Planar Equivalence: From Type 0 Strings to QCD

Armoni, Adi; Shifman, M.; Veneziano, G.

doi:10.1142/9789812701756_0066

Cited by 27 publications

(45 citation statements)

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“…Let us imagine integrating out the fermions in an SU (N ) gauge theory with either adjoint, symmetric or antisymmetric fermions [216]. In all cases, the logarithm of the fermion determinant can be expressed as a sum of Wilson loops in R 4 ; in a geometry like R 3 × S 1 or T 4 , the sum includes Polyakov loops as well as Wilson loops.…”

Section: B Planar Equivalencementioning

confidence: 99%

Phases of gauge theories

Ogilvie¹

2012

J. Phys. A: Math. Theor.

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One of the most fundamental questions we can ask about a given gauge theory is its phase diagram. In the standard model, we observe three fundamentally different types of behavior: QCD is in a confined phase at zero temperature, while the electroweak sector of the standard model combines Coulomb and Higgs phases. Our current understanding of the phase structure of gauge theories owes much to the modern theory of phase transitions and critical phenomena, but has developed into a subject of extensive study. After reviewing some fundamental concepts of phase transitions and finite-temperature gauge theories, we discuss some recent work that broadly extends our knowledge of the mechanisms that determine the phase structure of gauge theories. A new class of models with a rich phase structure has been discovered, generalizing our understanding of the confinement-deconfinement transition in finite-temperature gauge theories. Models in this class have space-time topologies with one or more compact directions. On R 3 ×S 1 , the addition of double-trace deformations or periodic adjoint fermions to a gauge theory can yield a confined phase in the region where the S 1 circumference L is small, so that the coupling constant is small, and semiclassical methods are applicable. In this region, Euclidean monopole solutions, which are constituents of finite-temperature instantons, play a crucial role in the calculation of a non-perturbative string tension. We review the techniques use to analyze this new class of models and the results obtained so far, as well as their application to finite-temperature phase structure, conformal phases of gauge theories and the large-N

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Section: B Planar Equivalencementioning

confidence: 99%

Phases of gauge theories

Ogilvie¹

2012

J. Phys. A: Math. Theor.

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“…The new expansion based on quarks in the two-index antisymmetric representation is denoted as QCD(AS). While the study of QCD(AS) at large N c was largely motivated by the appearance of elegant field theoretic dualities [18][19][20][21], one may instead develop the formalism for physical baryons [22][23][24] and investigate whether QCD(F) or QCD(AS) is phenomenologically superior for a given set of observables [25][26][27]. In the case of mesons, it was shown very recently [28] that the presence two distinct color indices on each QCD(AS) quark field allows one to define a single-color-trace source J with tetraquark quantum numbers.…”

Section: Introductionmentioning

confidence: 99%

Are there tetraquarks at largeNcin QCD(F)?

2014

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Weinberg recently pointed out a flaw in the standard argument that large Nc QCD with colorfundamental quarks [QCD(F)] cannot yield narrow tetraquark states. In particular, he observed that the argument does not rule out narrow tetraquarks associated with the leading-order connected diagrams; such tetraquarks would have a width scaling as N −1 c . It is shown here, however, that while the standard analysis of tetraquarks does not rule them out, a more thorough analysis rules out quantum-number exotic tetraquarks associated with the leading-order connected diagrams. This analysis is based entirely on conventional assumptions used in large Nc physics applied to the analytic properties of meson-meson scattering. Our result implies that one of three possibilities must be true: i) quantum-number exotic tetraquarks do not exist at large Nc; ii) quantum-number exotic tetraquarks exist, but are associated with subleading connected diagrams and have anomalously small widths that scale as N −2 c or smaller; or iii) the conventional assumptions used in large Nc analysis are inadequate.

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“…Such theories are renormalizable and are asymptotically free in 3+1 space-time dimensions or fewer, provided that there are not too many flavors. There has been significant interest in such theories since 2003, when it was argued that a sector of the theory becomes equivalent at large N c to an analogous sector of theories with quarks in the adjoint representation [59,60]. This is significant for the present purpose since, the theories with matter in the adjoint representation have an explicit center symmetry, so that these theories have an emergent center symmetry at large N c in the sense used in this paper.…”

Section: +1 Space-time Dimensionsmentioning

confidence: 95%

Center symmetry and the Hagedorn spectrum

2015

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This paper explores the conjecture that large Nc gauge theories have a Hagedorn spectrum, if, and only if, they are confining and posses an explicit or emergent center symmetry. Evidence in support of this conjecture is presented. Many classes of large Nc gauge theories are considered. In all cases, we find that theories for which there exists a strong plausibility argument for a Hagedorn spectrum at large Nc are also believed to be confining and possess either an explicit center symmetric or have a strong plausibility argument for the existence of an emergent center symmetry at large Nc. Conversely, all theories we considered which are believed not to have a Hagedorn spectrum at large Nc, either were known not to be confining or else were believed to lack an emergent center symmetry. This is consistent with expectations based on the conjecture.

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Planar Equivalence: From Type 0 Strings to QCD

Cited by 27 publications

References 0 publications

Phases of gauge theories

Phases of gauge theories

Are there tetraquarks at largeNcin QCD(F)?

Center symmetry and the Hagedorn spectrum

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