Valley Instanton in the Gauge-Higgs System

Aoyama, Hideaki; Harano, Toshiyuki; Sato, Masatoshi; Wada, Shinya

doi:10.1142/s0217732396000072

Cited by 16 publications

(48 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(2.15a)-(2.15c) ff.) However, as in the N = 2 models considered in [26,47,81], it turns out that the integrations can nevertheless be accomplished using Gauss's law, and that only the asymptotic expressions (2.31) are actually needed. Here are the details.…”

Section: Construction Of the Multi-instanton Actionmentioning

confidence: 99%

Multi-instanton calculus and the AdS/CFT correspondence in = 4 superconformal field theory

et al. 1999

View full text Add to dashboard Cite

We present a self-contained study of ADHM multi-instantons in SU(N) gauge theory, especially the novel interplay with supersymmetry and the large-N limit. We give both field-and string-theoretic derivations of the N = 4 supersymmetric multi-instanton action and collective coordinate integration measure. As a central application, we focus on certain n-point functions G n , n = 16, 8 or 4, in N = 4 SU(N) gauge theory at the conformal point (as well as on related higher-partial-wave correlators); these are correlators in which the 16 exact supersymmetric and superconformal fermion zero modes are saturated. In the large-N limit, for the first time in any 4-dimensional theory, we are able to evaluate all leading-order multi-instanton contributions exactly. We find compelling evidence for Maldacena's conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of a single copy of AdS 5 × S 5 . (2) The integration measure on this space includes the partition function of 10-dimensional N = 1 SU(k) gauge theory dimensionally reduced to 0 dimensions, matching the description of D-instantons in Type IIB string theory. (3) In exact agreement with Type IIB string calculations, at the k-instanton level,

show abstract

Section: Construction Of the Multi-instanton Actionmentioning

confidence: 99%

Multi-instanton calculus and the AdS/CFT correspondence in = 4 superconformal field theory

et al. 1999

View full text Add to dashboard Cite

show abstract

“…First instanton tests of pure N = 2 supersymmetric SU(2) theories were performed in [54] at a one-instanton level and in [25] at a two-instanton level. Two-instanton contributions to the prepotential in SU(2) theories with N F fundamental hypermultiplets were calculated in [48,61,78] and the general expression for the k-instanton contribution to the prepotential as an integral over the ADHM moduli space was derived in [48]. The relation of Matone [80] between the prepotential and the condensate u 2 in SU(2) was tested at a two-instanton level in [81] and derived to all orders in instantons in [82].…”

mentioning

confidence: 99%

“…For a recent careful treatment of these issues see [92]. In addition to these effects, explicit instanton calculations are also necessary in order to fix the dictionary between the quantum moduli used in constructing exact solutions and the gauge-invariant VEVs u n , see [20,58,61,84,[91][92][93][94] for more detail. A completely new technique for evaluating the instanton contributions to the prepotential has been pioneered in [95,96] leading to the first calculations of instanton effects for all instanton number (beyond the large-N calculations reported in Chapters VII and IX) and the first test of Seiberg-Witten theory to all orders in the instanton expansion.…”

mentioning

confidence: 99%

The calculus of many instantons

et al. 2002

View full text Add to dashboard Cite

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-Kähler 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 higherdimensional 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.

show abstract

“…Note that there is an ambiguity in the relation between u and z due to the integration constant u 0 . It is constrained to zero, either by an explicit 2-instanton computation [9,10,11,12] or by imposing invariance under the discrete R-transformations φ → e 2πi/3 φ [2].…”

Section: Solution Of the Modelmentioning

confidence: 99%

“…Here we show that, in conjunction with the SL(2, Z)-structure, the superconformal anomaly determines the low-energy effective Lagrangian and completely parametrises the quantum moduli space. What distinguishes the 4-dimensional model is that the non-perturbative contributions are not computable by other means (except for 1 and 2 instantons contributions [8,9,10,11,12]). …”

Section: Introductionmentioning

confidence: 99%