{"arxiv_id":"hep-th/9408099","incoming":{"papers":534,"sentences":1028,"groups":[{"kind":"extends","label":"Builds on it","papers":8,"sentences":8,"quotes":[{"arxiv_id":"2206.10937","title":"On the Nekrasov Partition Function of Gauged Argyres-Douglas Theories","url":"/paper/2206.10937","section":"S-duality from the curve","sentence":"As discussed in [ref] , there is an S-duality transformation involving [equation] which is equivalent in our case to [equation] Since this is precisely the action of [ref] on $𝗊$ and $c_00$, we conclude that our T-transformation [ref] (or equivalently [ref]) is an extension of this S-duality transformation to the case of generic values of $c_ij$.","intent_p":0.88,"contests_p":null},{"arxiv_id":"2307.13454","title":"String amplitudes and mutual information in confining backgrounds: the partonic behavior","url":"/paper/2307.13454","section":"Introduction","sentence":"In the holographic QCD models with a non-trivial dilaton field such as Maldacena-Nunez [ref] or even Witten-QCD [ref] , where the dilaton field depends on the radial coordinate, the above relation should instead be written as [equation]","intent_p":0.86,"contests_p":null},{"arxiv_id":"1609.06724","title":"A tale of two cones: the Higgs Branch of Sp(n) theories with 2n flavours","url":"/paper/1609.06724","section":"Introduction","sentence":"In section [ref] we recall the description of [ref] for the case of $SU(2)$ with 2 flavours and recast their calculations in the language we will use to check for higher rank cases.","intent_p":0.83,"contests_p":null},{"arxiv_id":"2205.13185","title":"On odd number of fermion zero modes on solitons in quantum field theory and string/M theory","url":"/paper/2205.13185","section":"An example in $3+1$ dimensions","sentence":"The computation for even $n$ was given in the classic paper [ref] , which can be carried over to the more general case.","intent_p":0.94,"contests_p":null},{"arxiv_id":"1206.2317","title":"Wall-Crossing in Supersymmetric Gauge Theories","url":"/paper/1206.2317","section":"Interpolating to three dimensions","sentence":"In this chapter, we extend the semiclassical analysis conducted in chapter [ref] to theories with $N_f≤4$ fundamental flavours compactified on $ℝ^3×S^1$ focusing on gauge group $SU(2)$ [ref] .","intent_p":0.98,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":14,"sentences":16,"quotes":[{"arxiv_id":"1608.06635","title":"Kinetic Mixing at Strong Coupling","url":"/paper/1608.06635","section":"Introduction","sentence":"In the limit where the extra sector enjoys approximate $𝒩 =2$ supersymmetry, we show how to adapt formal methods from Seiberg-Witten theory [ref] to extract the exact form of electric and magnetic mixing.","intent_p":0.93,"contests_p":null},{"arxiv_id":"0708.0668","title":"Meta-stable Vacuum in Spontaneously Broken N=2 Supersymmetric Gauge Theory","url":"/paper/0708.0668","section":"Introduction","sentence":"The effective potential along the pseudo flat direction can be analyzed beyond perturbation theory by using the exact results in $𝒩=2$ SUSY QCD [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"1012.1122","title":"Stringy instanton effects in N=2 gauge theories","url":"/paper/1012.1122","section":"Introduction and motivations","sentence":"We have computed such non-perturbative effects with the same localization methods [ref] -Losev:2003py [ref] used to find the gauge instanton terms in the $=2$ super Yang-Mills theory predicted by the Seiberg-Witten curve [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"2607.09485","title":"Unified description of color-electric and color-magnetic strings in hybrid vacua of $\\mathcal{N}=2$ supersymmetric QCD","url":"/paper/2607.09485","section":"Seiberg-Witten solution","sentence":"To take into account the quantum effects, we go to the limit of small $μ$, where the theory is close to $𝒩=2$ SQCD; this allows us to use the exact Seiberg-Witten (SW) solution [ref] .","intent_p":0.9,"contests_p":null},{"arxiv_id":"0811.2207","title":"The