The Calculus of many instantons

By N. Dorey, T. Hollowood, V. Khoze, M. Mattis. 2002

360 citations recorded by the source corpus.

We describe the modern formalism, ideas and applications of the instanton calculus for gauge theories with, and without, supersymmetry. Particular emphasis is put on developing a formalism that can deal with any number of instantons. This necessitates a thorough review of the ADHM construction of instantons with arbitrary charge and an in-depth analysis of the resulting moduli space of solutions. We review the construction of the ADHM moduli space as a hyper-Kahler quotient. We show how the functional integral in the semi-classical approximation reduces to an integral over the instanton moduli space in each instanton sector and how the resulting matrix partition function involves various geometrical quantities on the instanton moduli space: volume form, connection, curvature, isometries, etc. One important conclusion is that this partition function is the dimensional reduction of a higher- dimensional gauged linear sigma model which naturally leads us to describe the relation of the instanton calculus to D-branes in string theory. Along the way we describe powerful applications of the calculus of many instantons to supersymmetric gauge theories including (i) the gluino condensate puzzle in N = 1 theories (ii) Seiberg-Witten theory in N = 2 theories; and (iii) the AdS/CFT correspondence in N = 2 and N = 4 theories. Finally, we brielfy review the modifications of the instanton calculus for a gauge theory defined on a non-commutative spacetime and we also describe a new method for calculating instanton processes using a form of localization on the instanton moduli space.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b6f8f5e1ff068fc36657b4943bf6fd0db02bc3bf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Ralph Blumenhagen
2. T. Weigand
3. C. Vafa
4. Frederik Denef
5. S. Kachru
6. M. Cvetič
7. Eran Palti
8. Y. Nakayama

In Nuclear and High Energy Physics

1. C. Vafa
2. T. Weigand
3. Ralph Blumenhagen
4. Eran Palti
5. Thomas W. Grimm
6. M. Cvetič
7. Amer Iqbal
8. Frederik Denef

In Statistical and Nonlinear Physics

1. C. Vafa
2. Amer Iqbal
3. C. Kozçaz
4. A. Tanzini
5. T. Hollowood
6. Marcos Mariño
7. Babak Haghighat
8. G. Lockhart

Citations in the corpus

• d-Brane Instantons in Type II Orientifolds (2009, background): “Historically the string theoretic derivation [9, 10] of the famous ADHM construction of gauge instantons [53] was among the first appearances of Euclidean D-branes in the context of instanton computations and has been the subject of many early investigations including [15, 16, 17] (for reviews and m”
• Matone's Relation in the Presence of Gravitational Couplings (2004, neutral): “e winding number) the action becomes dependent upon the moduli. It can be evaluated by computing the norm of the zero mode Dϕ, where D is the covariant derivative with respect to the gauge connection [8, 22]. An alternative representation of Sis given as a BRST variation, Q, of a one-form, Ω = hξ∗,D”
• Les Houches Lectures on Constructing String Vacua (2008, background): “tantons which have finite action in t he F-theory limit of vanishing fiber size. Some classic referencesforinstantonseffectsin stringtheoryare[82–86]. The general calculus of instantons was reviewed in [87], and the lecture notes [88] give an introduction to instanton effects in quantum mechanics and ”
• ABCD of Instantons (2004, background): “There exist several nice descriptions of the construction of instantons for the SU (N) case [9, 8 , 4]. We give below the version of the original work [3], adapted for our purposes.”
• Matrix models, geometric engineering and elliptic genera (2003, methodology): “In the conventional setting charge k instanton effects are calculated in terms of a zero-dimensional (matrix) supersymmetric sigma model with the k-instanton moduli space of U(N) Mk,N as target (see [58]).”
• Multi-instanton calculus and equivariant cohomology (2002, methodology): “We examine the cases of N = 4 and N = 2 gauge theories with adjoint and fundamental matter.”
• Liouville Field Theory — A decade after the revolution (2004, background): “36 For the other part of (36)This reminds us of the instanton calculation for the supersymmetric gauge theory (for reviews, see [125], [126]).”
• M-Strings (2013, background): “In the case of the massive adjoint hypermultiplet the supersymmetric partition function of the gauge theory reduces to the partition function of supersymmetric quantum mechanics on the instanton moduli space [29].”
• TOPICAL REVIEW: Solitons in the Higgs phase: the moduli matrix approach (2006, background): “In quantum theory, for instance, the instanton calculus is reduced to the integration over the instanton moduli space [30].”
• On instantons as Kaluza-Klein modes of M5-branes (2011, neutral): “We mostly follow the notations of [38].”