Controlled soft breaking of N = 1 SQCD

Evans, Nick; Hsu, Stephen; Schwetz, Myckola

doi:10.1016/s0370-2693(97)00541-8

Cited by 52 publications

(70 citation statements)

References 16 publications

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“…The same result can be found using the equation of motion for the auxiliary field F [27]. The degeneracy between the scalar and pseudoscalar mesons is lifted too [27,28]. The vacuum energy density takes the form…”

Section: N → ∞ Finite Msupporting

confidence: 61%

Effective Lagrangians for orientifold theories

Sannino¹,

Shifman

2004

Phys. Rev. D

106

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We construct effective Lagrangians of the Veneziano-Yankielowicz (VY) type for two non-supersymmetric theories which are orientifold daughters of supersymmetric gluodynamics (containing one Dirac fermion in the two-index antisymmetric or symmetric representation of the gauge group). Since the parent and daughter theories are planar equivalent, at N → ∞ the effective Lagrangians in the orientifold theories basically coincide with the bosonic part of the VY Lagrangian.We depart from the supersymmetric limit in two ways. First, we consider finite (albeit large) values of N . Then 1/N effects break supersymmetry. We suggest seemingly the simplest modification of the VY Lagrangian which incorporates these 1/N effects, leading to a non-vanishing vacuum energy density. We analyze the spectrum of the finite-N non-supersymmetric daughters. For N = 3 the two-index antisymmetric representation (one flavor) is equivalent to one-flavor QCD. We show that in this case the scalar quark-antiquark state is heavier than the corresponding pseudoscalar state, " η ′ ". Second, we add a small fermion mass term. The fermion mass term breaks supersymmetry explicitly. The vacuum degeneracy is lifted. The parity doublets split. We evaluate the splitting. Finally, we include the θ-angle and study its implications.

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Section: N → ∞ Finite Msupporting

confidence: 61%

Effective Lagrangians for orientifold theories

Sannino¹,

Shifman

2004

Phys. Rev. D

106

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“…Since so much information follows from the solution of the pure N = 2 one would like to be able to break N = 2 supersymmetry down to N = 0 in terms of a collection of soft breaking terms preserving all the holomorphy and monodromy properties which were crucial to determine the solutions in [3,4]. This was begun in [14,15] (for N = 1 similar soft breaking analysis was done in [12,13] to understand the implications of the non-perturbative superpotentials obtained by Seiberg and collaborators [1,2] in the absence of supersymmetry). In this paper we study the most general soft breakings in N = 2 QCD-like theories including massive hypermultiplets.…”

Section: Introductionmentioning

confidence: 99%

Softly Broken N=2 QCD With Massive Quark Hypermultiplets, I

Álvarez‐Gaumé

Mariño

Zamora

1998

Int. J. Mod. Phys. A

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We present a general analysis of all possible soft breakings of N = 2 supersymmetric QCD preserving the analytic properties of the Seiberg-Witten solutions for the SU(2) group with N f = 1, 2, 3 hypermultiplets. We obtain all the couplings of the spurion fields in terms of properties of the SeibergWitten periods, which we express in terms of elementary elliptic functions by uniformizing the elliptic curves associated to each number of flavors. We analyze in detail the monodromy properties of the softly broken theory, and obtain them by a particular embedding into a pure gauge theory with higher rank group. This allows to write explicit expressions of the effective potential which are close to the exact answer for moderate values of the supersymmetry breaking parameters. The vacuum structures and phases of the broken theories will be analyzed in the forthcoming second part of this paper.

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“…Consider supersymmetric gluodynamics with SUSY slightly broken by a small mass term of gluino. At N = ∞ the vacuum structure of this theory is exactly the same as the vacuum structure of pure Yang-Mills (the latter was derived by Witten [28], see also [29,30]). Thus, I would say that the expansion in the number of fermion loops should work.…”

Section: Recent Developmentsmentioning

confidence: 55%

Theoretical Developments in SUSY

Shifman

2008

Eur. Phys. J. C

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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 =...

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Controlled soft breaking of N = 1 SQCD

Cited by 52 publications

References 16 publications

Effective Lagrangians for orientifold theories

Effective Lagrangians for orientifold theories

Softly Broken N=2 QCD With Massive Quark Hypermultiplets, I

Theoretical Developments in SUSY

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