N=2 cascade revisited and the enhancon bearings","url":"/paper/0811.2207","section":"Introduction and summary","sentence":"We first discuss the case where the cutoff is at finite energy: by means of the relevant Seiberg-Witten curves [ref] , we provide a detailed analysis of several vacua on the Coulomb branch, together with the corresponding supergravity duals.","intent_p":0.99,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":4,"sentences":5,"quotes":[{"arxiv_id":"0811.3393","title":"Thermal Evolution of the Non Supersymmetric Metastable Vacua in N=2 SU(2) SYM Softly Broken to N=1","url":"/paper/0811.3393","section":"The $N=2$ $SU(2)$ moduli space","sentence":"The Kahler metric on the Coulomb branch is exactly calculated in [ref] and it turns out to be [equation] where [equation]","intent_p":0.86,"contests_p":null},{"arxiv_id":"2111.08022","title":"Deconfining $\\mathcal{N}=2$ SCFTs, or the Art of Brane Bending","url":"/paper/2111.08022","section":"Even $k$k Coulomb branch","sentence":"Note that since $τ= e^πi/3$ at the origin of the Coulomb branch of the $N_f=1$ $(2)$ Seiberg-Witten theory [ref] , the $(1)$ holomorphic gauge coupling is frozen at this value along this portion of the Coulomb branch.[In fact, this is required for the discrete symmetries to match between the UV and IR.","intent_p":0.84,"contests_p":null},{"arxiv_id":"2312.13360","title":"Disconnected gauge groups in the infrared","url":"/paper/2312.13360","section":"The case of","sentence":"The SW data before the discrete gauging are [ref] : [equation] with $e_i$ being defined by [equation] where $θ_j$ are the Jacobi $θ$-functions on the elliptic curve of modular parameter $τ$, [equation] with $q = e^2 πi τ$.","intent_p":0.85,"contests_p":null},{"arxiv_id":"1601.00011","title":"Geometric constraints on the space of N=2 SCFTs II: Construction of special K\\\"ahler geometries and RG flows","url":"/paper/1601.00011","section":"${ I_2^3}$ with $(2)$ flavor symmetry","sentence":"The ${I_2^3}$ deformation of the $I_0^*$ singularity was found in [ref] to have a curve [equation] The $e_j()$ are modular forms of the marginal coupling, and $M=m/2$, $U=u$, $Y=y$, and $Ξ=x$ in the notation of [ref] .","intent_p":0.88,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":24,"sentences":32,"quotes":[{"arxiv_id":"2607.09485","title":"Unified description of color-electric and color-magnetic strings in hybrid vacua of $\\mathcal{N}=2$ supersymmetric QCD","url":"/paper/2607.09485","section":"Introduction","sentence":"We calculate BPS kink masses in the world-sheet theory on the non-Abelian string using the exact superpotential and compare them with the masses of monopoles and quarks on the Coulomb branch at $μ→0$ given by the exact Seiberg-Witten solution [ref] .","intent_p":0.85,"contests_p":null},{"arxiv_id":"0911.4797","title":"Penner Type Matrix Model and Seiberg-Witten Theory","url":"/paper/0911.4797","section":"Asymptotically free theory with $N_f = 3$","sentence":"The discriminant of the polynomial above completely matches with that of the Seiberg-Witten curve for $N_f=3$ in [ref] : y^2 = x^2 (x - u) - 1/4 Λ_3^2 (x - u)^2 - 1/4 (m_+^2 + m_-^2 + m̃_+^2) Λ_3^2 (x - u) + m_+ m_- m̃_+ Λ_3 x - 1/4 (m_+^2 m_-^2 + m_-^2 m̃_+^2 + m̃_+^2 m_+^2) Λ_3^2.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1105.1869","title":"Holographic non-perturbative corrections to gauge couplings","url":"/paper/1105.1869","section":"The $τ$ profile","sentence":"Introducing the quantity [equation] which in the holographic correspondence parametrizes the Coulomb branch of the dual $=2$ SU(2)$∼$Sp(1) gauge theory, and adding to $τ_n.p.