Theoretical Developments in SUSY

Abstract

Invited Talk at PLANCK 2008, Barcelona, Spain, 19 -23 May, 2008 Main topics:• Heterotic strings from N = 1 gauge theories;• Planar equivalence and emergent center symmetry in QCD-like theories;• Exact result for gluon scattering amplitudes in N = 4 (dual conformality). 1 1 Non-Abelian heterotic strings in N = 1: setting the stage Seiberg and Witten presented [1] the first ever demonstration of the dual Meissner effect in non-Abelian theory, a celebrated analytic proof of linear confinement, which caused much excitement in the community. The Seiberg-Witten flux tubes are essentially Abelian (of the Abrikosov-Nielsen-Olesen type), so that the hadrons they create are not alike those in QCD [2]. What do we mean when we speak of Abelian versus non-Abelian flux tubes? In the former case, gauge dynamics relevant to distances where the tubes are formed is that of an Abelian theory (although short-distance dynamics can well be nonAbelian, as in the Seiberg-Witten case). In the latter case, in the infrared, at distances relevant to the tube formation, dynamics is determined by non-Abelian theory, with all gauge bosons equally operative. Correspondingly, we can speak of Abelian versus non-Abelian confinement. There are reasons to believe that no phase transition occurs between these two regimes in the Seiberg-Witten solution.1 However, in the limit of large-µ deformations, when a non-Abelian regime presumably sets in and non-Abelian strings develop in the model considered by Seiberg and Witten, theoretical control is completely lost. What was badly needed and sought for was a model in which non-Abelian strings develop in a fully controllable manner, i.e. at weak coupling.Ever since, searches for non-Abelian flux tubes and non-Abelian monopoles continued, with a decisive breakthrough in 2003-04 [3, 4]. By that time the program of finding field-theoretical analogs of all basic constructions of string/D-brane theory was in full swing. BPS domain walls, analogs of D branes, had been identified in supersymmetric Yang-Mills theory [5]. It had been demonstrated that such walls support gauge fields localized on them. BPS saturated string-wall junctions had been constructed [6]. Non-Abelian flux tubes and monopolesNon-Abelian strings were first found in N = 2 super-Yang-Mills theories with U(2) gauge and two matter hypermultiplets [3,4]. The N = 2 vector multiplet consists of the U(1) gauge field A µ and the SU(2) gauge field A a µ , (here a = 1, 2, 3), and their Weyl fermion superpartners (λ 1 , λ 2 ) and (λ 1a , λ 2a ), plus complex scalar fields a, and a a . The global SU(2) R symmetry inherent to N = 2 models manifests itself through rotations λ 1 ↔ λ 2 . The quark multiplets consist of the complex scalar fields q kA andq Ak (squarks)1 It was argued [7] that, under certain conditions, transition from Abelian to non-Abelian confinement is smooth in non-supersymmetric QCD compactified onThe 't Hooft−Polyakov monopole and the Weyl fermions ψ kA andψ Ak , all in the fundamental representation of the SU(2) gauge group (k =...

Planar Limit of Orientifold Field Theories and Emergent Center Symmetry

“…This expectation comes true: the center symmetry of SYM theory turns out to be an emergent symmetry of the orientifold daughters in the large-N limit. This fact was first noted in [6] while the first mention of the problem of center symmetry on both sides of planar equivalence can be found in [7]. Here we investigate the reasons that lead to the emergence of the center symmetry and its implications, as they manifest themselves at small and large values of the S 1 radius.…”

“…As was argued in [6], the center symmetry emerges dynamically in the planar limit N → ∞. Here we will carry out a thorough consideration and present independent albeit related arguments.…”

“…(28) is automatically invariant under the C transformation. Therefore, planar equivalence between SYM and orientifold theories must hold both in the Higgs regime, and at strong coupling where C invariance was argued to hold too [32,6].…”

Emergent gravity from Eguchi-Kawai reduction

“…More simply, the fundamental matter decouples at leading order in N , so the center symmetry is emergent at infinite N . As explored heavily in the literature on large-N volume independence and mentioned in the introduction, orbifold/orientifold dualities in many cases imply an emergent center symmetry at infinite N , even when center-breaking matter does not naively decouple [21,22]. It is this generalized emergent sense in which the Eguchi-Kawai mechanism is necessary.…”

“…This is simply because quarks decouple at leading order and one is left with the pure Yang-Mills theory. Interestingly, by orientifold dualities, even matrix representations (which break center symmetry and for which the matter does not decouple) have an emergent center symmetry at infinite N [21,22].…”