Multi-instanton calculus and equivariant cohomology

By U. Bruzzo, F. Fucito, J. F. Morales, A. Tanzini. 2002

337 citations recorded by the source corpus.

We present a systematic derivation of multi-instanton amplitudes in terms of ADHM equivariant cohomology. The results rely on a supersymmetric formulation of the localization formula for equivariant forms. We examine the cases of N = 4 and N = 2 gauge theories with adjoint and fundamental matter.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/62192aeac5e200f2e4ee70fb25ae26ae80fea7d1

How researchers see this paper

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In Mathematical Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Amer Iqbal
5. H. Kanno
6. A. Kashani-Poor
7. Mina Aganagic
8. B. Eynard

In Nuclear and High Energy Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Masato Taki
5. H. Kanno
6. Amer Iqbal
7. Hee-Cheol Kim
8. Mina Aganagic

In Statistical and Nonlinear Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Masato Taki
5. Amer Iqbal
6. H. Kanno
7. T. Hollowood
8. A. Kashani-Poor

Citations in the corpus

• Instantons on the 5-sphere and M5-branes (2012, background): “See [35, 7] for more explanations with examples.”
• Direct integration of the topological string (2007, background): “Nekrasov’s formula for the k-instanton contribution to the partition sum Zk(a, ~) can be written as [12]”
• Refined Topological Vertex and Instanton Counting (2007, methodology): “On the other hand, we can perform the instanton caluclation in the more general background of non self-dual graviphoton configuration, and we get the K-theoretic version of the Nekrasov’s partition function [7][14][15].”
• 5-dim superconformal index with enhanced En global symmetry (2012, methodology): “For a given colored Young diagram, we can fully evaluate the contour integral and write it in the simple form [30, 31, 38]”
• Instanton counting, Macdonald function and the moduli space of D-branes (2005, neutral): “2 SU(2)L × SU(2)R decomposition In [42] [43] [27] the Nekrasov’s partition function for SU(Nc) Yang-Mills theory in a general Ω background is written in the following form;”
• How instanton combinatorics solves Painlevé VI, V and IIIs (2013, background): “In particular, the recently proven [1] AGT conjecture [2] relates them to instanton partition functions in N = 2 SUSY 4D Yang-Mills theories [6, 21, 43, 44], which can be expressed as sums over tuples of partitions.”
• Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops (2007, positive): “From [4, 5, 77] we get that the instanton partition function is given by”
• General instanton counting and 5d SCFT (2014, methodology): “In fact, this should be the original method used by [1, 50] to get the result (3.”
• Recursion relations in CFT and N=2 SYM theory (2009, methodology): “adjoint hyper-multiplets 5”
• Matrix models, geometric engineering and elliptic genera (2003, positive): “·+ℓR N . (6.8) Let us denote the corresponding Young diagrams by µi (and the transpose diagram by µt,i) then given a fixed points of Mk,N labelled by (µ1,...,µN) the corresponding weights are given by [5,73,74,75] X i,j ewi,j = XN α,γ=1 eβ(aα−aγ) X (i,j)∈Rα qµα i +µ t,γ j −i−j+1 + X (i,j)∈Rγ q−µγ i ”
• SU(N) Geometries and Topological String Amplitudes (2003, background): “The open geometry related via flops and blowdowns to the SU(3) geometry is depicted in”
• 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]:”
• On instantons as Kaluza-Klein modes of M5-branes (2011, background): “See [17] for earlier works on these D0-D4 bound states.”