$ the classical contribution ([ref]), we can exhibit the resulting axio-dilaton $τ$ as an expansion in inverse powers of $a$, namely [equation] As shown in Ref. [ref] , this is in perfect agreement with the effective coupling derived from the SW curve for the SU(2) $N_f=4$ theory [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"1109.5728","title":"The Omega deformed B-model for rigid N=2 theories","url":"/paper/1109.5728","section":"The $SU(N)$ $N_f=2N$ curves","sentence":"Our result proved to coincide with that of Seiberg and Witten [ref] , requiring solely a different identification of the UV coupling.","intent_p":1.0,"contests_p":null},{"arxiv_id":"0809.5060","title":"Quantum Vortex Strings: A Review","url":"/paper/0809.5060","section":"Quantum Kinks","sentence":"We can compare this calculation to the exact quantum mass of the 4d BPS monopole computed using the Seiberg-Witten solution [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":6,"sentences":6,"quotes":[{"arxiv_id":"1606.08429","title":"Infrared Computations of Defect Schur Indices","url":"/paper/1606.08429","section":"Introduction","sentence":"The situation with the Schur index appears to be similar, and recent work by some of the authors [ref] strongly indicates that: * The Schur index is a meaningful quantity for non-conformal $N=2$ field theories. * The Schur index can be computed in the IR using the Seiberg-Witten description [ref] as an Abelian gauge theory enriched by BPS particles.","intent_p":0.97,"contests_p":null},{"arxiv_id":"1505.04814","title":"Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations","url":"/paper/1505.04814","section":"Introduction and summary","sentence":"These seven geometries have been realized as CBs of physical $=2$ SCFTs [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"2311.00093","title":"Anomaly Enforced Gaplessness for Background Flux Anomalies and Symmetry Fractionalization","url":"/paper/2311.00093","section":"$4d$ $=2$ $SU(2)$ QCD with $N_f>1$ Hypermultiplets","sentence":"We thus find again that the theory has a background flux anomaly[Note that we cannot apply Wu identities to trivialize the $N_f$-odd anomaly since the fluxes are $_4$-valued.] = πi ∫w_2^(L)∪w_3^(R) N_f even πi ∫w_2(_4)∪w_3(_4) N_f odd It is known that these theories flow to gappless theories in the IR via the work of Seiberg-Witten [ref] , thereby matching our theorem.","intent_p":0.98,"contests_p":null},{"arxiv_id":"2110.11969","title":"Four flavours, triality and bimodular forms","url":"/paper/2110.11969","section":"Fundamental domains","sentence":"This is consistent with the fact [ref] that $u=∞$ does not correspond to a cusp of the curve anymore.","intent_p":0.97,"contests_p":null},{"arxiv_id":"2107.12287","title":"Yang-Mills at Strong vs. Weak Coupling: Renormalons, OPE And All That","url":"/paper/2107.12287","section":"Introduction","sentence":"Confinement of the Nambu-Mandelstam-'t Hooft type in the SUSY setting was demonstrated [ref] , [ref] to emerge from the dual Meißner effect – a very special non-perturbative feature of the Yang-Mills vacuum – and so is $χ$SB.","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":341,"sentences":417,"quotes":[{"arxiv_id":"1604.06184","title":"Gauge interactions and topological phases of matter","url":"/paper/1604.06184","section":"The model and the S-duality","sentence":"The S-duality: This theory is known to have a strong-weak duality, which is usually simply called the S-duality [ref] .","intent_p":0.8,"contests_p":null},{"arxiv_id":"1307.2691","title":"Singularity Structure of N=2 Supersymmetric Yang-Mills Theories: A Review","url":"/paper/1307.2691","section":"Review of $N=2$ Seiberg-Witten theory and geometry","sentence":"In late 1990s, Seiberg and Witten made a profound discovery on $N = 2$, $d = 4$ supersymmetric Yang-Mills theory with gauge group $G=SU(2)$ [ref] , giving a huge impact both on physics and 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and Witten [ref] on four-dimensional $𝒩=2$ $SU(2)$ supersymmetric gauge theories using holomorphy and electric-magnetic duality has revolutionized our understanding of non-perturbative dynamics in quantum field theory.","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":544},"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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