{"arxiv_id":"hep-th/0103067","incoming":{"papers":48,"sentences":104,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1004.2917","title":"The matrix model version of AGT conjecture and CIV-DV prepotential","url":"/paper/1004.2917","section":"Conclusion","sentence":"It is actually the celebrated CIV-DV prepotential [ref] , just modified (generalized) in three different directions: from polynomial to logarithmic potential $V$, to $β≠1$ and to arbitrary genus.","intent_p":0.86,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":10,"sentences":13,"quotes":[{"arxiv_id":"1108.6049","title":"Confining vacua in SQCD, the Konishi anomaly and the Dijkgraaf-Vafa superpotential","url":"/paper/1108.6049","section":"Introduction","sentence":"The analysis of the more interesting $SU(N)$ case along these lines requires the use of the Dijkgraaf-Vafa superpotential [ref] , which allows us to capture all the holomorphic data of the theory by means of a planar calculation in a matrix model, and of the generalized Konishi anomaly [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1004.2917","title":"The matrix model version of AGT conjecture and CIV-DV prepotential","url":"/paper/1004.2917","section":"Conclusion","sentence":"$∙$Another side of equality is the same integral, but treated differently: as Givental decomposition [ref] into a system of Gaussian models with the filling numbers $(N_1,…,N_r)$.","intent_p":0.8,"contests_p":null},{"arxiv_id":"1309.5299","title":"Confinement and duality in supersymmetric gauge theories","url":"/paper/1309.5299","section":"Introductory remarks","sentence":"The analysis of the more interesting $SU(N)$ case along these lines requires the use of the Dijkgraaf-Vafa superpotential [ref] , which allows us to capture all the holomorphic data of the theory by means of a planar calculation in a matrix model, and of the generalized Konishi anomaly [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"0906.0591","title":"The unwarped, resolved, deformed conifold: fivebranes and the baryonic branch of the Klebanov-Strassler theory","url":"/paper/0906.0591","section":"The superpotential","sentence":"The superpotential superpot can be evaluated explicitly by a computation as in [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"2106.10265","title":"Liberating Confinement from Lagrangians: 1-form Symmetries and Lines in 4d N=1 from 6d N=(2,0)","url":"/paper/2106.10265","section":"Rotations via the Dijkgraaf-Vafa Curve","sentence":"Here we present the derivation of some $=1$ curves using the Dijkgraaf-Vafa (DV) curve [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":4,"sentences":4,"quotes":[{"arxiv_id":"0906.0591","title":"The unwarped, resolved, deformed conifold: fivebranes and the baryonic branch of the Klebanov-Strassler theory","url":"/paper/0906.0591","section":"The superpotential","sentence":"As we discussed around diff we can define a bare scale parameter as $Λ̂= ρ_c /√(α' M)$, and then, to compare directly with with [ref] , let us also define $S=e^-t_∞- i ψ_∞$ and a “complex coupling” $2πα' α̃= -(j+i b)$.","intent_p":0.87,"contests_p":null},{"arxiv_id":"1004.2917","title":"The matrix model version of AGT conjecture and CIV-DV prepotential","url":"/paper/1004.2917","section":"The case of $β= 1$ and genus zero: ordinary CIV-DV prepotential","sentence":"8pt0pt + ∑_a ≠b 1Δ_aΔ_b ( S_aS_b(4S_a^2 + 11S_a S_b + 4S_b^2) 4(μ_a - μ_b)^4 - ∑_c ≠a_d ≠b S_a S_b(S_a + S_c)(S_b + S_d)2 (μ_a - μ_b)^2 (μ_a - μ_c) (μ_b - μ_d) - ∑_c ≠b S_aS_b(S_a+2S_b)(S_b+S_c) (μ_a - μ_b)^3 (μ_b - μ_c) ) These formulas reproduce and generalise various explicit results, available in the literature [ref] , in particular the cubic contribution coincides with the one obtained in [ref] by different methods.","intent_p":0.9,"contests_p":null},{"arxiv_id":"0808.1286","title":"Instantons and SUSY breaking in F-theory","url":"/paper/0808.1286","section":"Introduction","sentence":"This is to be contrasted with the case of pure $𝒩 = 1$ $SU(N)$ gauge theory engineered from D5-branes wrapping a rigid $ℙ^1$ in a local Calabi-Yau 3-fold as in [ref] , where the corresponding volume modulus is non-dynamical.","intent_p":0.99,"contests_p":null},{"arxiv_id":"1012.4018","title":"D-brane non-perturbative effects and geometric deformations","url":"/paper/1012.4018","section":"Discussion","sentence":"These results, based on local ten-dimensional arguments, have been compared with well-known results on geometric transition in the context of the gauge/gravity correspondence [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1511.00574","title":"An elliptic Virasoro symmetry in 6d","url":"/paper/1511.00574","section":"Introduction","sentence":"This chain of results, together with large $r$ duality [ref] , strongly supports a 6d version of the AGT correspondence by identifying generic chiral blocks of the elliptic Virasoro algebra with $ℝ^4×𝕋^2$ Nekrasov instanton partition functions.","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":24,"sentences":30,"quotes":[{"arxiv_id":"0710.4377","title":"Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry II","url":"/paper/0710.4377","section":"Introduction","sentence":"It has been conjectured in the context of the topological string theory and the gauge/gravity correspondence [ref] that the effective superpotential is related to the matrix model free energy [ref] , which we refer to as Dijkgraaf-Vafa relation.","intent_p":0.83,"contests_p":null},{"arxiv_id":"0804.4006","title":"Nonsupersymmetric Flux Vacua and Perturbed N=2 Systems","url":"/paper/0804.4006","section":"Prepotential for Dijkgraaf-Vafa (CIV-DV) Geometries","sentence":"In this appendix, we first review different approaches to computing the prepotential $_0$ for the Dijkgraaf-Vafa (CIV-DV) geometries [ref] given in eqs.","intent_p":0.99,"contests_p":null},{"arxiv_id":"1004.2917","title":"The matrix model version of AGT conjecture and CIV-DV prepotential","url":"/paper/1004.2917","section":"$ħ$-expansion for the generic case","sentence":"[equation] Such models have been studied for quite a long time: in the case, when $V(z)$ is a polynomial, their free energy $F = logZ$ gives rise to the CIV-DV prepotential [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"2212.05074","title":"Smearing and Unsmearing KKLT AdS Vacua","url":"/paper/2212.05074","section":"Self-consistency and interpretation","sentence":"At large $N$, one has a geometric transition where the 2-cycle shrinks to zero size, and a 3-cycle opens up, thus leading to the deformed conifold geometry [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"0704.1060","title":"Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry","url":"/paper/0704.1060","section":"Introduction","sentence":"In recent years, analyses from superstring theory have revealed an interesting perturbative window into nonperturbative physics with the use of the gluino condensate superfield variable [ref] .","intent_p":0.86,"contests_p":null}]}],"unlabelled_sentences":55},"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. 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