Small Instantons, Little Strings and Free Fermions

By A. Losev, A. Marshakov, N. Nekrasov. 2003

238 citations recorded by the source corpus.

We present new evidence for the conjecture that BPS correlation functions in the N=2 supersymmetric gauge theories are described by an auxiliary two dimensional conformal field theory. We study deformations of the N=2 supersymmetric gauge theory by all gauge-invariant chiral operators. We calculate the partition function of the N=2 theory on R^4 with appropriately twisted boundary conditions. For the U(1) theory with instantons (either noncommutative, or D-instantons, depending on the construction) the partition function has a representation in terms of the theory of free fermions on a sphere, and coincides with the tau-function of the Toda lattice hierarchy. Using this result we prove to all orders in string loop expansion that the effective prepotential (for U(1) with all chiral couplings included) is given by the free energy of the topological string on CP^1. Gravitational descendants play an important role in the gauge fields/string correspondence. The dual string is identified with the little string bound to the fivebrane wrapped on the two-sphere. We also discuss the theory with fundamental matter hypermultiplets.

Subfields: Political Science and International Relations

View Paper: https://www.semanticscholar.org/paper/d8d47de6686e521fffc7a7c0b78d74f982ec7762

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Citations in the corpus

Instanton counting with a surface operator and the chain-saw quiver (2011, background): “26) The tangent space of the moduli space at the fixed point ~λ is given by the cohomology of the following complex [52, 57, 3]:”
ABCD of Instantons (2004, background): “ns consist of identiﬁcations (y,~x) ∼ (y+ β,expβΩ · ~x), where Ω is the generator (7) of inﬁnitesimal SO(4) rotation. More on the deﬁnition of the Ω-background and further explanation can be found in [16, 22]. In [20] it is explained that in the limit of small bare gauge coupling the pure N = 2 ﬁve ”
Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops (2007, unknown): “Instanton corrections to the operator exp(βΦ) in the N = 2 equivariant theory on R(4) for a given asymptotic of Φ at infinity were computed in [5, 79, 82, 83].”
Quantization of Integrable Systems and Four Dimensional Gauge Theories (2009, background): “violet, (2.16) Ftree → Ftree + X k tkOk In the low energy the deformed theory is given by the family of prepotentials F(a;t;m,τ), t = (tk). For some models the deformed prepotentials were computed in [15, 17, 18]. For our purposes the tk deformation can be studied formally, i.e. without addressing t”
Hitchin systems, N = 2 gauge theories and W-gravity (2009, methodology): “The insertion of this operator, in the presence of the Ωbackground, has been computed in [22, 13, 14] and shown to cor respond to the derivative of the Nekrasov partition function with respect to the correspond ing complex gauge coupling.”
Lectures on instanton counting (2003, methodology): “on of the Gromov-Witten invariants for P , where ε 1 is mapped to an indeterminate for the domain genus, and ~τto those for gravitational descendants. This remarkable observation was done by [43] and [44] independently. We refer the precise statement and the proof to the original papers. 7.5. Geomet”
Orbifolds of M-strings (2013, background): “For more details on this bundle and its Chern characters we refer to [22].”
Gromov–Witten theory and Donaldson–Thomas theory, I (2003, methodology): “In [MNOP06], a GW/DT correspondence equating the two theories was proposed, and the Calabi–Yau case was presented.”
Topological strings and Nekrasov's formulas (2003, background): “In particular the cases of Calabi-Yau manifolds which are canonical bundles KS over rational surfaces S such as P2, Hirzebruch surfaces Fn and also del Pezzo surfaces have been studied in detail.”
The Topological Vertex (2003, background): “In the next section we explain how to interpret the free chiral boson as the relevant field for the Kodaira-Spencer theory of gravity [8] in this local context (related ideas have appeared in [23,24]).”
Quantum Geometry and Quiver Gauge Theories (2013, methodology): “An alternative approach is based on the Mayer expansion [20] and the ǫ2 → 0 analysis of the asymptotics of the gauge partition function expressed via the contour integral form of the ADHM integrals [1], leading to the TBA-like integral equations [5, 82].”
BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters (2015, methodology): “ the remarkable special functions, which generalize all the known special functions given by the periods, matrix integrals, matrix elements of group, Kac-Moody, and quantum group representations etc. [94, 67, 84]. The particular implementations of this correspondence are well-known under the names o”