13373610
Summing the instanton series in = 2 superconformal large-N QCD
We consider the multi-instanton collective coordinate integration measure in = 2 supersymmetric SU(N) gauge theory with NF fundamental hypermultiplets. In the large-N limit, at the superconformal point where NF = 2N and all VEVs are turned off, the k-instanton moduli space collapses to a single copy of AdS5 × S1. The resulting k-instanton effective measure is proportional to N1/2g4k(6), where k(6) is the partition function of = (1,0) SYM theory in six dimensions reduced to zero dimensions. The multi-instanton can in fact be summed in closed form. As a hint of an AdS/CFT duality, with the usual relation between the gauge theory and string theory parameters, this precisely matches the normalization of the charge-k D-instanton measure in type IIB string theory compactified to six dimensions on K3 with a vanishing two-cycle.
34905319
Minkowski space non-Abelian classical solutions with noninteger winding number change.
Working in a spherically symmetric ansatz in Minkowski space, we discover new solutions to the classical equations of motion of pure SU(2) gauge theory. These solutions represent spherical shells of energy, which move inward near the speed of light at early times, excite the region of space around the origin at intermediate times, and move outward at late times. The solutions change the winding number in bounded regions centered at the origin by noninteger amounts. They also produce a noninteger topological charge in these regions. We show that the previously discovered solutions of Luescher and Schechter also have these properties.
119379193
The calculus of many instantons
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.
119236962
Travels on the squark-gluino mass plane
Institut fur Theoretische Physik, Universitat Heidelberg, Germany(Dated: September 12, 2011)Soft supersymmetry breaking appears in the weak-scale e ective action but is usually generated athigher scales. For these models the structure of the renormalization group evolution down to theelectroweak scale leaves only part of the squark-gluino and slepton-gaugino mass planes accessible.Our observations divide these physical mass planes into three wedges: the rst can be reached byall models of high-scale breaking; the second can only be populated by models with a low mediationscale; in the third wedge squarks and gluinos would have to be described by an exotic theory. Allusual benchmark points reside in the rst wedge, even though an LHC discovery in the third wedge
14575937
The Instanton Hunter's guide to supersymmetric SU(N) gauge theories
Abstract We present a compendium of results for ADHM multi-instantons in SU ( N ) SUSY gauge theories, followed by applications to N = 2 supersymmetric models. Extending recent SU (2) work, and treating the N = 1 and N = 2 cases in parallel, we construct: (i) the ADHM supermultiplet, (ii) the multi-instanton action, and (iii) the collective coordinate integration measure. Specializing to N = 2, we then give a closed formula for F k , the k -instanton contribution to the prepotential, as a finite-dimensional collective coordinate integral. This amounts to a weak-coupling solution, in quadratures, of the low-energy dynamics of N = 2 SQCD, without appeal to duality. As an application, we calculate F 1 for all SU ( N ) and any number of flavors N F ; for N F N − 2 and N F = 2 N − 1 we confirm previous instanton calculations and agree with the proposed hyper-elliptic curve solutions. For N F = 2 N − 2 and N F = 2 N with N > 3 we obtain new results, which in the latter case we do not understand how to reconcile with the curves.
119447895
Multi-gluon collinear limits from MHV diagrams
We consider the multi-collinear limit of multi-gluon QCD amplitudes at tree level. We use the MHV rules for constructing colour ordered tree amplitudes and the general collinear factorization formula to derive timelike splitting functions that are valid for specific numbers of negative helicity gluons and an arbitrary number of positive helicity gluons (or vice versa). As an example we present new results describing the collinear limits of up to six gluons.
18665373
On minimum-bias effects at the LHC
Abstract In general, minimum-bias triggers planned for experiments at the LHC miss a considerable fraction of the total number of events. We exemplify the rejection rate using the Durham model of soft high-energy interactions to obtain quantitative estimates of the signals arising from the ATLAS scintillation counters positioned in the rapidity intervals 2 | η | 4 , and also from TOTEM detectors covering the intervals 3.1 | η | 6.5 . Typically we find that the expected signal is about half of the total cross section, σ tot . We also calculate the cross section for the so-called zero-bias measurement planned by CMS in the extended rapidity interval − 5 η 7 . We emphasize that only models which give satisfactory predictions for the measured minimum-bias or zero-bias cross sections can be used to obtain the value of the total inelastic cross section.
118925449
Inelastic $J/\psi$ and $\Upsilon$ hadroproduction
Abstract.We consider the prompt hadroproduction of $J/\psi, \psi'$ and the $\Upsilon (1S,2S,3S)$ states caused by the fusion of a symmetric colour-octet state, (gg)8s, and an additional gluon. The cross sections are calculated in leading-order perturbative QCD. We find a considerable enhancement in comparison with previous perturbative QCD predictions. Indeed, the resulting cross sections are found to be consistent with the values measured at the Tevatron and RHIC, without the need to invoke non-perturbative ‘colour-octet’ type of contributions.
115929216
Three-Reggeon description of inclusive proton spectra
123672226
THE STRING EFFECT AND QCD COHERENCE
Abstract In the framework of the idea of local parton-hadron duality we discuss the asymptotic predictions of QCD perturbation theory for angular distributions of hadron flows in three-jet events, e + e - → q q g → hadrons. The coherence of soft gluon emission provides the QCD explanation of the string effect observed in experiments.
119262459
From hard to soft high-energy pp interactions
We discuss how the main features of high-energy `soft' and `semihard' pp collisions may be described in terms of parton cascades and multi-Pomeron exchange. The interaction between Pomerons produces an effective infrared cutoff, k_sat, by the absorption of low k_t partons. This provides the possibility of extending the parton approach, used for `hard' processes, to also describe high-energy soft and semihard interactions. We outline a model which incorporates these features. Finally, we discuss what the most recent LHC measurements in the soft domain imply for the model.