Seiberg-Witten theory and random partitions

By N. Nekrasov, A. Okounkov. 2003

1,241 citations recorded by the source corpus.

We study \( \mathcal{N} = 2 \) supersymmetric four-dimensional gauge theories, in a certain 525-02 = 2 supergravity background, called theΩ-background. The partition function of the theory in the Ω-background can be calculated explicitly. We investigate various representations for this partition function: a statistical sum over random partitions, a partition function of the ensemble of random curves, and a free fermion correlator.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2a403acb5b23173b69edb2d7a46cd817e3278170

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In Mathematical Physics

1. C. Vafa
2. Marcos Mariño
3. Sergei Gukov
4. A. Klemm
5. D. Gaiotto
6. Mina Aganagic
7. Tudor Dimofte
8. Amer Iqbal

In Nuclear and High Energy Physics

1. Marcos Mariño
2. C. Vafa
3. Sergei Gukov
4. D. Gaiotto
5. F. Benini
6. Hee-Cheol Kim
7. A. Klemm
8. Yuji Tachikawa

Citations in the corpus

• Holomorphic anomaly in gauge theories and matrix models (2006, methodology): “can be calculated iteratively in the instanton number, 1/a(4) powers below, using localisation in the moduli space of gauge theory [15, 16, 18, 17] or worldsheet instantons [8, 9].”
• 5-dim superconformal index with enhanced En global symmetry (2012, methodology): “It is known [30, 31] that the instanton partition function can be computed by putting the theory in the Ω-background and thus using the equivariant localization technique.”
• The Ω Deformed B-model for Rigid N = 2 Theories (2011, background): “This expression appeared first as an equivariant instanton partition function of N = 2 SU(N) gauge theories in [3, 4] and was generalized to arbitrary gauge groups in [5, 6].”
• Topological Strings and Integrable Hierarchies (2003, background): “3 The relevance of this W∞ algebra in the context of N = 2 gauge theory has been noted in [17].”
• Quantization of Integrable Systems and Four Dimensional Gauge Theories (2009, methodology): “ε) is the quantum integrable system in question. To this end we need to remind the roˆle of the prepotential F(a;q) in the world of classical integrability [21]. Remark 1. Note that in the derivation [22] of the Seiberg-Witten prepotential F(a) from the direct instanton counting one evaluates the sm”
• On Combinatorial Expansion of the Conformal Blocks Arising from AGT Conjecture (2010, neutral): “F(x,ν,µ) = Y s∈ν (x− lµ(s)g− (aν(s)+1)) Y t∈µ (x+(lν(t)+1)g+aµ(t)), (B.2) 22 with g= −b2. There is another representation for the function F(x,ν,µ). Let Nand Mintegers such that N≥ l(ν), M≥ l(µ) then [10] F(x,ν,µ) = QN+1 i=1 QM j=1 Γ(x+µj − νi +(i− j)g) QN i=1 QM+1 j=1 Γ(x+µj − νi +(i−j+1)g) QN i=1 ”
• N=2 Supersymmetric Dynamics for Pedestrians (2013, background): “It was later extended to all k in [7, 47].”
• How instanton combinatorics solves Painlevé VI, V and IIIs (2013, methodology): “sentation for arbitrary level was found only recently in a surprisingly dierent framework. 3.2. N= 2 SUSY theories The AGT correspondence [2] relates conformal blocks of 2D CFT to Nekrasov functions [43, 44]. These functions represent the instanton parts of 1; 2-regularized partition functions in 4”
• Supersymmetric vacua and Bethe ansatz (2009, background): “7) This family of curves encodes [42], [43] the low-energy effective action of the N = 2 theory with the mass of the hypermultiplet equal to m.”
• Direct integration of the topological string (2007, methodology): “18) is massless SU(2), N = 4 super Yang–Mills theory, which has F (g) = 0 for all g ≥ 2 [52, 53, 12].”
• The Quiver Matrix Model and 2d-4d Conformal Connection (2009, methodology): “4 Dijkgraaf-Vafa’s proposal: multi-Penner potential In [7, 8], it was pointed out that the correlation function of An−1 Toda field theory (Liouville theory for n = 2) in two dimensions can be associated with Nekrasov’s partition function [9, 10] of SU(n) quiver gauge theory.”
• Matrix models, geometric engineering and elliptic genera (2003, methodology): “The additional insight of [57] was that if one, in addition, coupled to isometries corresponding to the abelian parts of the Lorentz group, involving two parameters 1 and 2, 5 then the fixed-point set becomes discrete.”