Small volume expansion of almost supersymmetric large<i>N</i>theories

Barbón, J.L.F.; Hoyos, Carlos

doi:10.1088/1126-6708/2006/01/114

Cited by 15 publications

(23 citation statements)

References 44 publications

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“…6 To summarize, the status of the large N "orientifold equivalence" discussed in Refs. [21][22][23][24][25][26][27] is no better (or worse) than that of similar large N orbifold equivalences. For all large N equivalences based on orbifold or orientifold projections, appropriate symmetry realization conditions are an unavoidable, and non-trivial, necessary condition for a useful equivalence.…”

Section: Introduction and Resultsmentioning

confidence: 95%

“…(See also Refs. [25][26][27].) This latter theory will be abbreviated as QCD(AS) or QCD(S) in the antisymmetric or symmetric case, respectively.…”

Section: Introduction and Resultsmentioning

confidence: 99%

“…A particular case, which has been previously considered by Barbon and Hoyos [26], is compactification on T 3 ×R, with a symmetric three torus and periodic boundary conditions for the fermions in all directions. For this finite volume spatial compactification, all dynamics is weakly coupled if the physical size of the three torus is much smaller than confinement scale Λ −1 .…”

Section: Compactification On T 3 × Rmentioning

confidence: 99%

“…For QCD(AS) (as well as the Z 2 orbifold projection of SYM), Ref. [26] analyzed the resulting one-loop effective potential for Wilson lines. This corresponds to a Born-Oppenheimer approximation in the quantum mechanics of these finite volume theories.…”

Section: Compactification On T 3 × Rmentioning

confidence: 99%

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(In)validity of largeNorientifold equivalence

2006

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It has been argued that the bosonic sectors of supersymmetric SU (N ) YangMills theory, and of QCD with a single fermion in the antisymmetric (or symmetric) tensor representation, are equivalent in the N → ∞ limit. If true, this correspondence can provide useful insight into properties of real QCD (with fundamental representation fermions), such as predictions [with O(1/N ) corrections] for the non-perturbative vacuum energy, the chiral condensate, and a variety of other observables. Several papers asserting to have proven this large N "orientifold equivalence" have appeared. By considering theories compactified on R 3 × S 1 , we show explicitly that this large N equivalence fails for sufficiently small radius, where our analysis is reliable, due to spontaneous symmetry breaking of charge conjugation symmetry in QCD with an antisymmetric (or symmetric) tensor representation fermion. This theory is also chirally symmetric for small radius, unlike super-Yang-Mills. The situation is completely analogous to large-N equivalences based on orbifold projections: simple symmetry realization conditions are both necessary and sufficient for the validity of the large N equivalence. Whether these symmetry realization conditions are satisfied depends on the specific non-perturbative dynamics of the theory under consideration. Unbroken charge conjugation symmetry is necessary for validity of the large N orientifold equivalence. Whether or not this condition is satisfied on R 4 (or R 3 × S 1 for sufficiently large radius) is not currently known.

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Section: Introduction and Resultsmentioning

confidence: 95%

“…(See also Refs. [25][26][27].) This latter theory will be abbreviated as QCD(AS) or QCD(S) in the antisymmetric or symmetric case, respectively.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Section: Compactification On T 3 × Rmentioning

confidence: 99%

Section: Compactification On T 3 × Rmentioning

confidence: 99%

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(In)validity of largeNorientifold equivalence

2006

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“…(Ref. [51] examined these theories on T 3 ×R where T 3 is small, and C in QCD(AS/S) and I in QCD(BF) are spontaneously broken. Since the necessary symmetry realization conditions do not hold in this phase, we do not expect an equivalence.…”

Section: Chiral Symmetriesmentioning

confidence: 99%

Phases ofN=∞QCD-like gauge theories onS3×S1and nonperturbative orbifold-orientifold equivalences

Ünsal

2007

Phys. Rev. D

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Abstract:We study the phase diagrams of N = ∞ vector-like, asymptotically free gauge theories as a function of volume, on S 3 × S 1 . The theories of interest are the ones with fermions in two index representations [adjoint, (anti)symmetric, and bifundamental abbreviated as QCD(adj), QCD(AS/S) and QCD(BF)], and are interrelated via orbifold or orientifold projections. The phase diagrams reveal interesting phenomena such as disentangled realizations of chiral and center symmetry, confinement without chiral symmetry breaking, zero temperature chiral transitions, and in some cases, exotic phases which spontaneously break the discrete symmetries such as C, P, T as well as CPT. In a regime where the theories are perturbative, the deconfinement temperature in SYM, and QCD(AS/S/BF) coincide. The thermal phase diagrams of thermal orbifold QCD(BF), orientifold QCD(AS/S), and N = 1 SYM coincide, provided charge conjugation symmetry for QCD(AS/S) and Z 2 interchange symmetry of the QCD(BF) are not broken in the phase continously connected to R 4 limit. When the S 1 circle is endowed with periodic boundary conditions, the (nonthermal) phase diagrams of orbifold and orientifold QCD are still the same, however, both theories possess chirally symmetric phases which are absent in N = 1 SYM. The match and mismatch of the phase diagrams depending on the spin structure of fermions along the S 1 circle is naturally explained in terms of the necessary and sufficient symmetry realization conditions which determine the validity of the nonperturbative orbifold orientifold equivalence.

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Planar Equivalence 2006

Armoni

Shifman

Lecture Notes in Physics

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Small volume expansion of almost supersymmetric largeNtheories

Cited by 15 publications

References 44 publications

(In)validity of largeNorientifold equivalence

(In)validity of largeNorientifold equivalence

Phases ofN=∞QCD-like gauge theories onS3×S1and nonperturbative orbifold-orientifold equivalences

Planar Equivalence 2006

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