is listed under a label only when the classifier gives one of its sentences that label at intent probability 0.8 or more (0.95 for support), Pith's reading of the sentence finds that the citing paper itself did it, and a second check of the paraphrase against the sentence passes. The section lists uses only: building on the paper, using its method, tool, data or values, comparing with it and citing it as support. It does not list criticism or disagreement, so their absence says nothing about how the paper has been received. Code counted the papers, wrote the summary from the listed entries, set the evidence level and linked each entry to its citing paper. Quotes are copied from the citing sentence and shown only when the citing paper's licence is CC BY, CC BY-SA or CC0; otherwise the paraphrase is shown. Papers that share an author with this one are listed apart. A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"4 later papers by other authors are listed below: 3 used its method or tool and 1 compared its own results with it. 1 more paper by the same authors is listed: 1 used its method or tool."},"_links":{"html":"https://pith.science/paper/hep-th/9412236"}}