Correlation functions of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>SU</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mo>∞</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:math>principal chiral model

Cubero, Axel Cortés; Orland, Peter

doi:10.1103/physrevd.88.025044

Cited by 12 publications

(11 citation statements)

References 27 publications

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“…For finite N , only the leading two-particle form factors of currents are known [23] and only a vacuum insertion can be made. The complete matrix element is known at large N [24], which should help in finding the relativistic corrections to the eigenvalues of Eq. (VI.2).…”

Section: Discussionmentioning

confidence: 99%

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Dynamical mass reduction in the massive Yang-Mills spectrum in1+1dimensions

Cubero

Orland

2014

Phys. Rev. D

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The (1 + 1)-dimensional SU(N ) Yang-Mills Lagrangian, with bare mass M, and gauge coupling e, naively describes gluons of mass M. In fact, renormalization forces M to infinity. The system is in a confined phase, instead of a Higgs phase. The spectrum of this diverging-bare-mass theory contains particles of finite mass. There are an infinite number of physical particles, which are confined hadron-like bound states of fundamental colored excitations. These particles transform under irreducible representations of the global subgroup of the explicitly-broken gauge symmetry. The fundamental excitations are those of the SU(N ) × SU(N ) principal chiral sigma model, with coupling g0 = e/M. We find the masses of meson-like bound states of two elementary excitations. This is done using the exact S matrix of the sigma model. We point out that the color-singlet spectrum coincides with that of the weakly-coupled anisotropic SU(N ) gauge theory in 2 + 1 dimensions. We also briefly comment on how the spectrum behaves in the 't Hooft limit, N → ∞.

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Section: Discussionmentioning

confidence: 99%

“…Another interesting special case is the 't Hooft limit N → ∞ [20], [24]. The mass gap of the sigma model should be fixed in this limit.…”

Section: Mesonic States Of Massive Yang-mills Theory: N >mentioning

confidence: 99%

Dynamical mass reduction in the massive Yang-Mills spectrum in1+1dimensions

Cubero

Orland

2014

Phys. Rev. D

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“…The integrability of the model, together with a few plausible assumptions, most crucially the existence of a mass gap, leads to a solution for the minimal factorized S-matrix for the PCM [44,45] which was discovered a long time ago. For some recent work see e. g. [46][47][48]. The spectrum as given by integrability contains N − 1 massive particles.…”

Section: Outlinementioning

confidence: 99%

Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles

Cherman

Dorigoni

Ünsal

2015

J. High Energ. Phys.

133

198

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Resurgence theory implies that the non-perturbative (NP) and perturbative (P) data in a QFT are quantitatively related, and that detailed information about nonperturbative saddle point field configurations of path integrals can be extracted from perturbation theory. Traditionally, only stable NP saddle points are considered in QFT, and homotopy group considerations are used to classify them. However, in many QFTs the relevant homotopy groups are trivial, and even when they are non-trivial they leave many NP saddle points undetected. Resurgence provides a refined classification of NP-saddles, going beyond conventional topological considerations. To demonstrate some of these ideas, we study the SU(N ) principal chiral model (PCM), a two dimensional asymptotically free matrix field theory which has no instantons, because the relevant homotopy group is trivial. Adiabatic continuity is used to reach a weakly coupled regime where NP effects are calculable. We then use resurgence theory to uncover the existence and role of novel 'fracton' saddle points, which turn out to be the fractionalized constituents of previously observed unstable 'uniton' saddle points. The fractons play a crucial role in the physics of the PCM, and are responsible for the dynamically generated mass gap of the theory. Moreover, we show that the fracton-anti-fracton events are the weak coupling realization of 't Hooft's renormalons, and argue that the renormalon ambiguities are systematically cancelled in the semi-classical expansion. Our results motivate the conjecture that the semi-classical expansion of the path integral can be geometrized as a sum over Lefschetz thimbles.

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“…One can use the S-matrix to calculate exact form factors (matrix elements of local operators). Form factors of the PCSM in the 'tHooft large-N limit for different operators have been found in References [5], [6], [7]. At finite N, only the first nontrivial form factors have been found (with only two-particle states).…”

Section: Review Of the Principal Chiral Sigma Modelmentioning

confidence: 87%

The Hadronic Spectrum and Confined Phase in (1+1)-Dimensional Massive Yang-Mills Theory

Cubero

2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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Massive Yang-Mills theory is known to be renormalizable in 1+1 dimensions. The gluon mass is introduced by coupling the gauge field to an SU(N) principal chiral nonlinear sigma model. The proof of renormalizability relies on the asymptotic freedom of the sigma model. However, renormalization forces the gluon mass to infinity. The continuum theory is in a confined phase rather than a Higgs phase. The physical excitations of the system are hadron-like bound states of sigma model particles. We calculate the massive spectrum of meson-like bound states analytically, using the exact S-matrix of the sigma model. The baryon-like spectrum can be found in principle by solving a quantum mechanical N-body problem. We remark on the evidence for the confined phase found for SU(2) in recent lattice simulations by Gongyo and Zwanziger. Their simulations show evidence for a Higgs-like phase which seems to disappear with increasing volume, finding agreement with our analysis in the continuum.

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Correlation functions of theSU(∞)principal chiral model

Cited by 12 publications

References 27 publications

Dynamical mass reduction in the massive Yang-Mills spectrum in1+1dimensions

Dynamical mass reduction in the massive Yang-Mills spectrum in1+1dimensions

Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles

The Hadronic Spectrum and Confined Phase in (1+1)-Dimensional Massive Yang-Mills Theory

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